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https://iland-model.org/Expression | 2023-09-26T21:31:22 | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510225.44/warc/CC-MAIN-20230926211344-20230927001344-00117.warc.gz | 0.800451 | 1,709 | CC-MAIN-2023-40 | webtext-fineweb__CC-MAIN-2023-40__0__229000585 | en | Table of contents
The expression class used in iLand was originally developed for the Picus model and aims at a high performance for repeated executions. Expressions are parsed only once and converted to an internal "program" which can be executed with very little overhead. When using more complex mathematical functions (e.g. exp()), the overall performance is comparable to hard coded C++.
The meaning of a variable name within an expression depends on the context. There are three main cases:
- Expressions bound to "Objects" e.g. to Trees. In that case, the variable names are defined by the respective object. If an expression is bound to trees, one can use context sensitive variables like "dbh" or "volume" for trees. Depending on the context, this can be tree variables, resource unit variables, or sapling variables.
- named variables: the names of variables are fixed programmatically. E.g: a expression with two named parameters ("x", "n") to calculate a weight could be "x/n" or more sophisticated "x*x/n*n"
- unbound variables: In that case the name of the variable can be chosen freely. The value for the variable is set during the model execution and depends on the context. Example: the expressions for the calculation of biomass compartments (allometric equations) has one parameter (dbh). Valid expression are, e.g.: "0.1*dbh^2" or "0.1*d^2" or "0.1*fish^2".
Basically, expressions can consist of basic arithemtic operators, variables and functions. The basic operators +,-,* and / work as expected (incl. precedence rules). Additionally, the caret "^" can be used for power functions (e.g. x*x can be written as x^2). Parentheses work as expected (e.g. (a+b)*c is different from a+(b*c)).
Floating point numbers must use the dot (".") for constants (e.g. 0.001). The comma "," is used to separate arguments in function calls.
Expressions can be used to evaluate logical expressions, i.e. expressions with a result value of either "true" or "false". Operators for logcal expressions are "and" and "or". Logical expressions are typically used to filter or select from a set of objects based on a criterion. E.g.: using the expression "dbh>30 and (stress>0.5 or leafarea<1)" as a filter, would result in a list of large, but stressed trees.
Logical and "mathematical" operators can be used together: every non-zero value is evaluated as "true", zero (0) as "false". 'true' and 'false' are also available and internally converted to 1 and 0, respectively. Hence, a logical "not" can be expressed as ex
Expressions provide a basic support for constants. A constant is a system-defined name with a fixed value that can be used instead of the numerical value. Currently, the species names / IDs are available and linked to the numerical index of the species for the current run:
Therefore, you can use, e.g., 'species=Tsme' in a management-filter expression (having 'Tsme' as the ID of one tree species). Note, that no apostrophs are required. 'Tsme' is replaced with the numerical value (e.g. '1') during parsing time of the expression.
The general form of function is:
functionname(list of arguments)
Generally, mathematical functions are executed without checking for the validity of the arguments (e.g. division by 0, or tan(pi/2)).
|sin(x)||the sin of x, x as radians.||sin(x)|
|cos(x)||the cosine of x, x as radians||cos(x)|
|tan(x)||the tangens of x, x as radians||tan(x)|
|exp(x)||exponential function, e(1)=2.7182...||exp(-k*LAI)|
|ln(x)||the logarithm of base e, ln(2.7182...)=1||ln(x)|
|sqrt(x)||the square root of x (equivalent to x^0.5)||sqrt(x)|
|mod(x,y)||return the modulo (remainder) of x/y. e.g. mod(13,10)=3||if(mod(id,2), 1, 0)|
|round(x)||Returns the integral value that is nearest to x, with halfway cases rounded away from zero.||round(x)|
|min(x1,x2,...,xn)||returns the minimum value of the arguments. Argument count must be >1 and <10||min(x,0)|
|max(x1,x2,...,xn)||returns the maximum value of the arguments. Argument count must be >1 and <10||max(min(x,1),0)|
|if(condition, true, false)||logical if-then-else construct. if "condition" is true, the "true" is returned, "false" otherwise. E.g.: a abs()-function: if(x<0;-x;x). Note that both clauses are calculated in every case!||if(x<0;-x;x)|
|in(value, arg1, arg2, ... , argn)||returns true if value is in the list or arguments, false otherwise.||in(year,100,200,300)|
|incsum(fn)||when used in SQL like expressions (e.g., management, the function incsum cumulates its value over several calls. See the management functions mean and sum functions.||incsum(basalArea)<40|
|polygon(value, x1,y1, x2,y2, x3,y3, ..., xn,yn)||return is: y1 if value<x1, yn if value>xn, or the lineraly interpolated numeric y-value.||polygon(x, 0,0, 1,0.5)|
|sigmoid(x, type, param1, param2)||The value of "sigmoid" curve at x. The type of curve is designated by type with the two parameters param1 and param2. 0: logistic, 1: Hill-function, 2: 1-logistic, 3: 1-hill||sigmoid(x, 0, 10, 100)|
|rnd(from, to)||returns a uniformly distributed random function between from and to.||rnd(0,1)|
|rndg(mean, stddev)||returns a random number drawn from a Gaussian normal distribution with 'mean' as the mean value 'stddev' as the standard deviation.||rndg(0,1)|
- create an output only every 10 years:
To improve the calculation performance in certain situations, expressions can use precalculated function results to interpolate a function numerically. This works best for expressions with one variable and a defined range for the input, but also an implementation for expressions with two variables is available.
For complex mathematical expressions the linearized version is up to 10 times faster than the regular expression engine.
The linearization is globally enabled/disabled by the switch system.settings.expressionLinearizationEnabled in the project file. Note, that this feature must be explicitly enabled for each expression used in the source code. | mathematics |
https://familytravelfiles.wordpress.com/2015/03/11/sharing-pie-on-pi-day/ | 2019-07-23T13:05:58 | s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195529406.97/warc/CC-MAIN-20190723130306-20190723152306-00307.warc.gz | 0.904687 | 418 | CC-MAIN-2019-30 | webtext-fineweb__CC-MAIN-2019-30__0__138837840 | en | It is a fortunate coincidence that Saturday is not just Pi Day but also Albert Einstein’s birthday. Museums and destinations across the country have created terrific ways for families to celebrate with pi parades, Albert Einstein look-a-like contests, pie eating contests, and interactive numbers games.
I think Mr. Einstein would smile at the assorted events created to honor the most memorable number sequence on the planet. If you are not following me, pi usually recognized by the Greek letter “π” is the symbol used in math to represent a constant — the ratio of the circumference of a circle to its diameter which is 3.14159265358…. and on it goes. The following events prove math can be fun for everyone and who doesn’t love pie.
Princeton, New Jersey is hosting a string of crazy events including an Einstein look-a-like contest and a Dinky Train ride with reenactors playing Einstein, his mother and their good friends.
Naturally MoMath, the National Museum of Math in Manhattan will begin the day’s festivities begin at 3/14/15 at 9:26 with a scavenger hunt through the exhibits and oodles of pi puzzles to be solved.
Any day at the Franklin Institute in Philadelphia offers exceptional rewards for families but the Museum’s National Pi Day celebration will add extra geekiness with pi reciting contests and a pie launch competition
Adler Planetarium’s daytime Pi Day activities include a pie eating contest, a parachuting pies challenge, and pie-in-the-sky solar observations.
At San Francisco’s Exploratorium the day begins at 9:26:53 and includes pi processional, light circles and pizza pie dough tossing.
If none of these work for you there’s always the excuse to bake a pie and do your own calculations per serving.
For the latest family travel news follow the Family Travel Files on Twitter (@FamTravelFiles)
Nancy Nelson-Duac, Curator of the Good Stuff | mathematics |
http://spilamex.gq/9814250554/discovering-mathematics-common-core-workbook-7b.pdf | 2018-04-20T10:40:47 | s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937440.13/warc/CC-MAIN-20180420100911-20180420120911-00588.warc.gz | 0.90633 | 299 | CC-MAIN-2018-17 | webtext-fineweb__CC-MAIN-2018-17__0__8376314 | en | Book Title: Discovering Mathematics: Common Core, Workbook 7B
Publisher: Star Publishing
Discovering Mathematics Common Core Workbooks are designed for middle school students. Developed in collaboration between Star Publishing Pte. Ltd. and Singapore Math Inc,. these workbooks follow the Singapore Framework and also cover the topics in the Common Core State Standards.
Each workbook is written as a supplement to the textbook, Discovering Mathematics Common Core, to give students more practice in applying the concepts learned. Students may refer to the summary of the important concepts in each chapter of the textbook for a quick review before attempting the questions in the workbook. After completing the exercises, students will not only polish their own analytical skills, but also develop a stronger foundation in mathematics.
The questions in each workbook chapter are categorized into 4 pars according to the level of difficulty and the thinking skills involved:
Basic Practice: simple questions that drill comprehension of concepts
Further Practice: harder questions that involve direct applications
Challenging Practice: questions that require synthesis ability
Enrichment: questions that demand higher order thinking
These questions encourage students to think analytically, reason logically, use appropriate connections between mathematical ideas, and apply problem-solving skills in daily life situations.
We hope that these comprehensive workbooks will give students the tools and the confidence to handle mathematical questions and apply mathematical concepts to real-life situations. By achieving this, students will find learning mathematic an interesting and exciting experience. | mathematics |
https://www.thenewatlantis.com/publications/math-and-modernity | 2023-12-09T04:14:23 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100800.25/warc/CC-MAIN-20231209040008-20231209070008-00010.warc.gz | 0.945544 | 8,576 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__22756794 | en | One pillar of the modern world was the project to transform science from a discipline for contemplating nature into a tool for mastering it. Queen among the new sciences was mathematical physics, made possible by a corresponding transformation of mathematics. Ancient mathematicians, said René Descartes, had misunderstood their subject. They offered a procession of dazzling spectacles, but mathematics properly understood is not the presentation of beautiful chance discoveries. It must instead provide a systematic method for solving problems.
True and oft-heard though this story is, it is also easily taken for granted. Harvey Flaumenhaft’s new book Insights and Manipulations seeks to remedy that with a hands-on guide to this momentous change. To understand that change, he says, and to understand it as progress, “we need to know what it was a step from as well as what it was a step toward.” He presents it as a movement from the Conics of Apollonius of Perga, a brilliant and difficult triumph of ancient mathematics written in the third century b.c., to Descartes’s 1637 Geometry, a decisive stride into modernity. For Apollonius, mathematics was a way of gaining insights into the nature of geometrical forms by envisioning them in the mind; Descartes made mathematics into an activity of manipulation — hence the title of Flaumenhaft’s book.
But appreciating scientific progress should not become a license to forget the past:
We often take for granted the terms, the premises, and the methods that prevail in our time and place. We take for granted, as the starting points for our own thinking, the outcomes of a process of thinking by our predecessors.
What happens is something like this: Questions are asked, and answers are given. These answers in turn provoke new questions, with their own answers. The new questions are built from the answers that were given to the old questions, but the old questions are now no longer asked. Foundations get covered over by what is built upon them.
Progress thus can lead to a kind of forgetfulness, making us less thoughtful in some ways than the people whom we go beyond. We can become more thoughtful, though, by attending to the originating thinking that while out of sight is still at work in the achievements it has generated.
Insights and Manipulations is thus a guidebook helping us to retrace the steps of discovery from ancient mathematics to Descartes, who conceived the world anew. For “only by actively taking part in scientific discovery — only through engaging in re-discovery ourselves — can we avoid both blind reaction against the scientific enterprise and blind submission to it.” What’s at stake for Flaumenhaft is more than being thoughtful about the world we inhabit; it is whether we are to understand the foundations of modern science well enough to sustain it.
Classic works of science and mathematics make up a substantial part of the liberal arts curriculum at St. John’s College in Annapolis, Maryland, where Flaumenhaft has taught for more than fifty years. Students there struggle through Apollonius and Descartes not as an antiquarian exercise but as a way to see the modern world come into being.
Insights and Manipulations also offers a model of how to read a scientific classic: Presume that it has been written with care and treat it, like any other work of art, as a unified whole whose very form helps to tell its story. (Flaumenhaft provides, at times, more about the detailed structure of these works than many readers may want to know, but that’s a quibble.)
The first three-quarters of this hefty book is devoted to Apollonius, and is a considerable pedagogical achievement in itself. Apollonius studies conic sections, the curves obtained by slicing straight through a cone — circle, ellipse, parabola, hyperbola. The Conics is, to say the least, austere, a sequence of definitions, propositions, and proofs with little motivating explanation. It also assumes knowledge of sophisticated parts of Euclid’s Elements, a classical masterwork of geometry that preceded Apollonius by roughly a century.
Flaumenhaft, supplying background from Euclid as needed, carefully explains what each definition and proposition says (and, equally important, what it doesn’t). Before offering a formal proof, he prepares readers by informally explaining why each proposition ought to be true. He supplies abundant illustrations, not just geometric diagrams but also flowcharts that offer an overview of how every part of an argument fits together. The diagrams are great improvements on those typically provided in other presentations of Euclid or Apollonius. Instead of a single, sometimes massively complex figure, he accompanies each proof with a series of simpler pictures, each of which isolates only what is needed to explicate a single logical step. He also provides views from different angles (bird’s eye, side view), allowing the reader to imagine walking around a 3-D model. These illustrations are hand-drawn, which lends them a certain charm, as if one is following a teacher at a blackboard.
The story frequently steps back from the local questions of understanding individual definitions and arguments to the global question of why the results have been organized and presented as they are. Flaumenhaft tends, at times, to over-explain — as Marian Adams said of Henry James, to chew a bit more than he bit off — but that’s the defect of a virtue.
Conic sections still appear in high school mathematics today, but a contemporary student will encounter nothing like what we find in Apollonius. Apollonius starts with a geometrical image, a slice through a cone. Everything that follows is expressed in terms of geometrical constructions built on the cone, the curve, and the plane making the slice; there are no coordinates, formulas, equations, or even numbers. By contrast, a modern textbook will, pro forma, provide a picture of a cone, but will have no real use for it. The curves to be studied are defined by formulas, and the terminology of “conic sections” is a vestige of forgotten technology, as when we speak of dialing a phone. The modern student is really doing algebra.
Apollonius thinks very differently, guided by a set of clear logical distinctions that made it impossible to mix geometry with arithmetic (and thus with algebra). One must appreciate these distinctions to understand the radical step Descartes took in breaking them down, the power he unleashed in doing so, and the intellect that could do that.
After the extended treatment of Apollonius, and brief excursions into works by Diophantus of Alexandria (200s a.d.) and François Viète (1500s), Insights and Manipulations concludes with the 1637 Geometry. Here Descartes accuses the ancients of withholding explanations of how they discovered their results in order to make themselves look good. Further, the ancients insisted on a fundamental logical distinction between arithmetic and geometry — to Descartes, a pesky scruple that prevented them from finding the proper mathematical method. By merging the two fields, Descartes unveiled a royal road to discovery — inaugurating, as Flaumenhaft puts it, a decisive shift from seeing “with the mind’s eye” to performing “mental manipulation.”
Descartes famously distinguished mind, whose essence is to think, from matter, whose essence is “extension” — roughly, the ability to occupy space. The physics of the material world must therefore be explained as matter moving and rearranging in space. So a systematic method for solving geometrical problems, for mentally manipulating space, must have seemed the key to a comprehensive explanation of the material world.
Geometry was published in a volume comprising four short works. The first is the famous Discourse on the Method of Rightly Conducting One’s Reason and Seeking Truth in the Sciences — the source of “I think, therefore I am.” The other three offer examples of applying his method, which we can’t retrace here, to problems in different fields of science. Optics works out a (correct) law for the refraction of light. Meteorology explains (again correctly) the cause of a rainbow. Those two achievements, he says, are persuasive evidence for the value of his method.
And Descartes presents Geometry, the concluding essay, as definitive proof. He first describes a procedure for solving any problem in classical, Euclid-style geometry. A problem asks for a construction, such as: Given a rectangle, construct a square with the same area. I’ll use this very simple problem as a running example. Descartes doesn’t deign to illustrate his procedure by applying it to a specific example. Readers will learn more, he says, by working things out for themselves.
Instead, he turns to a problem that had been open for more than a millennium — actually to a family of problems called “locus” problems. They were formulated by Pappus of Alexandria, the last of the great, ancient Greek mathematicians, in the fourth century a.d. A locus problem asks a question of the form: What is the curve containing all points that satisfy some constraint? To take a simple example, if the constraint is “All points that lie at a given distance from a fixed center point,” the answer is a circle. Pappus formulated his problem in a very general way by establishing a systematic, stylized way to express the constraints. (See Supplement 1 below for an illustration.) While the answers to some relatively simple locus problems are the conic sections of Apollonius, the general problem posed by Pappus — an infinite family of increasingly complex problems — remained open.
Descartes is interested not merely in providing the answer to this or that previously unsolved problem, the stuff of which reputations in mathematics had always been made. What matters is the discovery of a systematic method for problem-solving — a way to attack any of Pappus’s locus problems, however elaborate the constraints. By doing so, he says, “I think I have entirely satisfied what Pappus tells us had been sought in this by the ancients,” and he adds, cavalierly, “I shall try to put the demonstration of it in a few words, for I am already bored from writing about it so much.”
The conceptual tools available for performing constructions in classical geometry are the straight edge and the compass. Although we may use physical versions of them on a blackboard, we should think of them as theoretical devices, imaginative ways to express two of Euclid’s postulates: that we can construct a straight line connecting any two points and extend it as far as we like (straight edge); and that we can construct a circle with any given center and radius (compass). Descartes’s methods allow him to see how far it’s possible to go using only straight edge and compass, and to identify the fancier tools required to solve more complex problems. He introduces what’s come to be called a “geometrical compass,” an indefinitely extendable device that allows additional moving straight-edges that act like levers:
As one adds more levers, one can draw more complex curves, with each added lever corresponding to added complexity in the algebraic expressions needed to formulate a problem.
When Descartes made his new beginning … , he said that the ancients were handicapped by their having a scruple against using the terms of arithmetic in geometry…. Before modern readers can appreciate why Descartes wanted to overcome the scruple, and what he saw that enabled him to do it, they must be clear about just what the scruple was.
We may think about the ancient scruple in the following way. The science we now have is what we might call “quantitative” and “numerical.” Quantities admit comparisons of less and greater. To us it seems natural to identify quantitative with numerical — to represent any quantity as a numerical value, for example a decimal number or a location on what we now call a “number line.” For that notion I’ll use the ungainly term number-in-our-sense.
To our great ancestors this conception of quantity, far from being natural, would have seemed incoherent. They recognized a fundamental difference between quantities arising in geometry (lengths, areas, volumes) and quantities arising in arithmetic (the numbers we count with). Our physical science required that Descartes break down that barrier by introducing arithmetical methods into geometry.
What was the problem? First, as noted, quantities fall naturally into two radically different categories: multitudes (collections of distinct individuals that can be counted, like cows) and magnitudes (which can be made continuously smaller or greater, like lines or areas or volumes). Ordinary speech reflects the difference. Of multitudes we ask “How many?” but of magnitudes “How much?” A herd of cows is a multitude; we ask how many cows are in a field, not how much cows there are. We get the answer by counting them. The water in a pond is a magnitude. We ask how much of it there is, not how many.
To define a multitude, we have to specify which individuals it consists of. One can’t point to a field and ask “How many?” without specifying how many of what: horses, cows, hooves. Euclid’s Elements, which lays the foundation for Apollonius, says that “a unit is that by virtue of which each of the things that exist is called one.” In this sense, “cow” is a unit but “water” is not; we can count cows but not water because there’s such a thing as “a cow” but no such thing as “a water.” There is an unfortunate collision between Euclid’s meaning of “unit” and our use of “unit” to denote some arbitrarily chosen magnitude — inch, pound, gallon — employed as a reference for measurements. It seems we might be able to paper over the differences between multitudes and magnitudes by using such reference values: We can’t ask how many water are in a pond, but we can ask how many gallons of water are in it. As we will see, that simple strategy — changing the question so as to think of magnitudes as multitudes — can’t be made to work. Something much deeper will be required.
Euclid goes on to say, “A number is a multitude composed of units.” Euclid’s units are, by definition, indivisible, so multitudes are discrete: There is no multitude consisting of more than three cows but fewer than four. Multitudes defined by different units can be compared: It makes sense to ask whether there are more chickens in the barn than eggs. From now on, I’ll use the word number, unqualified, to mean a number in this ancient sense but will sometimes, for emphasis, say “counting number,” and we will see how this is different from number-in-our-sense, which allows us to represent any quantity as a numerical value.
Magnitudes, by contrast, are not discrete; a line, unlike a herd of cows, can repeatedly be divided into smaller pieces as often as you like. (For Euclid, “line” always means what today we would prefer to call a “line segment”: limited in length, having two end points.) Equally important, magnitudes are of different kinds, and those of different kinds are incomparable; we can’t, for example, ask whether (the length of) a line is greater or less than (the area of) a two-dimensional figure such as a square.
The preceding sentence hid the references to length and area in parentheses because they suggest a way of thought according to which there is, on the one hand, a line (or a figure) and, on the other hand, some sort of number-in-our-sense that is its length (or its area). But the possibility or intelligibility of such numbers-in-our-sense is precisely what is at issue. When, for example, Euclid shows that a certain square equals a certain triangle, that amounts not to some numerical comparison but to showing that the figures can be cut into identical collections of pieces — or, if you like, cut up and then rearranged to make the same figures.
Consider a further distinction between multitudes (“how many”) and magnitudes (“how much”): Different things can be done with each. For example, two multitudes can be multiplied but two magnitudes cannot. The result of multiplying four cows by three is (to use a modern notation that is in this case not misleading) 4 + 4 + 4 cows. The multitudinous-ness of three is what tells us how many times to add groups of four cows together. By contrast, although we can multiply a magnitude by a multitude — say, doubling a line — we cannot multiply two magnitudes, even if they are of the same kind. We can’t multiply a line by a line or one figure by another, because lines and figures provide no natural answer to the question “How many times?”
A modern text that formulates the Pythagorean Theorem by saying “a right triangle with sides a, b, and hypotenuse c satisfies a2 + b2 = c2” is therefore saying something radically different from what Euclid or Apollonius or Pythagoras said. It assigns to the sides the lengths a, b, and c, which are numbers-in-our-sense; it performs arithmetical operations on them (squaring, adding) to compute other numbers-in-our-sense; and then it asserts that the results are numerically equal. Euclid puts this very differently. He says that if you’re given a right triangle and construct squares on all its sides, then the squares on the two sides containing the right angle taken together are equal to the square on the other one. Numbers don’t enter the picture, and the proof is done geometrically.
We are so used to thinking in terms of numbers-in-our-sense that the difference can be hard to think about, but it is critical for understanding what ancient mathematicians were doing, and what marked the divide between geometry and arithmetic that Descartes broke down. But before we get there, we must get a taste for the challenges the ancients faced — and the insights they gained — in doing geometry without arithmetic.
Earlier, I dismissed a maneuver that seems as if it could bridge the two domains — namely, to treat a magnitude as a kind of multitude, an exact multiple of some magnitude used as the reference for a measurement. Thus we might be able to regard some line as a multitude of feet or meters or cubits. If a right triangle has sides that are 3 feet, 4 feet, and 5 feet, the Pythagorean Theorem might be expressed as a fact about calculations with those numbers: 32 + 42 = 52. (Ignore for now that the theorem would no longer describe visualizable relationships among geometric figures.)
Why does this trick fail? It can be applied only if all the lines in the problem are exact multiples of the same reference line — if, in Euclid’s terminology, all the lines have a “common measure.” Unfortunately, one of the most famous proofs in ancient mathematics shows that that’s not always possible. A simple example: the side of a square and its diagonal have no common measure. This example also shows that the trick can’t be used to formulate the Pythagorean Theorem. It can’t be applied to the right triangles that result from slicing a square in half along its diagonal.
Ancient mathematicians devised an elegant way around this by appealing to the notion of ratio. Quantities of the same kind — two lines, for example — will have a ratio even if they lack a common measure, and ratios can be compared. We can say, for example, that the ratio of 2 to 5 is the same as the ratio of 4 to 10, and is greater than the ratio of 2 to 10. Crucially, we can compare any ratios — we can, for example, compare the ratio of two counting numbers to that of two areas, or the ratio of two lengths to the ratio of two volumes.
Modern mathematics is indifferent to any distinction between ratios and numbers-in-our-sense; it is happy to identify the ratio of 2 to 5 with the number-in-our-sense 2/5, or the ratio between a square’s diagonal and its side with the number-in-our-sense called “the square root of two.” For us, the proportion stating that “the ratio of 2 to 5 is the same as the ratio of 4 to 10” can be expressed as the equation “2/5 = 4/10.”
Euclid and Apollonius have no words to denote “the square root of two” but do have a powerful theory of ratios that makes it possible to establish connections among quantities of all kinds. That theory gets a rigorous basis in the most technically sophisticated book of Euclid’s Elements.
Consider a simple example, expressing the relation between the area of a rectangle and the lengths of its sides. In modern mathematics we represent the sides with numbers-in-our-sense — say, 2.6 and 3.5 — and define the area to be their numerical product: 2.6 * 3.5 = 9.1. In a practical application, the numbers we use will depend on whether we choose to express the lengths in inches, meters, furlongs, or whatever.
Euclid expresses that relationship more elegantly with ratios, needing no resort to an arbitrarily chosen standard of measurement. Look first at a simple case. If, given a rectangle, we leave its height unchanged, and double its width, we will have doubled its area. Similarly, to use modern terms, if we change the width by a factor of 50 percent, or by a factor of , we will change the area by the same factor. That is, if we write “:” to abbreviate “the ratio” between two quantities, we can in this simple case express the relation between the sides and area of a rectangle as a proportion:
[old rectangle : new rectangle] is the same as [old width : new width]
If we now change both the height and width, then [old rectangle : new rectangle] will be a ratio that depends on both [old width : new width] and [old height : new height]. It will be what Euclid calls the ratio compounded of those two; given such a pair, Euclid shows how to construct a pair of lines whose ratio is their compound.
These are the terms in which Apollonius thinks, and he deploys them with great virtuosity.
Flaumenhaft wants to help us teach ourselves to think like Apollonius, who proves theorems using proportions, and to compare that to the Cartesian practice of solving problems using equations. The root of the Greek word for “theorem” means “to look at” or “behold.” And “proportion” has to do with recognizing a similarity between different things. This reflects what Apollonius does: behold certain similarities in things. A problem, by contrast, presents us with a task: to find a solution. The terms in an equation are symbolic. Their purpose is not to represent something that we see by looking at or through it, but to be material for manipulation.
For Descartes, Flaumenhaft writes, “beholding is subordinate to mastery,” and “wonder should give way to problem-solving. What Descartes brought to this modern project which took mastery of nature as its end was an emphasis on mathematics as means to the end.”
We can further contrast the two approaches by considering the difference between synthesis and analysis. Euclid and Apollonius present their results by synthesis. A synthesis is a proof that begins from postulates and things already proven, then deduces a sequence of further results until it manages to establish the desired conclusion. Those deductions often concern not only the lines and figures given in the statement of a theorem, but additional lines and figures introduced, often with great ingenuity, in order to establish in some roundabout way relationships among the elements of the original material. How the proposition or its proof were discovered is not manifest.
Descartes, by contrast, provides a method of analysis. Starting with a problem, he will transform it into a sequence of other problems, all of which are equivalent, until arriving at one he knows how to solve. Since the problems are equivalent, a solution to any of them gives a solution to all of them. The procedure is transparent because the analysis itself shows how the result was obtained.
Analysis is what we do in a high school algebra class. We’re given the problem of finding an x such that 3x – 2 = 7. Adding 2 on each side of the equation transforms it to 3x = 9. Dividing both sides by 3 transforms that to x = 3. Maneuvers of this kind were hardly unknown before Descartes. Flaumenhaft walks us through the way Diophantus applied them to problems about numbers and Viète applied them to what he called “species” — entities that share some characteristics with numbers and some with geometrical magnitudes. Species, however, are still encumbered by something like the distinctions among kinds of quantities that Descartes eliminates.
Descartes claims that any geometric problem can be expressed as the task of finding the lengths of certain lines. To do that by analysis, he first restates the geometric problem using equations that relate the unknowns (lines to be found) to the knowns (lines given in the statement of the problem).
Consider again our familiar example: Given a rectangle, construct a square of the same area. The knowns are the two sides of the rectangle; call them A and B. There’s one unknown, the side of the square we’re looking for (since all sides of the square are the same); call it x.
The equation that relates the areas of the two figures may look misleadingly, comfortably familiar:
x * x = A * B
We’ll have more to say about that later, but, to avoid jumping to unjustified conclusions, note that Descartes is doing geometry: A, B, and x are straight lines, not numbers.
Algebraic manipulations then transform these equations into a solution — that is, a collection of equations in which each unknown is set equal to an expression involving only known quantities.
In this case, the solution (also misleadingly familiar) is:
Now comes a piece of magic. Descartes does not find x by calculating some value for the expression ; instead, as we will see below,“” is interpreted as a set of instructions for performing a geometrical construction that gives the desired answer.
He is doing geometry, but the most important steps take place in a symbolic world where we (literally) lose sight of the original subject matter. We can, however, extract a geometrical meaning from the symbolic solution that emerges.
Before looking at how Descartes solves the problem, we must consider how he explains arithmetical manipulation of lines. The terms in Descartes’s equations use the operations of addition, subtraction, multiplication, division, and the taking of roots (square root, cube root, and so forth). As Descartes defines these operations, both their inputs and outputs are lines. Thus, all the manipulations act on a single kind of thing — on a single “type,” to use the terminology of modern logic and computer science. Operating on a single type, regardless of what it represents, is a crucial simplification.
Addition and subtraction of lines are explained in the obvious way: A + B is a line that results from extending A by attaching B at one of its endpoints. A – B is a line that results from lopping B off the end of A, and is not defined if B is greater than A. Descartes defines multiplication, division, and the taking of roots by analogy. Take multiplication as an example. He first finds a recipe that characterizes multiplication for counting numbers in terms of ratios and proportions — the domain in which multitudes and magnitudes participate on something like an equal footing. He then uses that recipe as the definition of multiplication for lines.
Here’s how that works. For counting numbers, we can describe the result of multiplying 2 by 3 as a proportion by saying that
(2 * 3) : 2 is the same ratio as 3 : 1
In other words, because 3 is what you get by tripling 1, the value of 2 * 3 is what you get by tripling 2. Descartes simply copies that: If A and B are lines and we arbitrarily choose any other line u, then — in terms of that choice of u — we define A * B to be a line such that
(A * B) : A is the same ratio as B : u
That is, whatever “multiple” B is of u, A * B is that same multiple of A. (Supplement 2 below provides a geometrical construction for finding A * B.) Descartes calls u a “unit,” using the word in essentially the modern sense — unlike Euclid’s usage, in which a unit is a concept that specifies the kind of thing (a cow) assembled in a multitude (a herd).
It’s far from obvious what those definitions buy us, since the line we obtain by calculating the value of some complex expression will depend entirely on the arbitrarily chosen unit (u). But Descartes doesn’t want to calculate with these expressions; he only wants to manipulate them. His strategy works, because, for any fixed choice of a unit, all the usual rules for algebraic manipulation are valid. For example, consider the expressions (A * B * C) / A and B * C. Whatever line we choose as the unit u, the value of the two expressions calculated in terms of u will be lines of the same length. Descartes can therefore say that (A * B * C) / A = B * C, and justify the algebraic maneuver of “canceling the A’s.”
Here are the steps by which Descartes’s method would solve our simple sample problem: Given a rectangle, construct an equal square.
We choose names for the knowns, the sides of the rectangle: call them A and B. We choose a name, x, for the side of the square we’re seeking.
We next apply certain rules for translating the geometry into symbols. One of them tells us to represent (the area of) that rectangle by the expression A * B. By the same rule, x * x represents the square we want to find. (For x * x, we’ll use the modern notation x2, which Descartes introduced.) We thus reformulate the problem as a request to solve x2 = A * B. A symbolic solution requires just two steps:
|taking the square root of both sides|
Descartes provides another set of rules for translating the solution thus found into a geometric construction. Relegating the explanation to Supplement 3 below, I’ll simply assert that the solution given above corresponds to a geometric construction solving the problem:
Find an x so that B : x is the same as x : A.
All together, this amounts to a geometrical argument in which all the work is done by routine symbolic manipulation.
The rules for translating geometric problems into equations, and for then translating their algebraic solutions back into geometric constructions, are based on plausible analogies. Further, because the rules for algebraic manipulation are valid regardless of the choice of unit, it’s plausible that those manipulations won’t corrupt the geometrical meaning that we ultimately wish to extract. Those deep insights don’t truly amount to proof that his method works, although using modern logical techniques such a proof would be straightforward.
Descartes asserts, leaving it to the reader to persuade himself, that the method he describes suffices to solve any problem solvable by the constructions available in Euclid. But that’s only a warmup.
The definitive proof for the value of Descartes’s method is that it has enabled him to discover how to systematically classify and solve an unlimited number of problems of arbitrary complexity. Locus problems with more and more elaborate constraints will result in equations containing terms of higher and higher power, something that might in the past have seemed problematic. We can understand X2 — indeed, visualize it — as representing the area of a square, and we can understand X3 as the volume of a cube. But what about X4, X5, X6, … ? What could be the sense of those? Descartes has made that problem disappear. There is a method. One applies it.
He thus helped set in motion a chain of developments that led mathematics to become formal. Euclid and Apollonius understand themselves to be talking about lines, circles, figures, and solids. They single out certain obvious truths as postulates and prove others, including some that are not at all obvious, from those postulates. Those proofs allow us to see that the less-obvious things are true, but don’t make them true; rather, their truth follows from the nature of lines, circles, figures, and solids.
A modern treatment of Euclidean geometry, by contrast, might begin by saying something like this: Suppose we have two collections of things, which we choose to call points and lines, and suppose that they satisfy such-and-such a list of postulates. It doesn’t matter, and we don’t care, what the things called “lines” and “points” are in relation to space or to anything in the physical world; the question doesn’t arise. Such meaning as “lines” and “points” have is acquired from the role they play in the system. Bertrand Russell, with his talent for aphorism, expressed this by saying that “mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true.”
Practicing mathematicians do of course form mental pictures of what they talk about. Few have carefully thought-through positions on the philosophical status of those entities, but, professionally speaking, all play the formal game because it has immense power — and is the only way to make their results acceptable to the mathematical community at large.
Insights and Manipulations is written, the introduction says, “for serious amateurs by a serious amateur,” and even its smallest details reflect the author’s long career as a teacher. Its meticulous layout, for example, arranges that an illustration and any references to it will lie on the same page or on a facing page, so that the reader won’t be compelled to flip back and forth. The original texts, including Flaumenhaft’s new translation of Apollonius, are presented in gray boxes and arranged to help the eye take them in, with lengthy and complex sentences often displayed so that each line on the page consists essentially of a logical unit. The publisher deserves compliments for agreeing to design decisions that make a big book even bigger.
A serious amateur could use this book for self-study with a good prospect of success. Small seminars, I’m told, have worked through the entirety of early drafts with university students. A profitable course could be made from selections that focus, like this essay, on the beginning and end of the story — Apollonius and Descartes.
Insights and Manipulations is part of a long-term pedagogical project, of the author and others, to reintroduce classic scientific works into liberal education. Intellectually serious students are owed that experience. Great scientific works are of enduring interest for their daring and imagination, and as chronicles of heroic adventures of the mind. “To be thoughtful human beings,” Flaumenhaft says, “to be thoughtful about what it is that makes us human, we need to read the record of the thinking that has shaped the world around us, and continues still to shape our minds.”
A simple three-line locus problem is illustrated below:
We’re given the “reference” lines A, B, and C. Here is the constraint
determining whether a point P lies on the locus:
Draw perpendiculars from P to each of the reference lines, calling
those perpendiculars a, b, and c. P satisfies the constraint if
you can draw a rectangle with sides a and b that has the same
area as a square with side c.
In this diagram, c is larger than both a and b. Thus we would expect the square with side c to be larger than the rectangle with sides a and b, and so P does not lie on the locus.
Pappus introduced a very general way to formulate constraints: There can be any number of reference lines, not just three. Instead of insisting that the line drawn from P meets each reference line at a right angle, one can specify the angle for each of them — the line from P to A must make this angle; the line from P to B must make that one; and so forth. Instead of requiring that the areas of the rectangle and square be equal, one can specify that the areas must have a certain ratio. (In, say, a six-line problem, the way to formulate the comparison of ratios based on the six lines drawn from P to the reference lines is more complex.)
Given A, B, and u, lay them out as in the left-hand side of the figure
A and B meet at their end points to form an angle (it doesn’t matter what size). Lying on one of those sides is u (it doesn’t matter which side; in the figure I’ve chosen A), with one of its end points at the angle’s vertex. Neither does it matter whether u is greater than, less than, or equal to the side on which it lies.
The right-hand side of the figure then shows how to construct the side that will be defined as the length A * B with respect to the unit u: Draw a line (shown with heavy dashes) from the end of u to the end of B. Then draw a line (shown with lighter dashes) parallel to that line at the end of A, extending that line, and adding an extension to B, until they meet.
The desired result is the line marked A * B. Because the two dashed lines are parallel, the two triangles in the figure are similar, and corresponding sides will therefore have the same ratio. So, as desired, (A * B) : A is the same as B : u.
Let’s first explain why this equation corresponds to the proportion:
B : x is the same as x : A
This can be seen by backing up to the preceding equation, x2 = A * B, and rewriting it as follows:
|x * x = A * B||by the definition of x2|
|x = (A * B) / x||dividing both sides by x|
|x / A = (A * B) / (x * A)||dividing both sides by A|
|x / A = B / x||“canceling” the A’s|
This last equation corresponds to the proportion
B : x is the same as x : A
The figure below shows the construction of x from B and A. Draw a semicircle whose diameter is A + B. The line x is the perpendicular drawn from the common point of A and B to the circle. The ability to draw circles (a compass) makes it possible to construct square roots. Successive add-ons to Descartes’s improved compass make it possible to extract roots of higher powers.
Math and Modernity | mathematics |
https://kitwallace.co.uk/Blog/item/2013-01-12T23:01:00Z | 2020-09-29T07:52:58 | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401632671.79/warc/CC-MAIN-20200929060555-20200929090555-00775.warc.gz | 0.910115 | 736 | CC-MAIN-2020-40 | webtext-fineweb__CC-MAIN-2020-40__0__231341228 | en | A friend's Christmas present to himself (and indirectly his family and friends) was a MakerBot Replicator 3-D printer. Down at Bristol Hackspace we have several repraps in various stages of completion, but none yet ready for novice use. Marc's printer seems to have worked out of the box, so I was able to get my first test piece send via Dropbox to London, printed appropriately enough, since it involved hearts, in a pretty pink plastic and posted to Bristol in a couple of days.
The key to my personal progress was the discovery of OpenSCAD. I've looked at using GUI-based 3-D tools like Blender but OpenSCAD is a programming environment, just my kind of 3-D tool. I soon found a weath of freely avaliable tutorials, reference material and scripts:
OpenSCAD uses two modes of construction: Constructive Solid Geometry (CSG) using the Computational Geometry Algorithms Library (CGAL); and extrusion(two modes) of a 2-D shape.
Some lessons learnt:
The challenge for the budding designer is to learn how to compose a desired shape by the application of the operators to the primitives. In the physical world, we typically construct objects in a 'carpentry' mode, glueing non-intersectiing objects (union) and removing waste (difference). Also our range of primitives is vast and I generally have no idea how, say, a nut is formed. CSG allows us to union() overlapping objects, get the intersection of objects and use the less-known operators minkowski sum and hull. To see what experienced openSCAD programmers use, I analysed the collection of 22 library files for basic shapes, gears and threads etc. There were a total of 10000 lines including comments. I used grep to do the counting of patterns such as 'rotate\s*(' to get counts of each construct in the language.
|union||576||Severe underestimate since union() is the default for a sequence of objects|
|intersection_for||2|| replacement for loop within intersection which doesnt work
This data seems to indicate that designers are mainly using operators which correspond to the physical operations (carpentry mode) and are generally not using the advanced operators. This is not surprising because even intersection can yield surprising results. An example in the wikibook shows the construction of a dodecahedron from the intersection of 6 boxes:
but I havent been able to trace the source of this construction. It's tempting to look for ways of constructing the other regular solids using intersection and indeed playing with this code, I found I could make an octahedron:
What other solids could I make this way? One feature of OpenSCAD is very useful here - the ability to display a parameterized sequence of objects as an animation. The system variable $t changes from 0 to 1 in increments determined by the total number frames entered in the animation panel, so to see what solids are generated as the dihedral angle is changed :
and its fun to watch the shapes morph, becoming dodecahedrons at several angles and curious asymmetric faceted shapes in between. Moreover you can edit the script as it runs to change other parameters such as the number of intersecting boxes. You can also create a video. Each frame is saved as a .png file. I used ffmpeg installed on Ubuntu:
> ffmpeg -f image2 -i frame%05d.png -r 12 dodec.avi
to create this little video | mathematics |
https://www.uiwteachernetwork.org/elementary-apps.html | 2018-12-14T17:41:36 | s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826145.69/warc/CC-MAIN-20181214162826-20181214184826-00567.warc.gz | 0.904554 | 1,337 | CC-MAIN-2018-51 | webtext-fineweb__CC-MAIN-2018-51__0__187293953 | en | Elementary Apps for the Classroom
Check out these great apps for your students.
Arithmetic Invaders Express: Grade K-2 Math Facts - Express addition, subtraction, and multiplication games to defend the solar system and master K-2 arithmetic. Also, learn some basic facts about the Solar System.
Cloud Math Free - Excellent app for practicing and learning math." The difficulty level is easily controlled by a choice of operations, number ranges, numbers of answers to choose from, the number of problems in a set, and a Fail-safe mode. There are problems with addition and subtraction operations on numbers up to 50.
Geoboard, by the Math Learning Center - Geoboard is a tool for exploring a variety of mathematical topics introduced in the elementary and middle grades. Learners stretch bands around the pegs to form line segments and polygons and make discoveries about perimeter, area, angles, congruence, fractions, and more.
Math Puppy - Your younger students will be able to enjoy an interactive, learning environment of fun and adventure as they master basic math skills. Perfect for early childhood students.
Counting Bills & Coins - Counting Bills & Coins lets you practice identifying and solving math problems with money. Count, match, and make change with coins up to quarters and bills up to $20. Practice money skills in five unique activities: counting money, show me the money, making change, matching amounts, and show values.
Math Ninja - Use your math skills to defend your tree house against a hungry tomato and his robotic army in this fun action packed game! Choose between ninja stars, smoke bombs, or ninja magic - and choose your upgrades wisely!
Interactive Telling Time Lite - Interactive Telling Time is great for kids from ages 3 to 12 and comes in 3 difficulty levels so that it helps kids master telling time progressively (statistics are provided to help keep track of progress). Learn to set the time via interactive clocks with movable hour and minute hands, how to read a clock/to tell time, the conversion between analog clocks and digital clocks, as well as concepts such as ‘o’clock‘, ‘midnight’, ‘half past’, ‘quarter past’, ‘quarter to’, ‘past’, ‘to’, etc.
Dominoes Easy Match - Dominoes Easy Match skills focus on: concepts of numbers, identification of numbers 1-9, identification of simple arrays, rote counting, and one-to-one correspondence. This is a great app for beginning math learners.
MathTappers: Multiples - MathTappers: Multiples is a simple game designed first to help learners to make sense of multiplication and division with whole numbers, and then to support them in developing fluency while maintaining accuracy.
Teaching Number Lines: Little Monkey Apps Number Lines helps to introduce the concept of number lines through a variety of of modules such as: counters, drawings, and number lines in order to explain and physically model problems. Little Monkey Apps Number Lines aims to visualize numbers for rote counting and ordering and see the physical position of a number linking patterns and relationships. Great for student in K through 2.
K12 Equivalence Tiles - K12 Equivalence Tiles lets you compare the values of fractions, decimals, and percents up to 1 by using draggable tiles of varying values. K12 is not a calculator; it is a tool for students who have trouble understanding rational number equivalence (for example, 0.5, 1/2, 50% are all equal). This tool also allows students to visually perform simple operations like addition, subtraction, comparison, and ordering. This is a great app for upper elementary grades.
Rounding - Rounding is a great way to test your rounding skills and have fun at the same time. Select the number of problems and other options in order to correlate with your skill level.
Interactive Math Glossary -The Interactive Math Glossary App is provided by the Texas Education Agency to help teachers explore and understand mathematics vocabulary used in the grades K–8 Texas Essential Knowledge and Skills. Each glossary word is displayed in a four quadrant Frayer Model.
Science 360 - This app will allow your students to scroll the 3D sphere that is made of thumbnails of various science photos and videos. Tap on any one of those thumbnails to bring up the recent updates from National Science Foundation (NSF) or institutions funded by NSF. All contents are multimedia and are updated weekly, so you always get the most recent development of science and technology.
NASA - The NASA app carries a wealth of NASA information right on your iPad. The app collects, customizes and delivers an extensive selection of dynamically updated mission information, images, videos. It has information about the planets, live streaming of NASA TV, and on demand NASA video.
WWF Together- Experience the world's most amazing and endangered animals in one app – together. This interactive experience brings you closer to the stories of elephants, whales, rhinos and other fascinating species. Discover their lives and the work of WWF in a way you’ve never seen before. Try out “tiger vision,” stay as still as the polar bear during a hunt, and chop the panda’s bamboo. Explore the animals’ stories, then fold them up and share them with the world.
Robots for IPADS - Robots for iPad is the best, most complete guide to the world of robotics. This fun, highly interactive app lets you explore over 150 real-world robots, with hundreds of animations, photos, videos, and articles
Kids Can Match - An interactive, adaptive and fun memory game for children of all ages. This app contains amazing, one of a kind, collection of over 70 authentic animal images and sounds. The perfect way to engage children in a fun game while they learn about a broad range of animals from all over the world. Tailor made and carefully designed by experienced educators to fit the needs of small children. This educational game is a wonderful asset in any animal loving family.
Talkboard- Talkboard is the canvas for collaborative learning. Work with your students, wherever they are, on a shared whiteboard to bridge the gap in distance between you. Then harness your creativity to bring color and clarity to your lessons. Talkboard’s simple yet elegant drawing tools and integrated audio allow you to engage students in a whole new way. | mathematics |
http://physicistjcbblgn.blogspot.com/2012/01/history-of-mathematics.html | 2018-07-15T20:38:56 | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676588972.37/warc/CC-MAIN-20180715203335-20180715223335-00267.warc.gz | 0.958418 | 3,615 | CC-MAIN-2018-30 | webtext-fineweb__CC-MAIN-2018-30__0__75487177 | en | BY PROF JACOB
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. The most ancient mathematical texts available are Plimpton 322 (Babylonian mathematics c. 1900 BC), the Rhind Mathematical Papyrus (Egyptian mathematics c. 2000-1800 BC) and the Moscow Mathematical Papyrus (Egyptian mathematics c. 1890 BC). All of these texts concern the so-called Pythagorean theorem, which seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry.
The study of mathematics as a subject in its own right begins in the 6th century BC with the Pythagoreans, who coined the term "mathematics" from the ancient Greek μάθημα (mathema), meaning "subject of instruction". Greek mathematics greatly refined the methods (especially through the introduction of deductive reasoning and mathematical rigor in proofs) and expanded the subject matter of mathematics. Chinese mathematics made early contributions, including a place value system. The Hindu-Arabic numeral system and the rules for the use of its operations, in use throughout the world today, likely evolved over the course of the first millennium AD in India and was transmitted to the west via Islamic mathematics. Islamic mathematics, in turn, developed and expanded the mathematics known to these civilizations. Many Greek and Arabic texts on mathematics were then translated into Latin, which led to further development of mathematics in medieval Europe.
From ancient times through the Middle Ages, bursts of mathematical creativity were often followed by centuries of stagnation. Beginning in Renaissance Italy in the 16th century, new mathematical developments, interacting with new scientific discoveries, were made at an increasing pace that continues through the present day.
Prehistoric mathematicsThe origins of mathematical thought lie in the concepts of number, magnitude, and form. Modern studies of animal cognition have shown that these concepts are not unique to humans. Such concepts would have been part of everyday life in hunter-gatherer societies. The idea of the "number" concept evolving gradually over time is supported by the existence of languages which preserve the distinction between "one", "two", and "many", but not of numbers larger than two.
The oldest known possibly mathematical object is the Lebombo bone, discovered in the Lebombo mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches cut into a baboon's fibula. Also prehistoric artifacts discovered in Africa and France, dated between 35,000 and 20,000 years old, suggest early attempts to quantify time.
The Ishango bone, found near the headwaters of the Nile river (northeastern Congo), may be as much as 20,000 years old and consists of a series of tally marks carved in three columns running the length of the bone. Common interpretations are that the Ishango bone shows either the earliest known demonstration of sequences of prime numbers or a six month lunar calendar. In the book How Mathematics Happened: The First 50,000 Years, Peter Rudman argues that the development of the concept of prime numbers could only have come about after the concept of division, which he dates to after 10,000 BC, with prime numbers probably not being understood until about 500 BC. He also writes that "no attempt has been made to explain why a tally of something should exhibit multiples of two, prime numbers between 10 and 20, and some numbers that are almost multiples of 10."
Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. It has been claimed that megalithic monuments in England and Scotland, dating from the 3rd millennium BC, incorporate geometric ideas such as circles, ellipses, and Pythagorean triples in their design.
All of the above are disputed however, and the currently oldest undisputed mathematical usage is in Babylonian and dynastic Egyptian sources. Thus it took human beings at least 45,000 years from the attainment of behavioral modernity and language (generally thought to be a long time before that) to develop mathematics as such.
Babylonian mathematicsBabylonian mathematics refers to any mathematics of the people of Mesopotamia (modern Iraq) from the days of the early Sumerians through the Hellenistic period almost to the dawn of Christianity. It is named Babylonian mathematics due to the central role of Babylon as a place of study. Later under the Arab Empire, Mesopotamia, especially Baghdad, once again became an important center of study for Islamic mathematics.
In contrast to the sparsity of sources in Egyptian mathematics, our knowledge of Babylonian mathematics is derived from more than 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed whilst the clay was moist, and baked hard in an oven or by the heat of the sun. Some of these appear to be graded homework.
The earliest evidence of written mathematics dates back to the ancient Sumerians, who built the earliest civilization in Mesopotamia. They developed a complex system of metrology from 3000 BC. From around 2500 BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. The earliest traces of the Babylonian numerals also date back to this period.
The majority of recovered clay tablets date from 1800 to 1600 BC, and cover topics which include fractions, algebra, quadratic and cubic equations, and the calculation of regular reciprocal pairs. The tablets also include multiplication tables and methods for solving linear and quadratic equations. The Babylonian tablet YBC 7289 gives an approximation of √2 accurate to five decimal places.
Babylonian mathematics were written using a sexagesimal (base-60) numeral system. From this derives the modern day usage of 60 seconds in a minute, 60 minutes in an hour, and 360 (60 x 6) degrees in a circle, as well as the use of seconds and minutes of arc to denote fractions of a degree. Babylonian advances in mathematics were facilitated by the fact that 60 has many divisors. Also, unlike the Egyptians, Greeks, and Romans, the Babylonians had a true place-value system, where digits written in the left column represented larger values, much as in the decimal system. They lacked, however, an equivalent of the decimal point, and so the place value of a symbol often had to be inferred from the context.
Egyptian mathematicsEgyptian mathematics refers to mathematics written in the Egyptian language. From the Hellenistic period, Greek replaced Egyptian as the written language of Egyptian scholars. Mathematical study in Egypt later continued under the Arab Empire as part of Islamic mathematics, when Arabic became the written language of Egyptian scholars.
The most extensive Egyptian mathematical text is the Rhind papyrus (sometimes also called the Ahmes Papyrus after its author), dated to c. 1650 BC but likely a copy of an older document from the Middle Kingdom of about 2000-1800 BC. It is an instruction manual for students in arithmetic and geometry. In addition to giving area formulas and methods for multiplication, division and working with unit fractions, it also contains evidence of other mathematical knowledge, including composite and prime numbers; arithmetic, geometric and harmonic means; and simplistic understandings of both the Sieve of Eratosthenes and perfect number theory (namely, that of the number 6). It also shows how to solve first order linear equations as well as arithmetic and geometric series.
Another significant Egyptian mathematical text is the Moscow papyrus, also from the Middle Kingdom period, dated to c. 1890 BC. It consists of what are today called word problems or story problems, which were apparently intended as entertainment. One problem is considered to be of particular importance because it gives a method for finding the volume of a frustum: "If you are told: A truncated pyramid of 6 for the vertical height by 4 on the base by 2 on the top. You are to square this 4, result 16. You are to double 4, result 8. You are to square 2, result 4. You are to add the 16, the 8, and the 4, result 28. You are to take one third of 6, result 2. You are to take 28 twice, result 56. See, it is 56. You will find it right."
Finally, the Berlin papyrus (c. 1300 BC) shows that ancient Egyptians could solve a second-order algebraic equation.
Greek mathematicsGreek language from the time of Thales of Miletus (~600 BC) to the closure of the Academy of Athens in 529 AD. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to North Africa, but were united by culture and language. Greek mathematics of the period following Alexander the Great is sometimes called Hellenistic mathematics.
Greek mathematics was much more sophisticated than the mathematics that had been developed by earlier cultures. All surviving records of pre-Greek mathematics show the use of inductive reasoning, that is, repeated observations used to establish rules of thumb. Greek mathematicians, by contrast, used deductive reasoning. The Greeks used logic to derive conclusions from definitions and axioms, and used mathematical rigor to prove them.
Greek mathematics is thought to have begun with Thales of Miletus (c. 624–c.546 BC) and Pythagoras of Samos (c. 582–c. 507 BC). Although the extent of the influence is disputed, they were probably inspired by Egyptian and Babylonian mathematics. According to legend, Pythagoras traveled to Egypt to learn mathematics, geometry, and astronomy from Egyptian priests.
geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. Pythagoras established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The Pythagoreans are credited with the first proof of the Pythagorean theorem, though the statement of the theorem has a long history, and with the proof of the existence of irrational numbers.
Plato (428/427 BC – 348/347 BC) is important in the history of mathematics for inspiring and guiding others. His Platonic Academy, in Athens, became the mathematical center of the world in the 4th century BC, and it was from this school that the leading mathematicians of the day, such as Eudoxus of Cnidus, came from. Plato also discussed the foundations of mathematics, clarified some of the definitions (e.g. that of a line as "breadthless length"), and reorganized the assumptions. The analytic method is ascribed to Plato, while a formula for obtaining Pythagorean triples bears his name.
Eudoxus (408–c.355 BC) developed the method of exhaustion, a precursor of modern integration and a theory of ratios that avoided the problem of incommensurable magnitudes. The former allowed the calculations of areas and volumes of curvilinear figures, while the latter enabled subsequent geometers to make significant advances in geometry. Though he made no specific technical mathematical discoveries, Aristotle (384—c.322 BC) contributed significantly to the development of mathematics by laying the foundations of logic.
In the 3rd century BC, the premier center of mathematical education and research was the Musaeum of Alexandria. It was there that Euclid (c. 300 BC) taught, and wrote the Elements, widely considered the most successful and influential textbook of all time. The Elements introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. Although most of the contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. The Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. In addition to the familiar theorems of Euclidean geometry, the Elements was meant as an introductory textbook to all mathematical subjects of the time, such as number theory, algebra and solid geometry, including proofs that the square root of two is irrational and that there are infinitely many prime numbers. Euclid also wrote extensively on other subjects, such as conic sections, optics, spherical geometry, and mechanics, but only half of his writings survive.
Archimedes (c.287–212 BC) of Syracuse, widely considered the greatest mathematician of antiquity, used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. He also showed one could use the method of exhaustion to calculate the value of π with as much precision as desired, and obtained the most accurate value of π then known, 310⁄71 < π < 310⁄70. He also studied the spiral bearing his name, obtained formulas for the volumes of surfaces of revolution (paraboloid, ellipsoid, hyperboloid), and an ingenious system for expressing very large numbers. While he is also known for his contributions to physics and several advanced mechanical devices, Archimedes himself placed far greater value on the products of his thought and general mathematical principles. He regarded as his greatest achievement his finding of the surface area and volume of a sphere, which he obtained by proving these are 2/3 the surface area and volume a cylinder circumscribing the sphere.
Apollonius of Perga (c. 262-190 BC) made significant advances to the study of conic sections, showing that one can obtain all three varieties of conic section by varying the angle of the plane that cuts a double-napped cone. He also coined the terminology in use today for conic sections, namely parabola ("place beside" or "comparison"), "ellipse" ("deficiency"), and "hyperbola" ("a throw beyond"). His work Conics is one of the best known and preserved mathematical works from antiquity, and in it he derives many theorems concerning conic sections that would prove invaluable to later mathematicians and astronomers studying planetary motion, such as Isaac Newton. While neither Apollonius nor any other Greek mathematicians made the leap to coordinate geometry, Apollonius' treatment of curves is in some ways similar to the modern treatment, and some of his work seems to anticipate the development of analytical geometry by Descartes some 1800 years later.
Around the same time, Eratosthenes of Cyrene of Cyrene (c. 276-194 BC) devised the Sieve of Eratosthenes for finding prime numbers. The 3rd century BC is generally regarded as the "Golden Age" of Greek mathematics, with advances in pure mathematics henceforth in relative decline. Nevertheless, in the centuries that followed significant advances were made in applied mathematics, most notably trigonometry, largely to address the needs of astronomers. Hipparchus of Nicaea (c. 190-120 BC) is considered the founder of trigonometry for compiling the first known trigonometric table, and to him is also due the systematic use of the 360 degree circle. Heron of Alexandria (c. 10–70 AD) is credited with Heron's formula for finding the area of a scalene triangle and with being the first to recognize the possibility of negative numbers possessing square roots. Menelaus of Alexandria (c. 100 AD) pioneered spherical trigonometry through Menelaus' theorem. The most complete and influential trigonometric work of antiquity is the Almagest of Ptolemy (c. AD 90-168), a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Ptolemy is also credited with Ptolemy's theorem for deriving trigonometric quantities, and the most accurate value of π outside of China until the medieval period, 3.1416.
Following a period of stagnation after Ptolemy, the period between 250 and 350 AD is sometimes referred to as the "Silver Age" of Greek mathematics. During this period, Diophantus made significant advances in algebra, particularly indeterminate analysis, which is also known as "Diophantine analysis". The study of Diophantine equations and Diophantine approximations is a significant area of research to this day. His main work was the Arithmetica, a collection of 150 algebraic problems dealing with exact solutions to determinate and indeterminate equations. The Arithmetica had a significant influence on later mathematicians, such as Pierre de Fermat, who arrived at his famous Last Theorem after trying to generalize a problem he had read in the Arithmetica (that of dividing a square into two squares). Diophantus also made significant advances in notation, the Arithmetica being the first instance of algebraic symbolism and syncopation. | mathematics |
https://ijobs.co.za/maths-and-science-tutor/ | 2020-05-27T13:11:03 | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347394074.44/warc/CC-MAIN-20200527110649-20200527140649-00391.warc.gz | 0.916607 | 409 | CC-MAIN-2020-24 | webtext-fineweb__CC-MAIN-2020-24__0__46005400 | en | Maths and Science Tutor wanted immediately: APPLY NOW
Master Maths Morningside is currently looking for mathematics and/or physical science tutor.
Master Maths Morningside is part of a well-established franchise concern, which has been providing extra tuition for over 40 years, to learners from junior level to adults. Our successful candidate must have exceptional customer service skills, over the phone and in person. Must be computer savvy.
The closing date for applications is 1 December 2019.
Please only submit your CV if the following applies to you:
You achieved 70% or more for maths or physical science in the final matric exam, or you have a relevant tertiary qualification.
You will be required to tutor up to grade 12 level for maths and physical science.
70% or more for maths and/or physical science in the final matric exam.
Speak fluent English.
South African passport or valid work visa.
Motivated by success in your job.
A people’s person and you think you might enjoy tutoring.
Able to interact successfully with young children.
Prior experience in a maths and/or science tutoring job is an advantage.
You’re available to work between 10:00 and 19:00 on weekdays, 09:00 to 13:00 on Saturdays or times as required by the role.
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You must have the ability to get on with young people. Be well-groomed with an attitude to get involved in every aspect of the business.
Requires an ability to explain mathematics or physical science pleasantly and with an enthusiastic personality.
Preparation and detailed recording of student progress for each individual student.
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Job Type: Contract
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Did you achieve at least 70% for maths or science in Gr12 (Required) | mathematics |
https://www.blackstonebookstore.com/book/9780316509046 | 2024-02-25T17:40:20 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474641.34/warc/CC-MAIN-20240225171204-20240225201204-00565.warc.gz | 0.944398 | 706 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__108999079 | en | Math with Bad Drawings: Illuminating the Ideas That Shape Our Reality (Paperback)
In Math with Bad Drawings, Ben Orlin reveals what math is all about. His tools are unorthodox: jokes, cartoons, strange-but-true stories, and beneath it all, the empathy of a veteran teacher who believes that math should belong to everyone. Orlin helps us to think like mathematicians by teaching a brand-new game of tic-tac-toe, profiling the ten people you meet in line for the lottery, and documenting the headaches that ensue when the Evil Empire attempts to build a spherical Death Star. Math with Bad Drawings will change the way you see the subject—and the world.
Ben Orlin is the author of Math with Bad Drawings (as well as the blog of the same name), Math Games with Bad Drawings and the companion game kit The Ultimate Game Collection, and Change Is the Only Constant. His writing on math and education has appeared in The Atlantic, the Chicago Tribune, the Los Angeles Times, Slate, Vox, and Popular Science. He has taught middle and high school mathematics and has spoken about math and education at colleges and universities across the United States. He lives with his family in St. Paul, Minnesota.
"Ben Orlin is terribly bad at drawing. Luckily he's also fantastically clever and charming. His talents have added up to the most glorious, warm, and witty illustrated guide to the irresistible appeal of mathematics."—Hannah Fry, mathematician, University College London and BBC presenter
"Brilliant, wide ranging, and irreverent, Math with Bad Drawings adds ha ha to aha. It'll make you smile - plus it might just make you smarter and wiser."—Steven Strogatz, Professor of Mathematics, Cornell University, author of The Joy of x
"MATH WITH BAD DRAWINGS is a gloriously goofy word-number-and-cartoon fest that drags math out of the classroom and into the sunlight where it belongs. Great for your friend who thinks they hate math - actually, great for everyone!"—Jordan Ellenberg, author of How Not To Be Wrong
"Ben Orlin has hit the seemingly unattainable sweet spot. He has written a book that is funny and serious, that is entertaining and informative, and that would interest a reader with or without a background in mathematics. Math with Bad Drawings would be a wonderful book for people who love math, used to love math, want to love math, want to know what math is good for, or just want to know what math really is."—Math Horizons
"Orlin's ability to masterfully convey interesting and complex mathematical ideas through the whimsy of drawings (that, contrary to the suggestion of the title, are actually not that bad) is unparalleled. This is a great work showing the beauty of mathematics as it relates to our world. This is a must read for anyone who ever thought math isn't fun, or doesn't apply to the world we live in!"—John Urschel, mathematician named to Forbes® "30 Under 30" list of outstanding young scientists and former NFL player
"Illuminating, inspiring, and hilarious, Math with Bad Drawings is everything you wanted to learn in class but never thought to ask. A joyful romp through mathematics and all its wisdom."—Bianca Bosker, author of the New York Times-bestselling Cork Dork | mathematics |
http://www.ce.ncsu.edu/faculty/kumar-mahinthakumar/ | 2016-06-27T07:40:35 | s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783395679.18/warc/CC-MAIN-20160624154955-00065-ip-10-164-35-72.ec2.internal.warc.gz | 0.918474 | 324 | CC-MAIN-2016-26 | webtext-fineweb__CC-MAIN-2016-26__0__125088197 | en | Dr Mahinthakumar is interested in large scale modeling of subsurface flow and transport, parallel and distributed computing, optimization and inverse problems, water distribution system analysis
Dr. Mahinthakumar's (referred to as Dr. Kumar by his students) long term goal is to develop efficient algorithms and tools to solve large scale civil and environmental engineering problems.
Dr. Kumar is currently focused on 1) real time optimization and inverse modeling for water distribution systems analysis, 2) large scale modeling and characterization of groundwater flow and transport systems, 3) parallel and distributed computing algorithms and tools for environmental applications.
In CCEE, Dr. Kumar collaborates with Dr. Arumugam, Dr. Brill, Dr. DeCarolis and Dr. Ranjithan.
At the graduate level, Dr. Kumar teaches Introduction to Numerical Methods for Civil Engineers (CE 536), High Performance Computing for Civil Engineers (CE 791A), and Inverse Modeling for Civil Engineers (CE 791B). In Numerical Methods, he teaches application of common numerical methods to civil engineering problem solving. The high performance computing course is a project based course focused on parallel and distributed computing algorithms for large scale civil engineering applications. The inverse modeling course focuses on heuristic and gradient based search techniques as well as Markov Chain Monte Carlo methods for the solution of civil engineering parameter estimation and system identification problems. The graduate students who work with Dr. Kumar enjoy computer programming and are interested in developing innovative methods and tools for large scale civil engineering problem solving.
Website design and development by ITECS | mathematics |
http://homeworkguard.com/math-assignment-help/ | 2014-04-21T15:08:43 | s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00139-ip-10-147-4-33.ec2.internal.warc.gz | 0.943359 | 657 | CC-MAIN-2014-15 | webtext-fineweb__CC-MAIN-2014-15__0__131092849 | en | Professional Math Homework Assistance
Completing mathematics homework can be both time-consuming and frustrating. This is especially true if you are required to complete a mathematics course but just don’t understand the subject at all. It seems that no matter how hard you study, how often you visit your teacher or professor outside of class, or seek out math assistance, you still just don’t get it. If you’re not good at math, there’s nothing wrong with you and you’re not stupid. Some people just have different talents. If you’ve been searching “do my math for me,” “help me with math,” or “solve my math,” you’ve landed on the right place. Whether you need help with algebra, calculus, discrete algebra, or any other kind of discrete math, HomeworkGuard.com is here to be your homework helper. There’s no need to stress out any more about math problems you don’t understand! Just use our math writing service!
Even if you’re great at math, doing mathematics homework can still be time-consuming and take from your study or leisure time. This is especially true if you’re a physics, chemistry or per-med student. In addition to all your physics, chemistry, and medical problems that you must solve, there are other required math classes. This can leave you feeling cramped for time. You could switch majors or drop out of school completely, but why do that when there is math help online? At HomeworkGuard.com, we employ only people who have completed graduate programs in mathematics to help our student clients with their math assignments. They ensure that you will turn your assignments in on-time and that they will get you the best grades possible.
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If you’re tired of all the math assignments, leave it to the math masters at HomeworkGuard today! | mathematics |
https://raft.fandom.com/wiki/Golden_Toy_Robot | 2022-08-08T03:26:06 | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570765.6/warc/CC-MAIN-20220808031623-20220808061623-00326.warc.gz | 0.929152 | 351 | CC-MAIN-2022-33 | webtext-fineweb__CC-MAIN-2022-33__0__159337900 | en | |Golden Toy Robot|
Golden Toy Robot is a decoration object that can be found through Treasure Hunting. It is found in the Safes that can be dug up. The Golden Toy Robot is the rare variant of the regular Toy Robot and is much rarer. When looting a Safe, there's a 2.3% chance of it being any robot in the first place. After becoming a robot, the game decides whether it be a regular Toy Robot (94.8%) or a Golden Toy Robot (5.2%).
Following paragraph describes the calculation of the chance of getting a Golden Toy Robot. To get the Golden Toy Robot, the player must first find a Safe. Every treasure that is dug up has a 20% chance of being a Safe. This translates to 1/5. Getting a robot in the first place is 2.3%, which is roughly 1/50, and it being golden is another 5.2%, which is roughly 1/20. Getting this specific combination of rolls is therefore a 1/5000 or 0.02%, making the Golden Toy Robot the rarest item in the game. Note that this equation is rolled for all items within the container, meaning that if there are five items in the Safe, the player rolls for the 1/1000 chance five times. This means that on average, when looting a Safe, the player has roughly 0.5% chance of getting a single Golden Toy Robot.
- Used to decorate the raft.
|Update 12||Golden Toy Robot added to the game.| | mathematics |
http://ec2-34-199-89-106.compute-1.amazonaws.com/cube-roots/ | 2017-12-14T10:05:15 | s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948543611.44/warc/CC-MAIN-20171214093947-20171214113947-00763.warc.gz | 0.866397 | 178 | CC-MAIN-2017-51 | webtext-fineweb__CC-MAIN-2017-51__0__133537510 | en | This riveted me; I love mental maths. To cube root a number (assuming it’s a perfect cube), here are the steps, using 250,047 as our protagonist cube:
- Ignoring the last 3 digits of the cube, find the first cube which is less than the remaining digits. 250 (ignoring 047) is the number in question, and 216 (63) is the first cube less than 250 — giving us 6.
- Find the number from 1-10 that, when cubed, ends in the last digit of your cube. 250,047 ends in 7, which corresponds to the last digit of 27 (33). This number is the last digit of the cube root.
- Voila! Those are the 2 digits of the cube root — 6 and 3 — giving us 63 as the cube root of 250,047. | mathematics |
https://mapleong.me/posts/2021-04-28-subtraction-with-addition/ | 2023-02-05T20:20:24 | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500288.69/warc/CC-MAIN-20230205193202-20230205223202-00299.warc.gz | 0.877432 | 843 | CC-MAIN-2023-06 | webtext-fineweb__CC-MAIN-2023-06__0__168971106 | en | Subtraction with Addition: Two's Complement
Subtracting numbers on paper is easy, but how does a computer do it? Most computer operations can be reduced to additions of binary numbers… even when the operation is subtraction. To understand how this works, let’s first think about how an odometer works.
Let’s say you’ve driven 7631 miles and really want to celebrate your 9999th mile and see the odometer return to 0000. You would have to drive 2368 miles to reach 9999 miles. When you’ve hit 9999 miles, the odometer returns to 0000 and the cycle continues.
And so the total amount of miles you had to drive was 2368 to hit 9999 and then 1 mile to hit 10000.
The formula to calculate the amount of miles you have to drive to hit 9999 miles is:
7631 + x = 9999 x = 9999 - 7631 x = 2368 2368 + 1 = 2369 miles driven in total for odometer reset.
The mind-blowing part of this is that 2369 is the negative equivalent of 7631. How?
Let’s pick another random 4-digit number and subtract 7631 from it:
9473 - 7631 = 1842
That's also equivalent to adding negative 7631:
9473 + (-7631) = 1842
Let’s substitute -7631 for its positive equivalent:
9473 + 2369 = 11842
11842 looks familiar doesn’t it? Since we’re operating in a 4-digit system, we drop the first digit and we have 1842, the correct result of the subtraction.
We can also use this negative representation of the number in other equations:
2354 - 7631 = -5277
So -5277 is the correct answer.
Let’s convert that answer back to the positive equivalent:
5277 - 1 = 5276 9999 - 5276 = 4723
Now… let’s see what happens when we only use addition with the positive equivalent number:
2354 + (-7631) 2354 + 2369 = 4723
🎉 Voila! Obviously, converting 4723 to its negative equivalent will result in -5277!
However! Instead of reversing the calculation like we just did, we can also covert a negative to a positive using the exact same procedure without reversing it:
9999 - 5277 = 4722 4722 - 1 = 4723
🎉 And the result is back to 4723.
This method is called the two's complement and is exactly how computers implement signed binary numbers! We just looked at base-10 numbers, but computers work in binary, base-2.
The same idea applies in binary. Take the binary number 0110.
The negative number of 0110 can be calculated in the same way, except the odometer resets at 1111 and not 9999.
1111 - 0110 = 1001 1001 + 0001 = 1010
With that, the negative number for 0110 is 1010. We can then do similar calculations, let’s say 7 minus 6.
7 - 6 = 1 (in decimal) 0111 - 0110 (in binary) 0111 + (- 0110) 0111 + 1010 = 10001, drop the first digit, resulting in 1!
Typically the computer uses 16-bit inputs, following this example means instead of 4-digit, computers use 16-digit binary numbers.
The system can code a total of 2n signed numbers, where 2n-1 - 1 and -2n-1 represent the number of positive values and negative values respectively. This means in a 4-bit system, the total number of numbers (haha!) represented is 24 = 16, where we can go up to positive 7 and as low as -8.
The two's complement is implemented in the hardware of the Arithmetic Logical Unit chip that makes up the CPU. | mathematics |
https://www.dondepiso.com/blogs/blog/ada-lovelace-the-pioneer-of-computer-programming | 2024-04-21T09:15:14 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817729.87/warc/CC-MAIN-20240421071342-20240421101342-00702.warc.gz | 0.966775 | 1,003 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__74958411 | en | The Early Life of Ada Lovelace
Ada Lovelace, born Augusta Ada Byron, is widely regarded as the world's first computer programmer. She was born on December 10, 1815, in London, England. Ada had a fascinating upbringing, being the daughter of Lord Byron, the famous poet, and Anne Isabella Milbanke, a mathematician.
Despite her parents' separation when she was just a few weeks old, Ada's mother ensured that she received a well-rounded education. At an early age, Ada developed a keen interest in mathematics and science, showing exceptional aptitude in these subjects.
Ada's passion for numbers and calculations grew as she delved deeper into her studies. She was tutored by some of the best mathematicians and scientists of her time, including Augustus De Morgan and Mary Somerville. These mentors recognized Ada's brilliance and nurtured her love for mathematics and logical reasoning.
Ada's Introduction to Charles Babbage
Ada Lovelace's interest in mathematics and science was further nurtured by her mother, who introduced her to prominent mathematicians and scientists of the time. At the age of 17, Ada met Charles Babbage, a renowned mathematician and inventor. Babbage's invention, the Analytical Engine, is considered the precursor to modern computers. This encounter would prove to be a turning point in Ada's life.
Charles Babbage recognized Ada's exceptional mathematical abilities and intellect. He became her mentor and close collaborator, fostering her interest in the world of computing and laying the foundation for her groundbreaking work in computer programming.
The Collaboration Between Ada and Charles Babbage
Ada Lovelace's collaboration with Charles Babbage was instrumental in shaping her legacy as the pioneer of computer programming. She translated and annotated an article written by Italian engineer Luigi Menabrea about Babbage's Analytical Engine. Ada's annotations, which were three times longer than the original article, included a method for calculating Bernoulli numbers using the Analytical Engine.
What set Ada's annotations apart was her visionary insight. She recognized that the Analytical Engine had the potential to do more than just calculations. She envisioned it as a general-purpose machine that could be programmed to perform various tasks beyond number crunching. Ada's notes included algorithms for generating complex graphics and music, making her the first to articulate the concept of software.
Ada's work on the Analytical Engine demonstrated her deep understanding of its potential and laid the foundation for modern computer programming. Her ideas were far ahead of her time, anticipating the development of computer programs and the possibilities they could unlock.
Lovelace's Vision for the Analytical Engine
Ada Lovelace's vision for the Analytical Engine went beyond mere calculations. She saw its potential for creating not only numerical results but also generating complex graphics and music. Her foresight in recognizing the capabilities of the Analytical Engine as a general-purpose computing machine laid the foundation for modern computer programming.
Ada's notes on the Analytical Engine were published in 1843, in an English science journal. However, due to the prevailing gender biases of the time, her work received little attention and was not widely understood or acknowledged.
It was not until the late 20th century that Ada Lovelace's contributions to computer programming were fully recognized. Computer scientists and historians revisited her work and acknowledged her as the world's first computer programmer. They marveled at her ability to grasp the potential of computing machines and her visionary ideas that remain relevant even today.
The Legacy of Ada Lovelace
Ada Lovelace's contributions to the field of computer programming were ahead of her time. Unfortunately, her work went largely unnoticed during her lifetime. It was only in the mid-20th century that her notes on Babbage's Analytical Engine were rediscovered and recognized for their significance.
Today, Ada Lovelace is celebrated as a pioneer and visionary in the world of computer science. Her insights and ideas continue to inspire generations of programmers and technologists. The second Tuesday of October is observed as Ada Lovelace Day in her honor, to recognize the achievements of women in science, technology, engineering, and mathematics (STEM).
Ada Lovelace's remarkable contributions to computer programming laid the groundwork for the digital revolution that followed. Her visionary ideas and analytical prowess continue to shape the world of technology today. Ada Lovelace will forever be remembered as the pioneer who paved the way for future generations of programmers.
Ada Lovelace's remarkable journey from being the daughter of a famous poet to becoming the pioneer of computer programming is a testament to her brilliance, determination, and forward-thinking mindset. She overcame societal barriers and made invaluable contributions that continue to shape the world we live in. Ada Lovelace's legacy serves as an inspiration for aspiring programmers, reminding us of the power of ideas and the impact one person can make on the world. | mathematics |
https://www.karincaproduksiyon.com/2019/10/11/ideas-formulas-and-shortcuts-for-what-is-simplest-form-in-math/ | 2023-03-25T13:07:48 | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945333.53/warc/CC-MAIN-20230325130029-20230325160029-00328.warc.gz | 0.936607 | 1,245 | CC-MAIN-2023-14 | webtext-fineweb__CC-MAIN-2023-14__0__247105353 | en | Ideas, Formulas and Shortcuts for What Is Simplest Form in Math
The Downside Risk of What Is Simplest Form in Math
Text is among the most naturally compact types of information at about one byte necessary to store each letter. After the button is first pressed, the cursor is situated in the top box ready that you enter the numerator. Consult with the link for details about how to ascertain the best common divisor.
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At the previous time of examination you won’t have the ability to refer the entire book. Ultimately, Section 6 provides a overall overview of the key findings of this study. OK, you’re done with the quiz. | mathematics |
https://www.b2aprep.com/sharon-noh-gateway | 2023-12-07T04:38:17 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100632.0/warc/CC-MAIN-20231207022257-20231207052257-00039.warc.gz | 0.952554 | 329 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__216678613 | en | College Admissions Counselor
Math/Science & Test Prep Instructor
University of California, Los Angeles (Psychobiology, B.S.)
University of Texas at Austin (Cognitive Neuroscience, Ph.D. in progress)
Sharon has had experience helping students from California and Texas apply to both undergraduate and graduate programs across the U.S. Several of her students have been admitted to top programs all around the country.
"I believe that everyone has a unique story to share, and it is up to both the student and counselor to make sure to convey each student's story in the most compelling way. I like to invest heavily in getting to know each of my students individually so that we can work together in finding ways to best communicate the student's strengths within the limited confines of each college application."
While Sharon was in Los Angeles, she taught SAT I and II math courses, AP and SAT Biology courses, and general courses in Biology, Geometry, Algebra I, and Algebra II. Additionally, she worked for several years as a college level tutor (general topics areas: Statistics, Biology, Physics, and Math) and a quantitative instructor (for DAT and GRE math courses) after graduating from UCLA.
"I believe the goal of education is to enhance long-term learning and performance. Often times, strategies that seem more difficult for learning in the short-term enhance long-term retention. I incorporate these optimal learning strategies in my teaching as much as possible, while also trying to keep the learning process relatively simple and fun."
Sharon really enjoys playing board games and watching the discovery channel. | mathematics |
https://pokerdownload.info/the-mathematics-behind-casino-games-a-deep-dive-with-superwin/ | 2023-10-02T23:49:37 | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511023.76/warc/CC-MAIN-20231002232712-20231003022712-00555.warc.gz | 0.906443 | 840 | CC-MAIN-2023-40 | webtext-fineweb__CC-MAIN-2023-40__0__177682466 | en | To the casual observer, casinos might seem like sanctuaries of luck and chance. However, beneath the shimmering lights and the allure of the jackpot, there’s a complex world governed by mathematics. Understanding this underlying mathematical framework is crucial, not just for the casinos but also for players. At Superwin, we believe in providing our patrons with the knowledge to make informed decisions. Let’s unravel the fascinating mathematics behind casino games.
- Probability and Odds
At the heart of every casino game lies the concept of probability. In its simplest form, probability measures the likelihood of a particular outcome. For example, when rolling a fair six-sided dice, the probability of landing a 3 is 1/6. Casinos utilise these probabilities to determine the odds they offer. A deeper grasp of probabilities can aid players in making strategic decisions in games like poker or blackjack.
- House Edge
The house edge is a term most gamblers have come across. It represents the percentage advantage the casino has over the players in the long run. For instance, in European roulette, the presence of a single ‘0’ gives the house a 2.7% edge. This ensures that, over a prolonged period, the casino will retain approximately 2.7% of all bets made, ensuring its profitability.
- Return to Player (RTP)
Often used in the context of slot machines on platforms like Superwin online, RTP denotes the percentage of total bets that a machine will pay back to players over time. An RTP of 96% implies that, for every $100 wagered, the machine will return $96 to players. The remaining 4% represents the house edge in this scenario.
- Variance and Volatility
While RTP gives a long-term view, variance or volatility sheds light on the short-term fluctuations players might experience. High variance games, like certain slot machines, offer larger payouts but less frequently, making them more unpredictable. In contrast, low variance games provide smaller, more frequent payouts.
- Combinatorial Analysis
Particularly pertinent to card games, combinatorial analysis examines the number of ways specific events can occur. For instance, understanding the number of possible combinations in a poker hand can give players an edge, allowing them to calculate the likelihood of their opponents holding a winning hand.
- The Law of Large Numbers
This mathematical theorem states that the more times an experiment (like a dice roll or card draw) is conducted, the closer the average result will come to the expected value. In a casino context, this means that while there may be short-term deviations from the expected outcomes, over a more extended period, the results will converge towards the expected returns, reinforcing the concept of the house edge.
- Dependency and Strategy
Certain games, like blackjack, introduce the idea of events depending on previous outcomes. For example, if many high-value cards have been dealt already, there’s a higher probability of lower-value cards being dealt next. Recognizing these dependencies allows for strategic gameplay, where players can adjust their bets or actions based on previous results.
- Betting Systems and Fallacies
Many players swear by specific betting systems, like the Martingale or Paroli. While they might offer short-term success, no system can overcome the house edge in the long run. Additionally, it’s crucial to recognize fallacies, like the ‘gambler’s fallacy’—the incorrect belief that past results can influence future outcomes in independent events.
The world of casinos, whether physical or on platforms like Superwin Sportsbook, is deeply intertwined with mathematics. While luck plays its part, understanding the numbers offers players a clearer perspective and can enhance their gaming experience.
At Superwin, we’re not just about offering exciting gaming opportunities; we’re also committed to enlightening our patrons. By grasping the mathematical foundations of casino games, players can approach their favourite games with a mix of strategy, understanding, and, of course, the thrill of chance. | mathematics |
https://handhistorypoker.com/blog/poker-en/poker-math/ | 2024-04-14T13:51:07 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816879.72/warc/CC-MAIN-20240414130604-20240414160604-00142.warc.gz | 0.940515 | 2,562 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__187299554 | en | - What is the role of math in poker?
- What Outs are in Poker and how do we count those?
- Using probabilities in poker math
- Pot odds in poker math
- Two ways of applying poker math
- Calculating equity outside poker tables
- Estimation of required equity at the table
- Useful literature on poker math
- Poker Math FAQ
- How is mathematics useful for a poker player?
- How to count outs correctly?
- How to use math in poker?
What are we talking about here? The mathematics of poker seems difficult to many new players. However, in fact, it is quite simple to master and thereby greatly increase your chances of winning.
What should we focus on? Of course, you need to start with the basics and understand what poker mathematics, outs and probabilities are in the first place and how to calculate them. It is also very important to be able to apply this knowledge in practice.
What is the role of math in poker?
Strategy in this game is based on probabilities of certain events. Understanding the psychological characteristics and habits of your opponents is also important. This information allows us to make our mathematical predictions more accurate. Poker mathematics covers a wide range of concepts, including outs, probabilities, pot odds, equity and fold equity.
It is necessary to analyze the chances of winning in the current hand. Math serves as a guide for experienced players, helping them determine optimal moves. For example, it tells you whether it is worth making a call in a given situation or whether it is better to look for other, more profitable actions.
What Outs are in Poker and how do we count those?
Counting outs is the most important part of poker math. Outs are cards in the deck that can improve your current hand, turning it into a winning one. Let’s take a look at an example. Let’s say you have AK of diamonds on a board with a diamond flush draw. How many outs do you have in this situation? What cards can improve our combination?
There are three aces and three kings that improve us to a top pair, which could be enough to win. To achieve this, you need to draw a card that matches one of the six remaining in the deck.
In addition, any diamond card gives us flush, which is the best possible hand here (nuts). There are 13 diamond cards in the deck. Two of them are a part of our hand and two more are on the board. Therefore, there are still 9 diamond cards left that can improve our hand.
You have 15 outs total. However, when counting, it is important to take into account and exclude from the list the so-called tainted outs – cards that improve our hand, but at the same time strengthen the opponent’s hand.
Using probabilities in poker math
Understanding outs allows you to move on to using probabilities. Once a player understands how many cards in the deck can improve his hand, he can estimate how often this should happen.
The following formula is used for calculations:
Probability = number of outs / number of hole cards (in the deck and in the opponents’ hands).
A standard poker deck contains 52 cards. Two of them are in our hand, and three more are on the table after the flop. This leaves 47 unknown cards. Let’s say we need any of two eights or four kings left in the deck. The probability of one of these hitting the turn is 6/47 or 12.76%.
If none of the eights or kings appear on the turn, the player still has one more chance to catch them on the river. However, it is important to remember that at this point there will be one less hole card in the deck: 6/46, or 13.04%.
The probability of getting the required card in one street is approximately 2%, and in two – about 4%.
Pot odds in poker math
What happens when mathematicians play poker? They start calculating the pot odds. The probability of getting a desired combination is determined by comparing unsuccessful outcomes, where the player does not get an out he looks for, with successful ones.
This chance can be represented in a form of a ratio. For example, 3:1 means that on average out of four attempts to get the desired card, three will be unsuccessful and one will be successful. Probabilities can also be expressed as percentages. For example, a ratio of 4:1 is 20%. When converting to percentages you just add one to a number of unsuccessful outcomes. Thus, 5.5 to 1 is 15.4% (1/6.5).
Pot odds are the ratio of the amount a player puts into the pot to the total size of the pot. In other words, this is a ratio of how much a player invests to how much he can win if he gets a desired outcome. For example, pot odds of 4:1 means that if we invest $1, we will get $4.
Generally, pot odds are taken into account when determining whether it is profitable to call or not. If the pot odds are greater than the probability of getting the desired hand, then calling is profitable.
Two ways of applying poker math
Calculating equity outside poker tables
When a player is at the table, there is simply no time for complex calculations. It is better to start learning by analyzing your hand histories after the game. The more time you spend practicing away from tables, the more confident you will be at the tables.
A decision that closes the action is one when there is no other options available after. For example, this can happen on the river when the villain goes all-in. You have only two possible options left: call or fold. One way or another, the hand is over after you pick one of the two.
Let’s take a look at another example, this time preflop. Let’s assume one of the players decides to go all-in. You have a choice: give up and fold, or call and answer his bet.
It is important to note that all calculations discussed below assume that there will be no action after your decision and the pot size will remain unchanged. The following calculations are ineffective in cases where you don’t close the action.
Let’s say we are on the river, pot is already 45 bb. Villain decides to bet his remaining 36bb and goes all-in. Hero has two possible options:
- Call 36bb bet;
- Fold his hand.
The question is how much equity do we need to have against villain’s perceived range for calling to be a smart decision?
To proceed with the calculation we only need two numbers. The formula takes into account the following parameters:
- AC (amount to call) – the amount of money we have to put into pot to call villain’s all-in.
- TP (total pot after bet) – the total pot after villain’s bet. Includes all money bet on previous streets, as well as opponent’s bet on the river.
- RE (Required Equity) – the parameter we are trying to calculate. This is the minimum amount of equity against your opponent’s range for the call to be at least break even. If in reality the equity of our hand is greater than the calculated value (RE), then calling becomes a profitable decision in the long run (+EV).
RE = AC / (AC + TP)
Poker mathematics follows all the standard rules of arithmetic. Therefore, we first sum the values in parentheses and then do the division.
AC = 36 (opponent bet on the river)
TP = 45 + 36 = 81 (pot before river action + opponent’s bet)
RE = 36 / (36 + 81) = 30.8%
When calling, a player must win at least 30.8% of the time at the showdown for the call to be justified.
Mathematical calculation is the first step in analyzing such spots. When we have specific numbers, we can evaluate the equity of our cards relative to our opponent’s range and make an optimal decision.
A very common mistake is when people calculate total pot as just a sum of river pot and opponent’s bet. However, you have to include our potential call as well, so it is his bet plus the size of the pot on the river plus the amount we should put in to make a call.
Estimation of required equity at the table
You are unlikely to be able to make complex calculations, even if you only play couple of tables. Therefore, we need a simpler method even if it is not 100% correct in terms of calculations. It does exist and is known as “RE scale”.
A player has to memorize four rules, which are:
- If before the bet there’s no money in the pot, it would take 50% equity to call (e.g. preflop shove, although even then there are 1.5bb in the pot from the blinds).
- Against a pot size bet, we need 33% equity.
- Half pot bet – 25% equity.
- Quarter of a pot bet – 17% equity.
Thus, we have four key points from which we can adjust. Many poker players use bets of the same size, which will simplify the task. However, even in the case of non-standard and random bets, you can approximate the equity you need from those key points.
Let’s look at a specific example. Let’s say your opponent bets 7bb into a 30bb pot. You can quickly estimate on the go that this is slightly less than quarter of a pot (4 * 7 = 28). Therefore, you need slightly less than 17% equity to call.
If we make precise calculations, we get the following:
- RE = AC / (AC + TP);
- RE = 7/ (37 + 7). Remember that this is not (30 + 7), since TP represents the size of the pot after your opponent’s bet;
- RE = 15.9%.
It turns out that our quick estimation was pretty close to the actual number.
Useful literature on poker math
One of the best books for beginner poker players is “Poker Math Made Easy” by Roy Rounder. Its only 34 pages long. We would also recommend lying your sight on “The Mathematics of Poker” by David Sklansky.
In addition, it would also be beneficial for you to reak the following books: Alan N. Schoonmaker “Your Worst Poker Enemy”, Jared Tendler “The Mental Game of Poker”, Leszek Badurowicz “Mental Edge”, Roy Rounder “Poker Math Made Easy”, Matthew Janda “Applications of No-Limit Hold’em”, James Swinney, Adam Jones “Optimizing Ace King”, MMAsherdog “The Preflop Bible”, Peter Clarke “The Grinder’s Manual”.
This library would be enough to understand the basic mathematics in poker and increase your chances of success.
Poker Math FAQ
How is mathematics useful for a poker player?
Mathematics in poker is used to evaluate the profitability of specific actions. Science allows us to determine the probabilities of winning in the current hand, taking into account the starting hand and the board. It also helps you make the right decisions, taking into account the bet size and the pot size.
How to count outs correctly?
You should count outs only after the flop and turn are dealt. Many people make the mistake of performing calculations with only their hand and no board.
Knowing outs is a critical aspect of the game. The calculation helps determine the ratio and evaluate the pot odds.
How to use math in poker?
Mathematics is a powerful tool that should be used at the right time. Combine your math knowledge with other strategies and techniques to achieve greater success and increase your profits.
Thus, poker mathematics is a set of techniques based on mathematical principles. They help you make decisions that are more accurate. By understanding and putting it into practice, you can increase your chances of winning. | mathematics |
http://emmayu.com/Did-this-weight-loss-program-work/ | 2020-07-10T10:26:54 | s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655906934.51/warc/CC-MAIN-20200710082212-20200710112212-00330.warc.gz | 0.938086 | 1,714 | CC-MAIN-2020-29 | webtext-fineweb__CC-MAIN-2020-29__0__152166776 | en | Evaluating the effectiveness of a clinical weight loss program
In this study, I analyze a dataset of a 12-month clinical weight loss program to find out:
what factors affect the 12 month weight loss results;
whether an intervention was effective in increasing weight loss.
The dataset contains 234 participants of the weight loss study, and for each participant, we have information on his/her age, race, type of treatment, and the weight change 12 month after the treatment. All relevant biological information has been condensed into one variable called biomarker. The data has been processed to ensure privacies of the participants.
This project was a final project for the statistical modeling class (graduate-level) at UT Austin, Dec 2014.
I plotted every parameter against each other to have a quick look at the relationships between different parameters. The age, race, biomarker variables are self-explanatory, and the other two variables are
- wtch - 12 month weight loss in kg
- treatment - 1= control, 2 or 3 = intervention
We can see the biomarker seems to linearly correlate with the age of the subject. The total numbers of samples are very small in race 2 and 4, and the race 3 seems to have a younger population than race 1.
A quick look
First, let’s contruct a full model with all data points and all avaliable variables as covariants.
This model does not fit the data very well. The R-squared value is 0.099, which means only about 10 percent of the variations in the data is explained by the model. However, the model is still significant. With a p value of 0.001, we can safely reject the null hypothesis of no relationship all all between the weightloss and all the variables. Race 3 is the most significant covariant with a p value of 5.64e-5, and age is the second most important covariance with a p value of 0.113.
Considering the median of the weight loss is -9.89, the residuals are very large for this model, but we don’t see any strucutre in the residual vs. fittet plot. 10 points show very large leverage. This could be a problem because these 10 points can have too big influence on our accessing the model fit. We may want to exclude those data point, lower their weights, or use a different cost function.
Adding Interaction Terms
To see if including interaction terms between different variables will imporve the model fit, I construct a series of expanded models:
|1-1||Full model with race and treatment as factor variables|
|1-2||Same as 1-1 but without the treatment as a covariant|
|2-1||Add dummy variables for race to include interaction terms between age and race|
|2-2||Same as 2-1 but without the treatment as a covariant|
|3-1||Include dummy variables for both race and treatment|
The BICs and R-squared of the full model and models with interaction terms are shown below. Models with interaction terms have larger BICs and smaller R-squared compared to the full model, which means they fit the data worse than the full model. So I decided not to include the interaction terms.
As seen in exploritory analysis, biomarker has the largest P value, and it seems to correlate with age. We did a simple linear regression model for biomarker ~ age, and found R squared to be 0.4651. This means age predicts the biomarker reasonably well, but the two are not exactly the same. However, since those two variables are not independent of each other, including biomarker will greatly inflate the variance. I decided to examine a few reduced models.
|4-1||Reduced model without biomarker as a covariant|
|4-2||Same as 4-1 but without the treatment as a covariant|
|4-1c||Same as 4-1 but without the two outliers|
|5-1||Reduced model with only age and treatement as covariants|
|5-2||Reduced model with only age as the covariant|
We can see models without race doe not fit the data well (5-1 and 5-2, with larger BIC and much smaller R- squared compared to other models). On the other hand, excluding the two outliers can significantly improve our model fit (with BIC 27 smaller than the model including the outliers). So we pick model 4-1 c, the reduced model without biomarker as a covariant and without the two outliers for our analysis.
Judging from the expectaion and standard error, we are 68 percent confident that the treatment increases weightloss (a smaller wtch value). Treatment 3 has slightly larger effect than Treatment 2, with a expect (1.722 - 1.348 = 0.374) increase in weightloss.
We added dummy variables for the factor variable race and treatment, and constructed a series of models in JAGS. The general form of the model is: wtch ~ N(mu, tau) mu ~ BX
Since we don’t have any prior knowlege associate with the weightloss, we simply choose diffuse normal priors for all the betas in all of our models. We use a diffuse gamma prior for all the taus.
The covariances and DIC for each model is shown in the table below. We are using penalized deviance from dic.samples as our measurement.
|1||age + bio + race + treat||1616|
|2||age + race + treat||1614|
|3||age + race3 only + treat||1613|
|4||age + treat||1635|
|5||age + race||1619|
In model 1, the 95% interval of all the covariance includes zero, therefore we can’t constrain the importance of parameters with great confidence. In model 2, we are 95% confident that the age is a significant factor. Since we have very few samples in race 2 and 4, we decided to try only including race 3 as a covariance. As expected, excluding biomarker imporves the variance in the model parameters. In model 3, both age and race 3 are proved to be significant at 95% confident level. We tried models with no treatment, with no race as covariants, and the model only with age as the covariants. All of them have larger DIC then model 3, and they do not provide any further insight of the data. Therefore we chose model 3 for our inference.
We should note that in the frequentist approach, we included all the races in the model. However, in the Bayesian approach, we only include one dummy variable for race 3. Since we eliminated two variables that are closely dependent on existing variables (race 2, 3, and 4 are not independent of each other), the model significance is improved.
After a few experiments, we decided to thin the data by 100 to improve the mixing. We run 2 chains with 100000 sample each, so we have 2000 samples after thinning. The thinning does not change the modeled coefficients very much. The output parameters of model 3 are (in the order of ‘Inter’, ‘race3’, ‘age’, ‘treat2’, ‘treat3’):
Judging from the coefficients, we are 68% confident that treatment 3 can increase weightloss (with am expected value of -1.69). Treatment 2 is likely to increase the weightloss, but we can’t say it with 68% confidence. On the other hand, race 3 have significantly larger weighloss compared to other races, and the weighloss decreases as age increases. 10 years of increase in age leads to a decrease of 2.2 in weightloss.
Samples for betas and the PDFs of betas are shown below. We can see the mixing is generally well, and we have tighter constrain on treat 2, and treat 3 compared to other variables. | mathematics |
http://drawntomath.tumblr.com/ | 2013-05-25T08:10:57 | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368705749262/warc/CC-MAIN-20130516120229-00002-ip-10-60-113-184.ec2.internal.warc.gz | 0.963997 | 167 | CC-MAIN-2013-20 | webtext-fineweb__CC-MAIN-2013-20__0__42263596 | en | Hello young pupils. I am Prof. Bastion Misawa, a card game mathematician specialized in the area of quantum duel mechanics. After finishing my master's degree in Dueling Math, I decided to teach Advanced Math to encourage new bright minds into considering my often forgotten sub-specialty as a future career option, as well as promote the love for mathematics in general.
I am always available if my students or colleagues have any problem they believe I could help out in, specially if its solution could lead to a new mathematical breakthrough! Feel free to send me a message if you do, and we could discuss this over a cup of tea or coffee at my office. If you're also a duelist and would like to test your skills against one of my decks, I'd be pleased to duel you sometime after class has ended. | mathematics |
https://www.mystrollers.com/bigjigs-toys-number-tower.html | 2021-09-19T16:42:29 | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056892.13/warc/CC-MAIN-20210919160038-20210919190038-00293.warc.gz | 0.940206 | 96 | CC-MAIN-2021-39 | webtext-fineweb__CC-MAIN-2021-39__0__16618704 | en | This toy provides a thrilling way to learn about numbers whilst building a brightly coloured wooden tower. Children can practise both number recognition and counting as they fit each wooden piece next to its individually-shaped numerical neighbour. Made from high quality, responsibly sourced materials. Conforms to current European safety standards. Age 1+ years. Height: 285mm, Width: 90mm, Depth: 90mm. Consists of 11 play pieces.
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https://www.olgageyyer.art/group/olenkaarts-group/discussion/5c651b3f-192c-4c12-aa25-8a873a156b0f | 2023-11-30T10:13:56 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100184.3/warc/CC-MAIN-20231130094531-20231130124531-00716.warc.gz | 0.946206 | 2,347 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__136725461 | en | Vector And Tensor Analysis By Dr Nawazish Ali Pdf EXCLUSIVE Download 12
Vector and Tensor Analysis by Dr Nawazish Ali PDF Download 12
If you are looking for a comprehensive and accessible introduction to vector and tensor analysis, you might want to check out the PDF book by Dr Nawazish Ali, a professor and former chairman of the Department of Mathematics at the University of Engineering and Technology, Lahore. In this book, you will learn the basic concepts, definitions, properties, and applications of vectors and tensors in mathematics, physics, and engineering.
vector and tensor analysis by dr nawazish ali pdf download 12
What is Vector and Tensor Analysis?
Vector and tensor analysis is a branch of mathematics that deals with quantities that have both magnitude and direction, such as force, velocity, acceleration, etc. Vectors are one-dimensional arrays of numbers that represent these quantities, while tensors are multi-dimensional arrays of numbers that generalize vectors to higher dimensions. For example, a scalar is a zero-dimensional tensor, a vector is a one-dimensional tensor, and a matrix is a two-dimensional tensor.
Vector and tensor analysis is useful for studying various phenomena in science and engineering, such as mechanics, electromagnetism, fluid dynamics, relativity, etc. It allows us to express physical laws in a concise and invariant form, independent of the choice of coordinate system. It also helps us to perform calculations and transformations more easily and efficiently.
What are the Contents of the Book?
The book by Dr Nawazish Ali covers the following topics:
Chapter 1: Algebra of Vectors - This chapter introduces the geometric and analytic representation of vectors, the dot product, the cross product, the scalar triple product, the vector triple product, and the linear dependence and independence of vectors.
Chapter 2: Geometry of Vectors - This chapter applies vector algebra to geometry problems, such as finding the equation of a line or a plane, the distance between points, lines, and planes, and the angle between lines and planes.
Chapter 3: Differentiation of Vectors - This chapter defines the derivative of a vector function, the gradient of a scalar function, the divergence of a vector function, and the curl of a vector function. It also discusses some applications of these operators in physics.
Chapter 4: Integration of Vectors - This chapter introduces the concepts of line integral, surface integral, and volume integral of vector functions. It also explains some important theorems in vector calculus, such as Green's theorem, Stokes' theorem, and Gauss' divergence theorem.
Chapter 5: Curvilinear Coordinates - This chapter introduces some common curvilinear coordinate systems, such as cylindrical coordinates, spherical coordinates, polar coordinates, etc. It also shows how to express vectors and tensors in these coordinate systems.
Chapter 6: Tensor Analysis - This chapter defines tensors as generalizations of scalars and vectors. It also explains how to perform operations on tensors, such as addition, multiplication, contraction, etc. It also introduces some special types of tensors, such as symmetric tensors, antisymmetric tensors, metric tensors, etc.
Chapter 7: Applications of Tensor Analysis - This chapter applies tensor analysis to some topics in physics and engineering, such as mechanics of deformable bodies, elasticity theory, fluid mechanics, electromagnetism theory, relativity theory, etc.
How to Download the PDF Book?
If you are interested in downloading the PDF book by Dr Nawazish Ali for free,click here. You will need to create an account on Scribd or log in with your Facebook or Google account. You can also read the book online or download it to your device for offline reading.
The PDF book has 744 pages and is suitable for advanced undergraduate or graduate students in mathematics,
and engineering. It has clear explanations,
and solutions. It is also well-organized,
Vector and tensor analysis is an important branch of mathematics that has many applications in science and engineering. If you want to learn this subject in depth,
you should consider reading the PDF book by Dr Nawazish Ali,
a renowned professor and author. You can download it for free from Scribd or read it online at your convenience.
Why Should You Read This Book?
There are many reasons why you should read this book by Dr Nawazish Ali if you want to learn vector and tensor analysis. Here are some of them:
The book is written by an experienced and qualified author who has a PhD in mathematics from the UK and has taught this subject for many years at the university level.
The book is comprehensive and covers all the topics that you need to know about vector and tensor analysis, from the basics to the advanced applications.
The book is clear and easy to understand, with plenty of examples, exercises, and solutions to help you grasp the concepts and practice your skills.
The book is up-to-date and reflects the latest developments and research in this field.
The book is suitable for students and professionals who want to use vector and tensor analysis in their studies or work.
What are the Benefits of Vector and Tensor Analysis?
Vector and tensor analysis is not only a fascinating subject to learn, but also a powerful tool to use in various domains. Here are some of the benefits of vector and tensor analysis:
Vector and tensor analysis helps you to simplify complex problems and express them in a concise and elegant way.
Vector and tensor analysis helps you to perform calculations and transformations more efficiently and accurately.
Vector and tensor analysis helps you to understand the physical phenomena and laws that govern our world and universe.
Vector and tensor analysis helps you to develop your logical thinking, analytical skills, and creativity.
Vector and tensor analysis helps you to enhance your knowledge and career prospects in mathematics, physics, engineering, and other related fields.
How to Use This Book?
This book by Dr Nawazish Ali is designed to be used as a textbook for a course on vector and tensor analysis, or as a reference book for self-study. It assumes that you have some background in calculus, linear algebra, and differential equations. However, it also reviews some of the necessary concepts and techniques in the appendices.
The book is divided into seven chapters, each with a clear outline, objectives, summary, and exercises. You can follow the order of the chapters as they are presented, or you can skip or rearrange them according to your needs and preferences. You can also use the index and the table of contents to find the topics that interest you.
The book is written in a simple and straightforward language, with plenty of examples and illustrations to help you understand the concepts and methods. It also provides hints and solutions to some of the exercises at the end of each chapter. You can use these exercises to test your knowledge and skills, or to explore further applications and extensions of vector and tensor analysis.
What are the Reviews of This Book?
This book by Dr Nawazish Ali has received positive feedback from many readers and reviewers who have used it for learning or teaching vector and tensor analysis. Here are some of the reviews that you can find online:
"This is one of the best books on vector and tensor analysis that I have ever read. It covers all the topics that I need for my studies in physics and engineering. It is clear, concise, comprehensive, and well-organized. It has many examples and exercises that help me practice and apply what I learn. I highly recommend this book to anyone who wants to learn vector and tensor analysis." - A student from Amazon.com
"I have been using this book as a textbook for my course on vector and tensor analysis for several years. It is an excellent book that covers all the essential topics in a logical and systematic way. It is also very easy to read and follow, with clear explanations and diagrams. It has many exercises that challenge and motivate my students. It is a great book for both beginners and advanced learners of vector and tensor analysis." - A professor from Goodreads.com
"This book is a masterpiece of vector and tensor analysis. It is written by a renowned mathematician who has a deep understanding and insight into this subject. It is not only a textbook, but also a reference book that contains many useful results and formulas. It is also very well-written, with a smooth flow and a friendly tone. It is a pleasure to read this book and learn from it." - A reviewer from Scribd.com
Where to Buy This Book?
If you want to buy a hard copy of this book by Dr Nawazish Ali, you can order it online from A-One Publisher, the official publisher of this book. You can visit their website at www.aonepublishers.com and fill out the order form with your details and payment method. You can also contact them by phone at 37232276, 37357177, or 37224655, or by email at [email protected]. They will deliver the book to your address within a few days.
If you want to buy an electronic copy of this book by Dr Nawazish Ali, you can download it from Scribd, the world's largest digital library. You can visit their website at www.scribd.com and search for the title of the book. You will need to create an account on Scribd or log in with your Facebook or Google account. You can also read the book online or download it to your device for offline reading.
How to Cite This Book?
If you want to cite this book by Dr Nawazish Ali in your academic or professional work, you can use the following format:
For APA style: Shah, N. A. (2003). Vector and tensor analysis for scientists and engineers. Lahore: A-One Publisher.
For MLA style: Shah, Nawazish Ali. Vector and Tensor Analysis for Scientists and Engineers. A-One Publisher, 2003.
For Chicago style: Shah, Nawazish Ali. Vector and Tensor Analysis for Scientists and Engineers. Lahore: A-One Publisher, 2003.
Vector and tensor analysis is an important and useful branch of mathematics that has many applications in science and engineering. It helps us to understand and solve complex problems in a simple and elegant way. It also helps us to develop our logical thinking, analytical skills, and creativity.
If you want to learn vector and tensor analysis in depth, you should read the book by Dr Nawazish Ali, a renowned professor and author who has a PhD in mathematics from the UK. His book is comprehensive, clear, easy to understand, and well-organized. It covers all the topics that you need to know about vector and tensor analysis, from the basics to the advanced applications. It also has many examples, exercises, and solutions to help you practice and apply what you learn.
You can buy this book online from A-One Publisher or download it from Scribd. You can also cite this book in your academic or professional work using the appropriate format. This book is a valuable resource for anyone who wants to learn vector and tensor analysis. 6c859133af | mathematics |
http://shimazaki.arch.kanagawa-u.ac.jp/shimazaki/wcee/wcee.html | 2023-01-29T12:09:33 | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499713.50/warc/CC-MAIN-20230129112153-20230129142153-00396.warc.gz | 0.92807 | 1,885 | CC-MAIN-2023-06 | webtext-fineweb__CC-MAIN-2023-06__0__292055224 | en | For high rise buildings, if the stiffness distribution is unsuitable, whipping phenomenon can occur at the top, and the upper part will be subject to extreme shaking. On account of this, the section of the upper part is limited not from required strength considerations but by appropriate stiffness distribution. In the case of structural planning of a pure frame building, if the story and span numbers are fixed, column / beam sections of lower stories can be established by long term axial force limitation and base shear coefficient. Then the shear stiffness for lower stories is decided. After establishing a suitable shear stiffness distribution, dimensions of members can be decided.
This paper describes the examination of shear and bending deformation for reinforced concrete frame buildings, and the appropriate stiffness distribution to avoid whipping phenomenon. Finally, the method of deciding the member section is shown.
The bending stiffness EI of a frame building of height H and span m (building width B = ml) as shown in figure 1, is given by equation (1), in which the column section is square and section area is Ac.
The story shear stiffness GA is given by equation (2) by the Muto's D method when the story height is h and stiffness coefficients obtained from stiffness ratio of columns to beams are all "a".
With a model of the bending-shear system fixed at base with height H
, constant bending stiffness EI and shear stiffness GA, the bending deformation and the shear deformation at the top are obtained by equation (3) where x is the distance from base.
The deformation at the top (x = H) is given by equation (4).
EI and GA obtained from equations (1) and (2) are substituted into this expression. When the stiffness ratio of column / beam is equal, the coefficient "a" becomes 0.5. Usually it comes within the range 0.2-0.4 because beam span is longer than height and the section of a column is greater than the section of a beam for a building designed by the beam yielding method. is known as the column ratio and it is about 0.03 when the first floor column is a 95~95 cm section, and the supported area is 5.5~5.5 m. The ratio of deformation of bending and shear deformation at the top is given by equation (5).
On the other hand, for the bending-shear model in which shear stiffness GA varies linearly to zero toward the top, it is given by the following equation.
at the top,
It becomes double that of the model with uniform shear stiffness. The ratio of bending and shear deformation is given by equation (8).
The ratio is between equation (5) and (8) for a real building, and would be 0.02(n/m)^2 . The bending deformation is equal to the shear deformation at the top for a 7 span 50 story building, or a 6 span 40 story building. For a building having higher aspect ratio than these, bending deformation is larger than shear deformation.
From equation (1), bending stiffness is proportional to column cross-sectional area, and shear stiffness is in proportional to the square of column cross-sectional area according to equation (2). Therefore, bending stiffness reduction is proportional to the square root of shear stiffness reduction by decreasing cross-sectional area of the column. The effect of stiffness distribution on eigen mode was examined using this relation in the study.
These eigen modes and story drift modes are shown in figure 2. For the first mode, the story drift is large at the lower part when the bending deformation rate is small, and is greatest at the top part when there is considerable bending deformation. The greater the rate of bending deformation, the larger the story drift in the higher part.
When there are few bending deformation, the change of eigen mode with stiffness reduction is considerable. The shape becomes susceptible to whip with stiffness reduction. The change in eigen mode with stiffness reduction with a large bending deformation rate is small. If shear stiffness at the top is more than 0.5 times that at the base and the bending deformation is smaller than the shear deformation at the top, the first mode shape of story drift never become large at the upper part. When the bending deformation is larger than the shear deformation at the top, the story drift is large in the upper part even for the uniform system. The tendency increases with decreasing the shear stiffness.
For the case where the shear stiffness decreases to 0.2 at the top, the story drift mode becomes considerable at the upper part, and will lead to whipping phenomenon by a combination with response spectrum. To avoid whipping phenomenon, the shear stiffness at the top must be more than 30% to 50 % larger than that at the base. This shows that the column cross-sectional area at the top needs to be SQ(0.5)ą0.7 times that at the top, and column dimensions needs to be SQ(0.7)ą0.85 times those at the base when the top shear stiffness is larger than 50% of the bottom stiffness.
In reinforced concrete column members, limit deformation and relation of axial force ratio are suggested from meaning of ductility considerations (Inai et al., 1997). The following equation is given for a column with constant axial force.
Here,Å is the axial force ratio for core cross-sectional area and R is the drift limitation. When the drift limitation is taken to be 1/50, the axial force ratio becomes 0.36. Because core cross-sectional area is assumed to be 0.75 times that of the total section in the literature, it becomes around 0.27 at the axial force ratio limitation for total sections.
As the horizontal load is equivalent to weight of 4 story (Shimazaki et al., 1994), regardless of building height, column section is fixed only by the axial force limit for high rise buildings. Based on the assumption of a 0.25Fc axial force limit, 0.03 column rate and 1.1tonf/m^2 unit weight of floor, concrete strength required becomes Fc=15n (kgf/cm^2) for an n story building.
First, the sections of the lower story are set. Column sections are established from the long term axial force limit of 0.25Fc. Beam moment is calculated from base shear required, and section / reinforcing arrangement of the beam is established. Column strength at the base is made double the beam strength for yielding column at the base after beam yielding. If reinforcing bar can not be arranged in the column section, the section is changed. The calculation procedure and the section calculated are shown in table 1.
Next, section setting for each story is performed as follows:
Comparison with the estimated reinforcing arrangement of the lower story shown in table 1, the reinforcing arrangement amount becomes large for the 25 story building, because the first period is short and weight increases. For the 60 story building, because the section is less than that of general structures due to the use of high strength materials, and the period is longer than the abbreviated expression, the required shear force becomes small, and the reinforcing arrangement also becomes small.
The eigen periods agree well. There is almost no difference in both total eigen mode and drift mode. It can therefore be said that the eigen period and eigen mode shape obtained by this abbreviated algorithm have sufficient precision.
Calculated results are shown in figure 7. The response values by frame analysis are less than the estimated values and the distribution of drift for every ground motion is similar. Thus it can be said that if the section for a building is set by the proposed method, the building has the earthquake resistance intended by a design method such as drift limitation.
Shimazaki, K. (1992). Seismic coefficient distribution of high-rise reinforced concrete buildings. Proc. 10th WCEE, 4281-4286, Madrid, Spain
Inai, E. and H. Hiraishi (1997). Structural design charts and equations of deformation capacity of reinforced concrete columns after flexural yielding. Proc. 11th WCEE (will be published), Mexico
Shimazaki, K. and A. Wada (1994). Design base shear coefficients for high-rise reinforced concrete buildings. Journal of structural and construction engineering, AIJ, No. 458, 99-108, Tokyo, Japan | mathematics |
https://cel.csusb.edu/pace/courses-programs/education/teaching-elementary-math-conceptually | 2020-01-28T09:57:19 | s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251778168.77/warc/CC-MAIN-20200128091916-20200128121916-00300.warc.gz | 0.936238 | 277 | CC-MAIN-2020-05 | webtext-fineweb__CC-MAIN-2020-05__0__102674406 | en | The College of Extended Learning is proud to partner with Virtual Education Software (VESi), a leading provider of accredited online courses for educators. These online professional development courses are written by top educators and provide relevant and interactive instruction on a wide variety of subjects.
Online courses work with your schedule, allowing you to participate when it is convenient for you. Each course instructor is available for professional questions by e-mail or a toll-free phone number. The courses are offered for either three- or four-quarter units of continuing education-level credit. Most students can complete three-unit courses in about 30 hours and four-unit courses in about 40 hours. You may register for these courses at any time during a quarter.
VESi courses are now tablet compatible, making it easy for you to recertify anytime, anywhere with reliable, stable online access.
EDUC 3430. This course is designed to explain and connect the major concepts, procedures and reasoning processes of mathematics. Current research and trends in math education will be discussed to outline a teaching methodology that is conceptual, contextual and constructive. Activities are presented to explain underlying concepts and illustrate constructive teaching. The course has been divided into four chapters, each covering a math topic: number sense, addition and subtraction, multiplication and division and fractions. Emphasis is placed on exploring how to develop mathematical understanding in learners. | mathematics |
https://autopapers.ssrn.com/sol3/papers.cfm?abstract_id=2134703 | 2022-05-21T16:54:47 | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662539131.21/warc/CC-MAIN-20220521143241-20220521173241-00045.warc.gz | 0.738015 | 104 | CC-MAIN-2022-21 | webtext-fineweb__CC-MAIN-2022-21__0__150743262 | en | The Normalizing Transformation of the Implied Volatility Smile
10 Pages Posted: 23 Aug 2012
Date Written: October 2012
We study specific nonlinear transformations of the Black–Scholes implied volatility to show remarkable properties of the volatility surface. No arbitrage bounds on the implied volatility skew are given. Pricing formulas for European payoffs are given in terms of the implied volatility smile.
Keywords: implied volatility, no arbitrage bounds, variance swap, gamma swap
Suggested Citation: Suggested Citation | mathematics |
https://maxdoubt.wordpress.com/2014/01/14/james-clerk-maxwell-1831-1879-scotland-a-modern-pioneer-in-science-and-faith/ | 2018-07-19T21:22:15 | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591296.46/warc/CC-MAIN-20180719203515-20180719223515-00049.warc.gz | 0.958703 | 538 | CC-MAIN-2018-30 | webtext-fineweb__CC-MAIN-2018-30__0__209973068 | en | James Clerk Maxwell 1831-1879 Scotland
was a Scottish mathematical physicist. His most prominent achievement was to formulate a set of equations that describe electricity, magnetism, and optics as manifestations of the same phenomenon, namely the electromagnetic field. Maxwell’s achievements concerning electromagnetism have been called the "second great unification in physics", after the first one realised by Isaac Newton.
With the publication of A Dynamical Theory of the Electromagnetic Field in 1865, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. Maxwell proposed that light is in fact undulations in the same medium that is the cause of electric and magnetic phenomena. The unification of light and electrical phenomena led to the prediction of the existence of radio waves.
Maxwell helped develop the Maxwell–Boltzmann distribution, which is a statistical means of describing aspects of the kinetic theory of gases. He is also known for presenting the first durable colour photograph in 1861 and for his foundational work on analysing the rigidity of rod-and-joint frameworks (trusses) like those in many bridges.
His discoveries helped usher in the era of modern physics, laying the foundation for such fields as special relativity and quantum mechanics. Many physicists regard Maxwell as the 19th-century scientist having the greatest influence on 20th-century physics, and his contributions to the science are considered by many to be of the same magnitude as those of Isaac Newton and Albert Einstein. In the millennium poll—a survey of the 100 most prominent physicists—Maxwell was voted the third greatest physicist of all time, behind only Newton and Einstein. On the centenary of Maxwell’s birthday, Einstein himself described Maxwell’s work as the "most profound and the most fruitful that physics has experienced since the time of Newton."
Maxwell was an evangelical Presbyterian, and in his later years became an Elder of the Church of Scotland. Maxwell’s religious beliefs and related activities have been the focus of a number of papers. Attending both Church of Scotland (his father’s denomination) and Episcopalian (his mother’s denomination) services as a child, Maxwell later underwent an evangelical conversion in April 1853, which committed him to an antipositivist position. It needs to be said that this was theological evangelicalism, famous for opposing slavery and reforming prisons, not today’s highly conservative group known by that name.
All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers. | mathematics |
https://blog.yuantops.com/tech/understanding-xor/ | 2021-09-24T09:23:49 | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057508.83/warc/CC-MAIN-20210924080328-20210924110328-00141.warc.gz | 0.962287 | 292 | CC-MAIN-2021-39 | webtext-fineweb__CC-MAIN-2021-39__0__170470721 | en | We can interpret the action of XOR in a number of different ways, and this helps to shed light on its properties. The most obvious way to interpret it is as its name suggests, ‘exclusive OR’: A ⊕ B is true if and only if precisely one of A and B is true. Another way to think of it is as identifying difference in a pair of bytes: A ⊕ B = ‘the bits where they differ’. This interpretation makes it obvious that A ⊕ A = 0 (byte A does not differ from itself in any bit) and A ⊕ 0 = A (byte A differs from 0 precisely in the bit positions that equal 1) and is also useful when thinking about toggling and encryption later on.
The last, and most powerful, interpretation of XOR is in terms of parity, i.e. whether something is odd or even. For any n bits, A1 ⊕ A2 ⊕ … ⊕ An = 1 if and only if the number of 1s is odd. This can be proved quite easily by induction and use of associativity. It is the crucial observation that leads to many of the properties that follow, including error detection, data protection and adding.
Essentially the combined value x ^ y ‘remembers’ both states, and one state is the key to getting at the other. | mathematics |
https://www.hwcdsb.ca/200591--Canadian-Math-Kangaroo-Contest | 2018-06-19T14:16:14 | s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267863043.35/warc/CC-MAIN-20180619134548-20180619154548-00038.warc.gz | 0.88164 | 105 | CC-MAIN-2018-26 | webtext-fineweb__CC-MAIN-2018-26__0__2911910 | en | : Mar 26, 2017
Arcelor Mittal Dofasco presents the Canadian Math Kangaroo Contest
Sunday, March 26th, 2017 - 11:00am - 12:00pm at the F.H. Sherman Recreation and Learning Centre
Participate in this nation-wide math contest for students in Grades 1-12. Challenge yourself and compete with others in your grade.
For more information visit http://www.mathkangaroocanada.com
Registration opens January 2nd! | mathematics |
https://dear-woman.com/5372-the-future-of-math-tutoring-for-homeschooling-families-32/ | 2023-06-01T03:18:34 | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224647525.11/warc/CC-MAIN-20230601010402-20230601040402-00218.warc.gz | 0.944314 | 726 | CC-MAIN-2023-23 | webtext-fineweb__CC-MAIN-2023-23__0__131135059 | en | The Rise of Homeschooling and Math Tutoring
In recent years, homeschooling has become an increasingly popular educational choice for families across America. According to the National Home Education Research Institute, homeschooling in the United States has been growing at an average rate of 2 to 8 percent per year, with an estimated 2.5 million students currently being homeschooled. With the benefits of individualized attention, flexible schedules, and personalized curriculum, many homeschooling families seek additional support in the form of math tutoring.
In addition, math has long been considered one of the more challenging subjects to teach, particularly for parents who do not have a strong math background. For this reason, many families turn to dedicated math tutors for assistance. To keep growing your understanding of the topic, don’t miss out on the carefully selected external resource we’ve prepared to complement your reading. ACT/SAT Test Preparation!
The Role of Technology in Math Tutoring
Technology has played an increasingly important role in education over the past decade, and math tutoring for homeschooling families is no exception. Online tutoring platforms such as Khan Academy, Mathnasium, and Chegg offer personalized, one-on-one math instruction to students of all ages and abilities, allowing families to access quality tutoring Learn from this informative document the comfort of their own homes.
Another advantage of online math tutoring is the ability to record and review tutoring sessions. With online platforms, families can easily revisit lessons and concepts covered during previous sessions, enabling students to reinforce their understanding of key math concepts.
The Need for Personalization and Attention to Individual Needs
Despite the growing popularity of online math tutoring, there is still a need for personalized attention and instruction tailored to the individual needs of each student. Many students benefit from the one-on-one attention of a dedicated math tutor, particularly those who struggle with math concepts or who have unique learning styles.
This is especially true for homeschooling families, who rely heavily on personalized attention to ensure that their children are receiving an appropriate education that meets their individual needs and goals. While online platforms can provide quality instruction, they may not be able to offer the same level of personalization as a dedicated math tutor.
The Future of Math Tutoring for Homeschooling Families
Looking forward, it seems likely that math tutoring for homeschooling families will continue to grow and evolve as technology advances and the number of homeschooling families increases. While online platforms will likely play an increasingly important role in math tutoring, there will still be a need for personalized, one-on-one instruction that can be tailored to the unique needs of each student.
It is also likely that math tutoring for homeschooling families will continue to emphasize the importance of individualized attention and flexible scheduling. Homeschooling families value the ability to personalize their educational choices and schedules, and math tutoring will likely continue to adapt to meet these needs.
Math tutoring for homeschooling families has become an increasingly important educational choice for families seeking personalized attention and support in math instruction. While online platforms offer numerous advantages, there is still a need for dedicated math tutors who can provide personalized, one-on-one attention tailored to the needs and goals of each student. As technology continues to advance, it seems likely that math tutoring will continue to evolve and adapt to meet the changing needs of homeschooling families. Immerse yourself in the subject with this external content we suggest. ACT/SAT Test Preparation! | mathematics |
https://rightstartgo.com/what-is-the-best-way-for-calculating-interest-on-fixed-deposit-investment.html | 2023-12-06T04:56:29 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100583.13/warc/CC-MAIN-20231206031946-20231206061946-00058.warc.gz | 0.947244 | 653 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__50052170 | en | A fixed deposit (FD) is one of the simplest and hence one of the most popular forms of investment. Its popularity arises from the fact that it is a safe and secure investment with few of the risks associated with other investments such as stocks or real estate, and the fact that it gives higher returns as compared to regular deposits. Thus rather than having your money lying around in your savings account, it is always a better idea to invest it in a fixed deposit scheme where it can earn higher interest. The exact interest on a fixed deposit scheme varies from bank to bank. It also depends on the duration of your deposit – the longer the duration, the higher the interest rate is likely to be. Before you invest, however, is important to know what your returns are going to be. You do this either manually using a pen and paper or you can use an FD calculator such as this one provided by Finserv MARKETS.
How to Calculate Interest on Fixed Deposit Investment?
You can calculate the interest on your FD in two ways:
- Using Pen and Paper – When calculating the interest rate on FD yourself using pen and paper it is important to understand that there are two kinds of interest rates applicable to FDs:
Simple Interest – This is applicable to FDs with a tenure of up to 6 months. The formula for calculating simple interest is:
Interest = Principal x Rate of Interest x Tenure of FD/ 100
Compound Interest – This is usually applicable to FDs with a tenure longer than 6 months. Even in this case, there are two kinds of possibilities depending on the type of payout you want :
- Monthly Payout – You take your interest payments at the end of each month. The interest rate in this case is usually calculated at discounted rates.
- Payout at Maturity –You take your payout at the end of the term period of your FD.
In case you opt for the second option, you can utilize the power of compounding as compound interest is applicable in this case. The formula for calculating compound interest is slightly more complicated.
Maturity Amount = Principal (1+rate of interest/n) ^ (n * Tenure)
Where n = number of times the amount is compounded in a year.
- Using FD Interest Calculator – As you can see, calculating FD interest using pen and paper can get complicated. Therefore, it is more convenient to use an FD calculator that gives you more accurate results. You can use this simple FD rate calculator by Finserv MARKETS. All you need to enter in the calculator are the deposit amount, the tenure of the FD, and the interest rate. The FD calculator will do the rest. If you do not know the prevailing FD interest rate, you can check the best rates from Finserv MARKETS to enter in the FD interest calculator.
In a Nutshell
FDs are a safe and convenient vehicle for investing your savings. However, the rate of interest and the duration for which you are investing make a big difference. It is advisable to calculate the maturity amount you can expect at maturity beforehand. The most convenient way of doing this is using an online FD interest calculator that gives you fast and accurate results. | mathematics |
http://reforef.ru/outozuc/%D0%9E%D1%86%D0%B5%D0%BD%D0%BA%D0%B0+%D0%BF%D0%B0%D1%80%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D0%BE%D0%B2+%D0%BE%D0%B1%D1%8B%D0%BA%D0%BD%D0%BE%D0%B2%D0%B5%D0%BD%D0%BD%D1%8B%D1%85+%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%85+%D1%83%D1%80%D0%B0%D0%B2%D0%BD%D0%B5%D0%BD%D0%B8%D0%B9+%D1%81+%D0%B7%D0%B0%D0%BF%D0%B0%D0%B7%D0%B4%D1%8B%D0%B2%D0%B0%D1%8E%D1%89%D0%B8%D0%BC%D0%B8+%D0%B0%D1%80%D0%B3%D1%83%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D0%BC%D0%B8c/main.html | 2020-09-26T01:15:01 | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400232211.54/warc/CC-MAIN-20200926004805-20200926034805-00541.warc.gz | 0.713002 | 166 | CC-MAIN-2020-40 | webtext-fineweb__CC-MAIN-2020-40__0__280906990 | en | Subject: Parameter estimation of ordinary delay differential equations
Contains: 73 pages, 11 tables, 33 figures, 90 formulae, 13 references
The goal of this paper is to develop and implement fast and robust algorithm for parameter estimation of ordinary delay differential equations.
Based on the modern numerical methods the parameter estimation algorithm is proposed and its implementation is done in the MATLAB language.
Parameters of one demographical model are estimated.
The topicality of the paper – lack of theoretical basis and ready solutions for such problems.
Keywords: PARAMETER ESTIMATION, ORDINARY DELAY DIFFERENTIAL QUEATIONS, SPARSE SYSTEMS, LEAST SQUARES, NUMERIC INTEGRATION, CYCLIC REDUCTION, SQP, MATLAB | mathematics |
https://nugeryvymuh.gtbabowling.com/computing-methods-in-applied-sciences-and-engineering-book-29877pz.php | 2022-01-22T12:41:17 | s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303845.33/warc/CC-MAIN-20220122103819-20220122133819-00640.warc.gz | 0.86128 | 2,530 | CC-MAIN-2022-05 | webtext-fineweb__CC-MAIN-2022-05__0__25847737 | en | 3 edition of Computing methods in applied sciences and engineering found in the catalog.
|Statement||Second International Symposium, December 15-19, 1975 / [organized by] IRIA LABORIA, Institut de recherche d"informatique et d"automatique ; edited by R. Glowinski and J.L. Lions.|
|Series||Lecture notes in physics -- 58|
|Contributions||Glowinski, R., Lions, Jacques Louis., Iria Laboria.|
|The Physical Object|
|Pagination||viii, 593 p. :|
|Number of Pages||593|
8 issues per year. Subscription price. IJCSM is a peer-reviewed international journal that publishes high quality original papers and comprehensive survey articles in all areas of computing science and mathematics, with interfaces to physics, engineering, chemistry, biology, statistics, economics and the social sciences.
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Computing Methods in Applied Sciences and Engineering. by Roland Glowinski (Editor) ISBN ISBN Why is ISBN important. ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book.
Author: Roland Glowinski. Curved Finite Element Methods for the Solution of Integral Singular Equations on Surfaces in R3 Pages Nedelec, J. Computing Methods in Applied Sciences and Engineering Second International Symposium December 15–19, Computing Computing methods in applied sciences and engineering book in Applied Sciences and Engineering Computing Methods in Applied Sciences and Engineering International Symposium, Versailles, DecemberPart 2.
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Glowinski and J. Lions. Published by North‐Holland, No. of pages: Price: $Author: Peter Bettess. Computing Methods in Applied Sciences and Engineering Part 2 International Symposium, Versailles, December 17–21, Students have the opportunity to take courses offered by the Faculties of Civil Engineering and Geodetic Science, Mathematics and Physics, Mechanical Engineering and Computer Science.
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The book discusses important results in modern mathematical models and high performance computing, such as applied operations research, simulation of operations, statistical modeling and applications, invisibility regions and regular meta-materials, unmanned vehicles, modern radar techniques/SAR.
Book Annex Membership Educators Gift Cards Stores & Events Help. Auto Suggestions are available once you type at least 3 letters. Use up arrow (for mozilla firefox browser alt+up arrow) and down arrow (for mozilla firefox browser alt+down arrow) to review and enter to : $ In computer science, research methods have historically been passed from advisor to student via apprenticeship [, ].
Most of us learned these methods from a mentor or not at all. International Symposium on Computing Methods in Applied Sciences and Engineering, 2d, Versailles, Computing methods in applied sciences and engineering.
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Berlin ; New York: Springer-Verlag, (OCoLC) Material Type: Conference publication: Document Type: Book: All Authors / Contributors: R Glowinski; Jacques Louis Lions. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.
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[Roland Glowinski; Jacques-Louis Lions; Institut de recherche d'informatique et. Computational Science and Engineering. (IDA Center for Computing Sciences). this approach is applied to MMS for the finite element analysis. The major goal of the Journal of Computational Methods in Sciences and Engineering (JCMSE) is the publication of new research results on computational methods in sciences and engineering.
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Publication: Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI June Pages – Computing methods in applied sciences and engineering, Proceedings of the Fourth International Symposium on Computing Methods in Applied Sciences and Engineering, Versailles, France, December Edited by R.
Glowinski and J. Lions. Published by North-Holland, No. of pages: Price: $Author: Peter Bettess. Computational science and engineering (CSE) is a relatively new discipline that deals with the development and application of computational models and simulations, often coupled with high-performance computing, to solve complex physical problems arising in engineering analysis and design (computational engineering) as well as natural phenomena (computational science).Problem decomposition and the use of domain-based parallelism in computational science and engineering was the subject addressed at a workshop held at the University of Minnesota Supercomputer Institute in April Read the latest articles of Computer Methods in Applied Mechanics and Engineering atElsevier’s leading platform of peer-reviewed scholarly literature. | mathematics |
https://topebooks.offersupermarket.com/Quantum_Chemistry_7th_Edition/p5025784_17821744.aspx | 2018-05-21T12:38:13 | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864186.38/warc/CC-MAIN-20180521122245-20180521142245-00265.warc.gz | 0.86999 | 182 | CC-MAIN-2018-22 | webtext-fineweb__CC-MAIN-2018-22__0__40188249 | en | Known for its solid presentation of mathematics, this bestseller is a rigorous but accessible introduction to both quantum chemistry and the math needed to master it. Quantum Chemistry, Seventh Edition covers quantum mechanics, atomic structure, and molecular electronic structure, and provides a thorough, unintimidating treatment of operators, differential equations, simultaneous linear equations, and other areas of required math. Practical for readers in all branches of chemistry, the new edition reflects the latest quantum chemistry research and methods of computational chemistry, and clearly demonstrates the usefulness and limitations of current quantum-mechanical methods for the calculation of molecular properties.
Please note that this is a eBook PDF digital format and not a hardcover printed book and the PDF file will be sent to your email once the payment has been made and it can be read in all computers, smartphone, tablets etc. The digital book will be sent to your email address within 12 hours. | mathematics |
https://www.enarmour.com/blog?offset=1443431684338 | 2019-03-20T03:50:49 | s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202199.51/warc/CC-MAIN-20190320024206-20190320050206-00301.warc.gz | 0.981164 | 501 | CC-MAIN-2019-13 | webtext-fineweb__CC-MAIN-2019-13__0__79448830 | en | Leonardo Bonacci (c. 1170 – c. 1250), popularly known as Fibonacci or Leonardo of Pisa, was the first great Western mathematician after the decline of Greek science.
His well-known moniker “Fibonacci” is derived from the Latin words “filius Bonacci”, literally translated to “son of Bonacci”. Fi'-Bonacci could be considered the equivalent of the English William-son or John-son.
Fibonacci was born in Pisa, Italy, to Guglielmo Bonacci, a wealthy merchant who directed a trading post at a major port located in present day Algeria. As a boy, Fibonacci accompanied his father on his commercial trips to the Orient. It was during his travels along the Mediterranean coast that the budding mathematician became acquainted with the Hindu-Arabic number system and discovered its enormous practical advantages compared to the Roman numerals, which were still current in Western Europe.
Fibonacci ended his travels around the year 1200 and returned to Pisa. Upon his return, inspired by his interactions with the foreign merchants he met while under the tutelage of his father, Leonardo wrote a number of influential texts that played an important role in reviving ancient mathematical skills. His works garnered him recognition among his contemporaries and high esteem from the reigning Holy Roman Emperor, Frederick II.
His most well-known published book is Liber Abaci (1202), literally translated as “Book of Calculations” or “Book of the Abacus”. The book, which went on to be widely copied and imitated, was based on the arithmetic and algebra that Fibonacci had accumulated during his travels. In it, Fibonacci introduced the so-called modus Indorum (method of the Indians), today known as Arabic numerals and the Hindu-Arabic place-valued decimal system. The book showed the practical importance of the new numeral system by applying it to commercial bookkeeping, conversion of weights and measures, the calculation of interest, money-changing, and other applications. Furthermore, Abaci contains a large collection of problems aimed at merchants. They relate to the price of goods, how to calculate profit on transactions, how to convert between the various currencies in use in Mediterranean countries, and problems which had originated in China. The book was well received throughout educated Europe and had a profound impact on European thought. | mathematics |
https://thelab.dc.gov/kevin.html | 2022-05-27T15:22:19 | s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662658761.95/warc/CC-MAIN-20220527142854-20220527172854-00710.warc.gz | 0.95764 | 269 | CC-MAIN-2022-21 | webtext-fineweb__CC-MAIN-2022-21__0__49912345 | en | Kevin Wilson Ph.D.
Kevin was a Senior Data Scientist in The Lab @ DC. He played a leading role in envisioning and implementing The Lab’s data analytic standards and protocols, executing (and wherever possible automating) important data analytic tasks, and guiding the use of machine learning, as well as developing entirely novel uses of data that maximize how much we can learn from the District’s vast amount of administrative data.
Kevin brought years of experience in a wide array of data analytic topics, ranging from system and security architecture to advanced statistical techniques to the development of novel predictive models and commercial tools. As the Principal Data Scientist at Knewton-an education technology company-Kevin developed and implemented methods for drawing real time and retrospective insights from massive, complex datasets, and was especially involved in bridging the divide between classic techniques like psychometrics with the modern techniques of machine learning. Kevin also has experience explaining such complex topics to diverse audiences, ranging from small academic seminars to high school students. His work has appeared in such diverse venues as the Journal of Combinatorial Theory and Educational Data Mining, and some of his popular projects have been written up in the Washington Post and Daily Kos.
Kevin earned a B.S. in mathematics from University of Michigan and a Ph.D. in mathematics from Princeton University. | mathematics |
http://riudg.udg.mx/handle/20.500.12104/39074 | 2020-04-09T04:23:56 | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585371829677.89/warc/CC-MAIN-20200409024535-20200409055035-00378.warc.gz | 0.850819 | 240 | CC-MAIN-2020-16 | webtext-fineweb__CC-MAIN-2020-16__0__196695566 | en | Please use this identifier to cite or link to this item:
|Title:||A novel hybrid representation and control of convective spatially distributed systems|
|Abstract:||In this work we study spatially distributed convective systems described by first order partial differential equations and we show how this systems in a fixed spatial point can be exactly represented by a hybrid system with two commutable ordinary differential equations subsystems, where the first one is dominated by the initial condition, whereas the second one is governed by the boundary condition. Then we define the boundary control problem for spatially distributed convective systems and as a first approach, we propose a controller for one-dimensional systems which solves this problem. Finally, in order to test hybrid representation and controllers, a study case is presented for an enzymatic reactor, where dispersive terms can be neglected. � 2007 World Scientific Publishing Co. Pte. Ltd.|
|Appears in Collections:||Producción científica UdeG|
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http://solution-dailybrainteaser.blogspot.ca/2012/03/classic-hens-eggs-puzzle.html | 2018-05-27T13:22:53 | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794868316.29/warc/CC-MAIN-20180527131037-20180527151037-00363.warc.gz | 0.937316 | 392 | CC-MAIN-2018-22 | webtext-fineweb__CC-MAIN-2018-22__0__18553209 | en | Classic Hens Eggs Puzzle Solution - 22 March
A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?
Update Your Answers at : Click Here
the farmer needs 3 hens to produce 12 eggs in 6 days
This is a classic problem that many people get wrong because they reason that half of a hen cannot lay an egg, and a hen cannot lay half an egg. However, we can get a satisfactory solution by treating this as a purely mathematical problem where the numbers represent averages.
To solve the problem, we first need to find the rate at which the hens lay eggs. The problem can be represented by the following equation, where RATE is the number of eggs produced per hen·day:
1½ hens × 1½ days × RATE = 1½ eggs
We convert this to fractions thus:
3/2 hens × 3/2 days × RATE = 3/2 eggs
Multiplying both sides of the equation by 2/3, we get:
1 hen × 3/2 days × RATE = 1 egg
Multiplying both sides of the equation again by 2/3 and solving for RATE, we get:
RATE = 2/3 eggs per hen·day
Now that we know the rate at which hens lay eggs, we can calculate how many hens (H) can produce 12 eggs in six days using the following equation:
H hens × 6 days × 2/3 eggs per hen·day = 12 eggs
Solving for H, we get:
H = 12 eggs /(6 days × 2/3 eggs per hen·day) = 12/4 = 3 hens
Therefore, the farmer needs 3 hens to produce 12 eggs in 6 days. | mathematics |
https://lauratitolo.github.io/publication/2018lopstr/ | 2024-04-20T07:54:50 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817491.77/warc/CC-MAIN-20240420060257-20240420090257-00325.warc.gz | 0.950115 | 183 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__154457484 | en | Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This problem, which is called test in- stability, may result in a significant difference between the computation of a floating-point program and the expected output in real arithmetic. In this paper, a formally proven program transformation is proposed to detect and correct the effects of unstable tests. The output of this transformation is a floating-point program that is guaranteed to return either the result of the original floating-point program when it can be assured that both its real and its floating-point flows agree or a warning when these flows may diverge. The proposed approach is illustrated with the transformation of the core computation of a polygon containment algorithm developed at NASA that is used in a geofencing system for unmanned aircraft systems. | mathematics |
https://duarte.oflschools.com/student-resources/tutoring/ | 2023-12-05T08:39:04 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100550.40/warc/CC-MAIN-20231205073336-20231205103336-00320.warc.gz | 0.920699 | 157 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__107413793 | en | We know school can sometimes be difficult. That’s why we have dedicated Tutors at our centers every day to help you succeed!
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https://qofefofo.tk/compatibility-stability-and-sheaves.php | 2020-02-24T11:41:08 | s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145941.55/warc/CC-MAIN-20200224102135-20200224132135-00077.warc.gz | 0.89512 | 1,110 | CC-MAIN-2020-10 | webtext-fineweb__CC-MAIN-2020-10__0__74428417 | en | As a consistency check: an explicit calculation using these expressions leads to the sign predicted by Main Conjecture 6. We should therefore not separate these three terms. This motivates the following definition. The proof is similar to that of Proposition 6. The degenerate cases can be done similarly. In this section, we explain where the sign in Main Conjecture 6. The argument is a variation on [ 39 , Sect.
Examples 6. In this section, we prove Main Conjecture 6.
Pandharipande and Thomas need two conjectures for their argument [ 47 , Conj. We need completely similar analogs of their conjectures in our setting. The second will be described below. The analog of the second conjecture of Pandharipande and Thomas [ 47 , Conj. Their definition and equations 45 and 46 hold under the assumptions of Conjecture 6.
Suppose the setting is as in Conjecture 6. See Examples 6. We would like to thank K. Behrend, J. Bryan, J. Manschot, D. Maulik, and R. Thomas for useful discussions. We would also like to thank the anonymous referees whose comments led to an immense improvement of the exposition, e. Sign In. Advanced Search.
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Part I: Classical. Part II: Virtual. Oxford Academic. Google Scholar. Martijn Kool. Correspondence to be sent to: e-mail: m. Benjamin Young. Cite Citation. Permissions Icon Permissions. See [ 24 ] for the construction of the moduli space and its history. In this article, we do not consider strictly semi-stable sheaves so this moduli space may be non-compact.
In this case, the moduli space is compact. When the moduli space is compact, this leads to a virtual cycle, which can be used to define deformation invariants.
Its degree is known as a Donaldson—Thomas DT invariant. Equivariant torsion free sheaves are much harder to enumerate than equivariant reflexive sheaves. This can be viewed as the degree 0 part of rank 2 DT theory on smooth toric 3-folds.
Mentioned to us by Maulik and Manschot. Note that unlike the rank 1 case, there are no signs in this formula essentially because rank 2 is even. The following is strong evidence for Conjecture C. This formula is due to Klyachko [ 28 , 29 ]. Concretely, this works as follows. Let the situation be as in the previous definition. It is not hard to show this is a morphism [ 32 ]. The map 8 is therefore surjective but not injective. It can be made injective as follows. As discussed in the introduction, double duals of members of a flat family of torsion free sheaves do not need to form a flat family.
These data are represented by Figure 1. Open in new tab Download slide. We start with some definitions. Analogous to Definition 2. In Definition 2. The following generating function was introduced in Remark 2. Geometric proof. The geometric proof proceeds as follows. We first realize the left hand sides of Theorems 2. Proposition 2. Combining 17 , Prop. This problem is discussed in [ 10 , Ch. Theorem 3. Using formula 17 , Proposition 2. By the proof of [Kol, Thm. Consider the short exact sequence of Lemma 4.
Verschoren, electronic resource Resource Information. The item Compatibility, stability, and sheaves, J. Verschoren, electronic resource represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University Of Pikeville. This item is available to borrow from 1 library branch. Creator Bueso, J.
Contributor Jara, P. Language eng. Publication New York, Marcel Dekker, c Extent xiv, p. Isbn Label Compatibility, stability, and sheaves Title Compatibility, stability, and sheaves Statement of responsibility J. Verschoren Creator Bueso, J. Verschoren, A. Label Compatibility, stability, and sheaves, J. Verschoren, electronic resource Instantiates Compatibility, stability, and sheaves Publication New York, Marcel Dekker, c Bibliography note Includes bibliographical references p.
Preliminaries: There are lots of variations on the settings in which we define sheaves. I am concerned with the details linking the general definition below to the Grothendieck topology it generates; particularly, the assertion that sheaves with respect to a coverage are the same as sheaves with respect to the generated Grothendieck coverage. Descent can be phrased concisely in terms of subfunctors of Yoneda embeddings.
What is not clear to me is how, "One can then show that for every coverage, there is a unique Grothendieck coverage having the same sheaves. Sign up to join this community.
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Why are sheaves of a coverage the same as those on its generated Grothendieck coverage? Ask Question. Asked 1 year, 5 months ago. | mathematics |
http://endevco.com/our-resources/ask-the-experts/what-is-a-charge-amplifier-and-why-do-i-need-one | 2023-12-05T19:09:09 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100555.27/warc/CC-MAIN-20231205172745-20231205202745-00489.warc.gz | 0.860109 | 246 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__251918512 | en | Our analysis goal is to end up with a gain equation in terms of vout/qin. In the process, we will gain some insight into how a charge amplifier deals with the problem of changing cable capacitance.
First, let's sum all the charge flows:
qin = qp + qc + qf
Because of the relationship q = CV, we can rewrite the above as:
qin = vinCp + vinCc + vfCf
qin = vin(Cp + Cc) + vfCf
We know, however, that vin = 0, because of the virtual short across the input terminals of the op amp (assume an ideal op amp). So the equation above simplifies to:
qin = vfCf
Rearranging, we have:
vf = qin/Cf
Again, because of the virtual short across the terminals of the op amp, we can say:
vout = vf = qin/Cf
Rearranging again, we have:
vout/qin = 1/Cf where units are mV/pC. | mathematics |
https://baziwukikyjupu.ekodeniz.com/advanced-engineering-mathematics-9th-edition-with-wiley-plus-set-book-2979kp.php | 2021-10-27T06:11:05 | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588102.27/warc/CC-MAIN-20211027053727-20211027083727-00538.warc.gz | 0.827753 | 2,528 | CC-MAIN-2021-43 | webtext-fineweb__CC-MAIN-2021-43__0__19201236 | en | Published March 21, 2006 by John Wiley & Sons .
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https://www.clsong.com/ | 2022-11-29T00:06:34 | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710684.84/warc/CC-MAIN-20221128235805-20221129025805-00839.warc.gz | 0.889536 | 226 | CC-MAIN-2022-49 | webtext-fineweb__CC-MAIN-2022-49__0__185940433 | en | I am a theoretical and computational ecologist. My research program is motivated by the pervasive existence of context-dependency—results are only true under particular circumstances—in ecological systems, which fundamentally hinders generalization and prediction under uncertainty. To address this problem, my research centers on developing a theoretically rigorous and computationally feasible ‘common currency’, and using the common currency to synthesize empirical findings across study systems and scales.
I am currently a postdoc with Jonathan Levine at Princeton University. I was a postdoc co-supervised by Andrew Gonzalez at McGill University and Marie-Josée Fortin at University of Toronto from 2020-2022. I received a PhD in Civil and Environmental Engineering from MIT under the supervision of Serguei Saavedra, and a BS in Mathematics from Zhejiang University under the supervision of Yang-Yu Liu.
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PhD in Civil and Environmental Engineering, 2016 - 2020
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BSc in Mathematics, 2013 - 2016 | mathematics |
https://www.homeschoolplus.com/learn/faq | 2024-03-04T14:32:09 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476452.25/warc/CC-MAIN-20240304133241-20240304163241-00835.warc.gz | 0.925283 | 779 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__41541250 | en | Homeschool+™ Frequently Asked Questions
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https://tamrakgarcia.wordpress.com/category/math/ | 2021-10-24T22:16:56 | s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587606.8/warc/CC-MAIN-20211024204628-20211024234628-00712.warc.gz | 0.947327 | 335 | CC-MAIN-2021-43 | webtext-fineweb__CC-MAIN-2021-43__0__104412201 | en | I hate math. But life is all about numbers; especially a diabetic life. I guess my hatred for math could be one reason why I have such a difficult time getting through life and controlling my diabetes. I’m not bad at math, it actually isn’t all that difficult in a day-to-day perspective. I just hate doing it, especially all day, everyday, over and over again. Ugh!
For a diabetic, math comes up a million times a day. Counting carbs, protein, fat, and calories with every meal. Checking blood sugar at least four times a day. Determining insulin dosage based on those food counts and blood sugar readings at least four times per day.
Yeah, it’s a number game.
I was in bed trying to fall asleep the other night and I got to wondering just how many times I’ve pricked my finger and injected myself in my lifetime. Then the question evolved to how many doctors visits, tests, procedures, hospitalizations, surgeries, etc., I’ve had because of my diabetes.
I’ve been diabetic for 27 years. Let’s add up the numbers.
These are mostly estimates due to the fact that schedules and routines have changed year to year…and other factors.
Finger pricks: >40,000
Injections (not just insulin): >50,000
Doctor visits: >300
Lab Draws: >120
Tests (other than lab draws): >100
Procedures (not surgery): >30
And many, many more numbers to come! | mathematics |
https://intuitionism.askdefine.com/ | 2018-11-17T11:29:26 | s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743353.54/warc/CC-MAIN-20181117102757-20181117124757-00378.warc.gz | 0.886076 | 2,607 | CC-MAIN-2018-47 | webtext-fineweb__CC-MAIN-2018-47__0__189294652 | en | intuitionism n : (philosophy) the doctrine that knowledge is acquired primarily by intuition
- This article is about Intuitionism in mathematics and philosophical logic. For other uses, see Ethical intuitionism.
In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as the constructive mental activity of humans. That is, mathematics does not consist of analytic activities wherein deep properties of existence are revealed and applied. Instead, logic and mathematics are the application of internally consistent methods to realize more complex mental constructs.
Truth and proof
The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. As the name suggests, in Brouwer's original intuitionism, the truth of a statement is taken to be equivalent to the mathematician being able to intuit the statement. The vagueness of the intuitionistic notion of truth often leads to misinterpretations about its meaning. Kleene formally defined intuitionistic truth from a realist position, however Brouwer would likely reject this formalization as meaningless, given his rejection of the realist/Platonist position. Intuitionistic truth therefore remains somewhat ill defined. Regardless of how it is interpreted, intuitionism does not equate the truth of a mathematical statement with its provability. However, because the intuitionistic notion of truth is more restrictive than that of classical mathematics, the intuitionist must reject some assumptions of classical logic to ensure that everything he/she proves is in fact intuitionistically true. This gives rise to intuitionistic logic.
To claim an object with certain properties exists is, to an intuitionist, to claim to be able to construct a certain object with those properties. Any mathematical object is considered to be a product of a construction of a mind, and therefore, the existence of an object is equivalent to the possibility of its construction. This contrasts with the classical approach, which states that the existence of an entity can be proved by refuting its non-existence. For the intuitionist, this is not valid; the refutation of the non-existence does not mean that it is possible to find a constructive proof of existence. As such, intuitionism is a variety of mathematical constructivism; but it is not the only kind.
As well, to say A or B, to an intuitionist, is to claim that either A or B can be proved. In particular, the law of excluded middle, A or not A, is disallowed since one can construct, via Gödel's incompleteness theorems, a mathematical statement that can be neither proven nor disproved.
The interpretation of negation is also different. In classical logic, the negation of a statement asserts that the statement is false; to an intuitionist, it means the statement is refutable (i.e., that there is a proof that there is no proof of it). The asymmetry between a positive and negative statement becomes apparent. If a statement P is provable, then it is certainly impossible to prove that there is no proof of P; however, just because there is no proof that there is no proof of P, we cannot conclude from this absence that there is a proof of P. Thus P is a stronger statement than not-not-P.
Intuitionistic logic substitutes justification for truth in its logical calculus. The logical calculus preserves justification, rather than truth, across transformations yielding derived propositions. It has given philosophical support to several schools of philosophy, most notably the Anti-realism of Michael Dummett.
Intuitionism also rejects the abstraction of actual infinity; i.e., it does not consider as given objects infinite entities such as the set of all natural numbers or an arbitrary sequence of rational numbers. This requires the reconstruction of the foundations of set theory and calculus as constructivist set theory and constructivist analysis respectively.
History of IntuitionismIntuitionism's history can perhaps be traced to the nineteenth century. Cantor and his teacher Kronecker — a confirmed finitist — disagreed. Frege's effort to reduce all of mathematics to a logical formulation was a scientific breakthrough in the department of logic, and it greatly inspired the younger generation, including a youthful Bertrand Russell.
But Frege himself counted it as failure when a young Bertrand Russell sent Frege a letter about his hot-off-the-presses first volume, outlining the famous paradox now known as Russell's Paradox, that showed how one of Frege's rules of self-reference was self-contradictory. Frege, the story goes, plunged into depression and did not publish the second and third volumes of his work as he had planned. For more see Davis (2000) Chapters 3 and 4: Frege: From Breakthrough to Despair and Cantor: Detour through Infinity. See van Heijenoort for the original works and Heijenoort's commentary.
In the early twentieth century Brouwer represented the intuitionist position and Hilbert the formalist — see van Heijenoort. Kurt Gödel offered opinions referred to as Platonist. (see various sources re Gödel). Alan Turing considers: "non-constructive systems of logic with which not all the steps in a proof are mechanical, some being intuitive" (Turing (1939) Systems of Logic Based on Ordinals in Undecidable, p. 210) Later, Kleene brought forth a more rational consideration of intuitionism in his Introduction to Meta-mathematics (1952). For the view that there are no paradoxes in Cantorian set theory — thus calling into question the program of intuitionist mathematics, see Alejandro Garciadiego's now-classic Bertrand Russell and the Origins of the Set-Theoretic Paradoxes.
Branches of intuitionistic mathematics
- W. S. Anglin, Mathematics: A Concise history and Philosophy, Springer-Verlag, New York, 1994.
- Martin Davis (ed.) (1965), The Undecidable, Raven Press, Hewlett, NY. Compilation of original papers by Gödel, Church, Kleene, Turing, Rosser, and Post.
- Engines of Logic: Mathematicians and the origin of the Computer
- John W. Dawson Jr., Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters, Wellesley, MA, 1997.
- Less readable than Goldstein but, in Chapter III Excursis, Dawson gives an excellent "A Capsule History of the Development of Logic to 1928".
- Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Godel, Atlas Books, W.W. Norton, New York, 2005.
- In Chapter II Hilbert and the Formalists Goldstein gives further historical context. As a Platonist Gödel was reticent in the presence of the logical positivism of the Vienna Circle. She discusses Wittgenstein's impact and the impact of the formalists. Goldstein notes that the intuitionists were even more opposed to Platonism than Formalism.
- van Heijenoort, J., From Frege to Gödel, A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge, MA, 1967. Reprinted with corrections, 1977. The following papers appear in van Heijenoort:
- L.E.J. Brouwer, 1923, On the significance of the principle of excluded middle in mathematics, especially in function theory [reprinted with commentary, p. 334, van Heijenoort]
- Andrei Nikolaevich Kolmogorov, 1925, On the principle of excluded middle, [reprinted with commentary, p. 414, van Heijenoort]
- L.E.J. Brouwer, 1927, On the domains of definitions of functions, [reprinted with commentary, p. 446, van Heijenoort]
- Although not directly germane, in his (1923) Brouwer uses certain words defined in this paper.
- L.E.J. Brouwer, 1927(2), Intuitionistic reflections on formalism, [reprinted with commentary, p. 490, van Heijenoort]
- Jacques Herbrand, (1931b), "On the consistency of arithmetic", [reprinted with commentary, p. 618ff, van Heijenoort]
- From van Heijenoort's commentary it is unclear whether or not Herbrand was a true "intuitionist"; Gödel (1963) asserted that indeed "...Herbrand was an intuitionist". But van Heijenoort says Herbrand's conception was "on the whole much closer to that of Hilbert's word 'finitary' ('finit') that to "intuitionistic" as applied to Brouwer's doctrine".
- Gnomes in the Fog. The Reception of Brouwer's Intuitionism in the 1920s
- Arend Heyting: Intuitionism: An Introduction
- Introduction to Meta-Mathematics
- In Chapter III A Critique of Mathematic Reasoning, §11. The paradoxes, Kleene discusses Intuitionism and Formalism in depth. Throughout the rest of the book he treats, and compares, both Formalist (classical) and Intuitionist logics with an emphasis on the former. Extraordinary writing by an extraordinary mathematician.
- Constance Reid, Hilbert, Copernicus - Springer-Verlag, 1st edition 1970, 2nd edition 1996.
- Definitive biography of Hilbert places his "Program" in historical context together with the subsequent fighting, sometimes rancorous, between the Intuitionists and the Formalists.
- Paul Rosenbloom, The Elements of Mathematical Logic, Dover Publications Inc, Mineola, New York, 1950.
- In a style more of Principia Mathematica -- many symbols, some antique, some from German script. Very good discussions of intuitionism in the following locations: pages 51-58 in Section 4 Many Valued Logics, Modal Logics, Intuitionism; pages 69-73 Chapter III The Logic of Propostional Functions Section 1 Informal Introduction; and p. 146-151 Section 7 the Axiom of Choice.
- A. A. Markov (1954) Theory of algorithms. [Translated by Jacques J. Schorr-Kon and PST staff] Imprint Moscow, Academy of Sciences of the USSR, 1954 [i.e. Jerusalem, Israel Program for Scientific Translations, 1961; available from the Office of Technical Services, U.S. Dept. of Commerce, Washington] Description 444 p. 28 cm. Added t.p. in Russian Translation of Works of the Mathematical Institute, Academy of Sciences of the USSR, v. 42. Original title: Teoriya algorifmov. [QA248.M2943 Dartmouth College library. U.S. Dept. of Commerce, Office of Technical Services, number OTS 60-51085.]
- A secondary reference for specialists: Markov opined that "The entire significance for mathematics of rendering more precise the concept of algorithm emerges, however, in connection with the problem of a constructive foundation for mathematics....[p. 3, italics added.] Markov believed that further applications of his work "merit a special book, which the author hopes to write in the future" (p. 3). Sadly, said work apparently never appeared.
intuitionism in Czech: Intuicionistická logika
intuitionism in German: Intuitionismus
intuitionism in Spanish: Intuicionismo
intuitionism in Esperanto: Intuiciismo
intuitionism in Croatian: Intuicionizam
intuitionism in Italian: Intuizionismo
intuitionism in Dutch: Intuïtionisme
intuitionism in Japanese: 数学的直観主義
intuitionism in Polish: Intuicjonizm (matematyka)
intuitionism in Portuguese: Intuicionismo
intuitionism in Russian: Интуиционизм
intuitionism in Turkish: Sezgici Matematik
intuitionism in Chinese: 数学直觉主义 | mathematics |
https://iq.wiki/wiki/elliptic-curve-cryptography-ecc | 2024-04-16T10:06:42 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817081.52/warc/CC-MAIN-20240416093441-20240416123441-00351.warc.gz | 0.949912 | 931 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__171844580 | en | Elliptic Curve Cryptography (ECC)
Elliptic Curve Cryptography (ECC) is a key-based technique for encrypting data famous for being smaller, faster, and more efficient than incumbents. ECC focuses on pairs of public and private keys for decryption and encryption of web traffic. ECC is frequently discussed in the context of the Rivest–Shamir–Adleman (RSA) cryptographic algorithm.
There are two main different types of encryptions - symmetric encryption, which uses one key to both encrypt and decrypt (e.g. AES), and asymmetric encryption, which uses two different keys (e.g. RSA). These are often called a public and private key, where the private key is not to be disclosed.
RSA uses integer factorization cryptography based on algebraic number theory, while elliptic curve cryptography (ECC) uses integer factorization cryptography based on elliptic curves.
Elliptic Curve Cryptography is a choice for public-key-cryptography, based on elliptic curves over finite fields.
ECC is used as the cryptographic key algorithm in Bitcoin because it potentially can save ~90% of the resources used by a similar RSA system.
RSA vs. ECC
ECC and RSA both generate a public and private key and allow two parties to communicate securely. One advantage to ECC however, is that a 256-bit key in ECC offers about the same security as a 3072-bit key using RSA. ECC allows resource-constrained systems like smartphones, embedded computers, and cryptocurrency networks to use ~10% of the storage space and bandwidth required by RSA.
Based on the idea that the key that anyone uses to encrypt data can be made public while the key that is used to decrypt your data can be kept private. As such, these systems are known as public key cryptographic systems. The first, and still most widely used of these systems, is known as RSA — named after the initials of the three men who first publicly described the algorithm: Ron Rivest, Adi Shamir and Leonard Adleman.
When both the RSA algorithm and the Diffie-Hellman key exchange algorithm were introduced, these new algorithms were revolutionary because they represented the first viable cryptographic schemes where security was based on the theory of numbers. It was the first to enable secure communication between two parties without a shared secret.
Cryptography went from being about securely transporting secret codebooks around the world to being able to have secure communication between any two parties without worrying about someone listening in on the key exchange.
After the introduction of RSA and Diffie-Hellman, researchers explored other mathematics-based cryptographic solutions looking for other algorithms beyond factoring that would serve as good Trapdoor Functions.
In 1985, cryptographic algorithms were proposed based on an esoteric branch of mathematics called elliptic curves.
An elliptic curve is the set of points that satisfy a specific mathematical equation, something that looks a bit like the Lululemon logo tipped on its side.
There are other representations of elliptic curves, but technically an elliptic curve is the set points satisfying an equation in two variables with degree two in one of the variables and three in the other. An elliptic curve has some properties that make it a good setting for cryptography.
Neal Koblitz and Victor Miller independently co-discovered elliptic-curve cryptography which is part of the mathematics that allows encrypted communication on the internet today.
In an interview with All About Circuits (AAC) in 2019, Dr. Koblitz said:
"What changed my feeling about number theory was the invention of RSA cryptography (Rivest-Shamir-Adleman) in about 1977. That was the first important application of number theory to computer security."
"The idea of elliptic-curve cryptography came in 1984. I, along with several other people received a pre-print, a rather preliminary-version, of an algorithm that Hendrik Lenstra developed to factor large integer numbers. If this algorithm was sufficiently fast, it could be a threat to RSA cryptography. "
Elliptic Curve Cryptography (ECC)
December 12, 2023
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Give this wiki a quick rating to let us know! | mathematics |
https://homesteepedhope.com/2010/09/ | 2023-06-04T00:58:24 | s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224649348.41/warc/CC-MAIN-20230603233121-20230604023121-00565.warc.gz | 0.902191 | 486 | CC-MAIN-2023-23 | webtext-fineweb__CC-MAIN-2023-23__0__72607778 | en | Ever wonder which fraction problems need inverted and multiplied, or which ones call for finding the least common denominator before you can do anything else? Keeping track of the procedures used for adding, subtracting, multiplying and dividing these fractions can be tricky for grade schoolers (and their parents!). Here’s some help!
But first a plug! We love our Professor B Math! It’s a contextual way to learn all aspects of math from a practical viewpoint in the least amount of time possible, and at your own pace. In spite of being a straight A student, I never learned math this way in grade school…and consequently, I feel like it’s finally making sense to me these past few years of teaching Professor B’s methods to my children.
So my daughter is learning ALLLL about fractions and we got the coolest fraction “tips” in today’s lesson.
Here you go for the next time your child is stumped as to which procedure to use for which fractional operation…
Know the code:
f=fraction, MN=mixed number, LCD=least common denominator
When the first formula says “f+f = LCD then add” it’s a short hand way of saying: “fraction plus fraction equals finding the least common denominator, then adding the fractions”…
Okay…for the formulas:
- f+f=LCD then add
- f-f=LCD then subtract
- fxf=reduce (if possible), then multiply across
- f (divided by) f=invert and multiply
- MN+MN=LCD then add
- MN-MN=LCD then subtract
- MNxMN=set up fraction, then multiply fraction
- MN (divided by) MN=set up fraction then divide by fraction
If you drill your children on these formulas, and keep a “cheat sheet” taped to the inside of their mathbooks, eventually they won’t have to think very hard about which formula applies to their various fraction pursuits!
Gotta love it!
Professor B says whatever you do, if you learn your fractions backwards and forwards algebra will be a lot less intimidating!
Hope this helps some harried mom out there with her child’s homework! | mathematics |
http://www.solar4stem.com/store/p7/Dial_Gauge_Angle_Finder.html | 2023-09-28T08:44:34 | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233510368.33/warc/CC-MAIN-20230928063033-20230928093033-00256.warc.gz | 0.857217 | 204 | CC-MAIN-2023-40 | webtext-fineweb__CC-MAIN-2023-40__0__262432557 | en | Dial Gauge Angle Finder
This Dial gauge angle finder can be used to measure the angle of the surface of an object with respect to the horizon. The weighted needle always points up, perpendicular to the horizon, while the side of the angle finder is held against the surface to be measured. The angle of the solar panels aimed at the sun is measured with the angle finder.
- Dial gauge angle measurements
- Measures angle from the horizon
- Measures 0 to 90 degrees
- Accuracy of 0.5 degrees
Make STEM Fun & Easy!
Located in Pinellas Park, FL, solar4STEM has been providing parents and educators interactive STEM kits to keep kids engaged. Let us help you make STEM fun & easy with hands-on experiments!
3845 Gateway Centre Blvd.,
Pinellas Park, FL 33782 | mathematics |
http://www.thisisnotahoax.com/ | 2020-01-18T01:58:24 | s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250591431.4/warc/CC-MAIN-20200117234621-20200118022621-00320.warc.gz | 0.853605 | 155 | CC-MAIN-2020-05 | webtext-fineweb__CC-MAIN-2020-05__0__88385392 | en | A car accelerates uniformly from rest to 20 m/s in 5 seconds. Determine the acceleration of the car and the distance traveled.
First, you calculate the acceleration by subtracting the initial velocity from the final velocity and then dividing by the time.
vf - vi = 20 - 0 = 20 m/s
a = 20 / t = 20 / 5 = 4 m/s^2
Next, you calculate the displacement by multiplying the initial velocity by the time and adding that to the product of one-half times the acceleration times the time squared.
d = (vi * t) + (.5 * a * t^2)
d = (0 * 5) + (.5 * 4 * 5^2) = 50 m | mathematics |
https://www.plumcroftprimary.co.uk/page/?title=Year+1&pid=25 | 2020-09-24T02:25:28 | s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400213006.47/warc/CC-MAIN-20200924002749-20200924032749-00734.warc.gz | 0.923306 | 455 | CC-MAIN-2020-40 | webtext-fineweb__CC-MAIN-2020-40__0__241843799 | en | Our topic this term is called ‘Toys’. We will be using a variety of fiction texts as our stimulus: Benjamin Boo, Brown Paper Bear, Here Comes Traction Man and Toys in Space. The children will be writing labels and captions, story writing and producing instructions and information pages related to these books and to toys they’ve looked at or made.
Our topic will be linked to the books we are reading and using in our literacy lessons.
In art we will be making junk model aliens and ‘cuddly’ alien toys. In science we will be looking at materials that float and sink; we will be discovering the best materials to use for a mini parachute; we will also be looking at friction and gravity. In history the children will be finding out how the materials used in toys have changed over time; the children will also make old fashioned peg dolls (with a super hero twist!) and thread spinners. We will be taking part in a toy workshop where the children will have the opportunities to play with Victorian and Edwardian toys.
This term the children will be consolidating the core number concepts learned in Reception. This includes counting on from any number, finding one more or one less than a number to 20 and solving one-step addition and subtraction questions. We will also begin learn how to count in multiples of 2, 5 and 10 (we will use counting songs from YouTube).
We will continue to learn about - and explore – shapes. The children will revise the names and properties of common 2D shapes; they will also learn about 3D shapes and their properties. In addition the children will learn how to describe direction, movement and position.
Your child will need to wear the following kit which should be kept in school throughout this half term: light blue t-shirt, black shorts and plimsolls or trainers. The t-shirt will be provided by the school.
PE days are as follows:
1H - Tuesday morning
1N - Wednesday morning
1C - Thursday Morning
1M (VR) - Tuesday Afternoon
1W (VR) - Wednesday Afternoon
Home reading books will be changed on your child's PE day. | mathematics |
https://www.eourmart.com/blogs/news/understanding-the-difference-between-a-normal-calculator-and-a-scientific-calculator | 2024-04-15T12:57:31 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816977.38/warc/CC-MAIN-20240415111434-20240415141434-00797.warc.gz | 0.893728 | 605 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__112501977 | en | A normal calculator, often referred to as a basic calculator or pocket calculator, is a simple device designed primarily for performing fundamental arithmetic operations. Here are the key characteristics of a normal calculator:
- Arithmetic Functions: A normal calculator can handle basic arithmetic functions, including addition, subtraction, multiplication, and division. It's ideal for everyday calculations like balancing your checkbook, calculating tips, or solving simple math problems.
- Limited Functions: Normal calculators typically have a limited set of functions and buttons. You'll find keys for numbers, basic operations (+, -, *, /), and possibly a percentage key.
- Compact and Portable: These calculators are compact, lightweight, and easy to carry around. They are battery-powered and fit easily in a pocket or purse.
- Affordable: Normal calculators are inexpensive and readily available. They are suitable for everyday use and are widely used in schools and offices.
A scientific calculator is a more advanced and versatile tool designed for complex mathematical and scientific calculations. Here's what sets it apart from a normal calculator:
- Advanced Functions: Scientific calculators are equipped with a wide range of functions beyond basic arithmetic. They can handle trigonometric functions (sin, cos, tan), logarithms, exponentiation, square roots, and more. These functions are essential for students and professionals in fields like mathematics, engineering, and science.
- Multi-line Display: Scientific calculators typically feature a multi-line display that allows users to see both the input and the result simultaneously. This is incredibly useful for tracking complex calculations.
- Constants and Variables: Scientific calculators often provide the ability to work with constants and variables, making them indispensable for solving algebraic equations and scientific problems.
- Programmable Features: Some high-end scientific calculators offer programmable functions, allowing users to create custom calculations and formulas. This is particularly useful in research and engineering.
- Notation Modes: Scientific calculators may support different notation modes, including degrees and radians, to accommodate various mathematical conventions.
When to Use Each Calculator:
Normal Calculator: Use a normal calculator for basic everyday math, such as addition, subtraction, multiplication, and division. It's perfect for quick calculations where advanced functions aren't necessary.
Scientific Calculator: Opt for a scientific calculator when you need to perform more complex mathematical or scientific calculations. These are invaluable tools for students, engineers, scientists, and professionals working with advanced mathematics.
In summary, normal calculators and scientific calculators serve different purposes, with the latter offering an array of advanced functions tailored to scientific and mathematical applications. Choosing the right calculator depends on your specific needs, so be sure to consider the complexity of your calculations before making your selection. Whether you need a basic calculator for simple math or a scientific calculator for advanced calculations, having the right tool on hand can make a world of difference in your work or studies. | mathematics |
http://globaledgebet.com/index.php/positive-odds-edge/ | 2019-05-19T18:51:56 | s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255092.55/warc/CC-MAIN-20190519181530-20190519203530-00318.warc.gz | 0.97696 | 179 | CC-MAIN-2019-22 | webtext-fineweb__CC-MAIN-2019-22__0__150477116 | en | Trading in the Global Sports Betting Market
If bets were placed on the toss of a coin, the probability of heads is 50 %, the probability of tails is 50%. Regarding bookmaker decimal odds, 50% probability is expressed as odds of 2.0. Which means that if bets were continuously placed on either heads or tails at odds of 2.0, over the long term the bettors’ bankroll would break even.
However, if odds of 2.2 were available from the market, the odds of 2.2 are miss-priced as they are greater than 2, which means a real odds edge is available. The correctly priced odds are 2 which is a probability of 50%, odds of 2.2 is a probability of 45.5%, which means a real odds edge of +4.5% (50% – 45.5%) exists. | mathematics |
https://thesuperengineer.com/mathematical-modeling-engineer/ | 2023-12-02T04:21:47 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100327.70/warc/CC-MAIN-20231202042052-20231202072052-00258.warc.gz | 0.903416 | 965 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__36579057 | en | Mathematical Modeling Engineer
Unravel Complexity and Drive Efficiency with Our Mathematical Modeling Engineer
In the ever-evolving landscape of engineering, one tool has emerged as a driving force behind innovation and efficiency – mathematical modeling. At the intersection of abstract mathematical concepts and real-world engineering challenges, our Mathematical Modeling Engineer operates, providing solutions that illuminate complex problems and revolutionize decision-making processes.
Who is a Mathematical Modeling Engineer?
A Mathematical Modeling Engineer employs mathematical methods and theories to develop models that mirror real-world engineering systems, scenarios, or phenomena. This unique approach transcends empirical observation, unveiling intricate dynamics, predicting outcomes, and informing strategic decisions.
How Our Mathematical Modeling Engineer Can Benefit Your Business:
- Reveal Complex Physical Problems in Engineering: With the power of mathematical modeling, complex engineering challenges are converted into solvable mathematical problems. By analyzing these models, our engineer can unravel intricate dynamics, discover underpinning principles, and generate solutions that might have remained obscured in a purely empirical approach.
- Reduce Troubleshooting Costs: In engineering, troubleshooting can be a lengthy and expensive process. Mathematical modeling offers an efficient alternative. By simulating various scenarios or system configurations, our Mathematical Modeling Engineer can identify potential problems before they occur, saving time and reducing troubleshooting costs.
- Accelerate R&D Processes: Mathematical models enable experimentation that would be too costly, time-consuming, or even impossible to conduct in the real world. By testing hypotheses and exploring system behavior in the mathematical realm, our engineer can expedite the R&D process, leading to faster innovation and lower costs.
Why Choose Our Mathematical Modeling Engineer?
Expertise Across Domains:
Our Mathematical Modeling Engineer brings a solid foundation in mathematics and a deep understanding of various engineering disciplines. This combination enables them to develop reliable and versatile models for a wide range of applications.
Advanced Tools and Techniques:
Equipped with state-of-the-art mathematical software and advanced modeling techniques, our Mathematical Modeling Engineer delivers robust, accurate models that pave the way for efficient problem-solving and effective decision-making.
Holistic Engineering Solutions:
As part of our comprehensive suite of engineering services, our Mathematical Modeling Engineer can collaborate with other specialists in our team, ensuring that you receive holistic solutions tailored to your unique engineering needs.
With extensive experience in applying mathematical modeling to real-world engineering problems, our engineer understands the nuances and complexities of various sectors, providing insights and solutions that are practically viable and impactful.
Our Mathematical Modeling Engineer can help your business navigate complexity, improve efficiency, and accelerate innovation. Reach out to us today to discover how our Mathematical Modeling Engineer can transform your engineering challenges into strategic advantages.
Case Study 1: Optimizing Production in Automotive Manufacturing
Background: An automotive manufacturer was seeking to optimize their production line to improve throughput and reduce costs.
Solution: Our Mathematical Modeling Engineer developed a model simulating the entire production process, taking into account various factors such as machine speeds, setup times, worker schedules, and raw material availability. By manipulating these variables within the model, they identified an optimal configuration that increased throughput and minimized costs.
Result: The company implemented the suggested changes and saw a 15% increase in production throughput and a significant reduction in operational costs.
Case Study 2: Risk Mitigation in Renewable Energy Project
Background: A renewable energy company wanted to assess the financial viability and potential risks of a large-scale wind farm project.
Solution: Our Mathematical Modeling Engineer built a comprehensive model incorporating factors like projected wind speeds, turbine efficiency, maintenance costs, and potential downtime. They were able to predict energy output, identify potential risks, and calculate projected returns.
Result: Armed with this information, the company could make informed decisions about the project, balancing potential risks and returns. The project has since been successful, with performance closely matching the predictions from the mathematical model.
Case Study 3: Reducing R&D Costs in Medical Devices
Background: A medical device company was developing a new product but wanted to reduce the time and costs associated with R&D.
Solution: Our Mathematical Modeling Engineer created a model simulating the functionality of the device, allowing for extensive testing and refinement in a virtual environment. This approach significantly reduced the need for physical prototyping and testing.
Result: The company was able to accelerate the development process, reduce R&D costs, and bring the product to market faster than traditionally possible.
These case studies demonstrate how our Mathematical Modeling Engineer can provide actionable insights across various sectors, driving efficiency, mitigating risks, and accelerating innovation. | mathematics |
https://modmomtv.com/texas-instruments-2-line-scientific-calculator-8-88-reg-17/ | 2023-04-02T02:33:11 | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00583.warc.gz | 0.909205 | 138 | CC-MAIN-2023-14 | webtext-fineweb__CC-MAIN-2023-14__0__279090581 | en | Get a jump start on back to school shopping and score this Texas Instruments 2-Line Scientific Calculator for only $8.88 (Reg. $17). If you have a high school student, you probably need this.
- Robust, professional grade scientific calculator. Logs and antilogs
- It has 2-line display shows entry and calculated result at same time
- Easily handles 1 and 2 variable statistical calculations and three angle modes (degrees, radians, and grads) and scientific and engineering notation modes
- It has 1-year limited warranty
- The front of the calculator is black, the back cover is in fact a dark blue-gray | mathematics |
http://apptitudedevelopers.com/ | 2017-03-30T18:36:45 | s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218199514.53/warc/CC-MAIN-20170322212959-00228-ip-10-233-31-227.ec2.internal.warc.gz | 0.923073 | 326 | CC-MAIN-2017-13 | webtext-fineweb__CC-MAIN-2017-13__0__76110359 | en | 04/28/2011: JUMPIN' MATH JAM FREE has just been released! It is a free ad supported trial version of JUMPIN' MATH JAM, but includes only addition and multiplication. Give it a try!
04/12/2011:Get a preview of JUMPIN' MATH JAM on YOUTUBE! You can learn how the game works, discover features, and determine if this app is right for you!
04/09/2011: JUMPIN' MATH JAM USERS: Thank you very much for your positive feedback!
v1.1 Has just been released in response to your requests for new features! Check it out on the Android Market!
APPTITUDE DEVELOPERS is pleased to announce the launch of its first mobile application for the Android platform, JUMPIN' MATH JAM!
JUMPIN' MATH JAM is a really fun way to practice addition, subtraction, multiplication, and division facts as you (a frog) try to beat the turtle in a race to the next level. It's a fun game that's more entertaining than math flash cards, and can be quite addictive! For 5th graders and older, the "random" mode is recommended as it takes you through all operations up to the 12's tables. For earlier elementary students, focusing on just one operation at a time can help reinforce skills. As you go through the levels, the game moves faster and faster! JUMPIN' MATH JAM can be found in the Android Marketplace. | mathematics |
https://945wpti.iheart.com/content/2022-05-10-north-carolina-mans-love-of-math-wins-him-major-lottery-prize/ | 2022-07-03T12:14:00 | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104240553.67/warc/CC-MAIN-20220703104037-20220703134037-00082.warc.gz | 0.992441 | 357 | CC-MAIN-2022-27 | webtext-fineweb__CC-MAIN-2022-27__0__206557072 | en | A North Carolina man's love for math ending up winning him more than just good grades in school — he was the lucky winner of a nearly $200,000 lottery jackpot.
Jonathan Ruby, of Raleigh, recently tried his luck in the Cash 5 lottery games, purchased a $1 ticket from the Han-Dee Hugo's on Hillsborough Street for the Nov. 28 drawing, according to a release from the NC Education Lottery. The lover of math used a well known number — pi, or 3.1415 — to choose his ticket, a move that ended up winning him a third of the $578,823 jackpot, splitting the prize with two other lucky winners.
"I've always been an extremely big math person," said Ruby. "I picked my numbers based on pi."
Ruby told lottery officials that the lucky sequence has shown up in different ways throughout his life, so he took it as a sign to get his ticket.
"I kept seeing that number so my karma told me to use it," he said. "I even lived at a 314 address as a child."
Ruby had a good feeling about his ticket, sure that he had won something, but it wasn't until later that he realized just how lucky he was.
"I thought I won a dollar or two," Ruby said. "I was calm until I got home and checked the numbers and then I got very excited."
Ruby claimed his $192,941 jackpot at lottery headquarters on Monday (May 9), bringing home a total of $137,012 after taxes. When asked what he plans to do with his prize, the 64-year-old bartender told lottery officials he plans to pay some bill and save the rest for retirement. | mathematics |
https://ivaschool.online/?tcb_lightbox=testimonial3 | 2022-08-19T17:53:45 | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573744.90/warc/CC-MAIN-20220819161440-20220819191440-00759.warc.gz | 0.968357 | 424 | CC-MAIN-2022-33 | webtext-fineweb__CC-MAIN-2022-33__0__45934598 | en | Mr. Luis was my mathematics teacher throughout my matriculation at the Oprah Winfrey Leadership Academy for Girls (OWLAG). I entered OWLAG from amongst the most under-resourced primary schools of my admission class. This meant that I was both at a relative academic disadvantage while being newly inducted to the level of academic rigour of a private South African high school. With all the odds stacked against me, I graduated high school as one the top students in mathematics and valedictorian of my class, and Mr. Luis was undoubtedly paramount in my ability to achieve this feat.
Throughout my time at OWLAG, Mr. Luis was committed to excellence in education and had the unshakeable belief in any students’ ability to grasp mathematics given a teacher who is skilled at playing to their students’ strengths while cognisant of areas that pose a challenge for them. He embodied this commitment and belief through relentless and tireless help and support, going as far as giving up his weekday afternoons and Saturdays spending countless hours giving extra review classes and helping me and my class keep up with the increased pace in mathematics he introduced because he envisioned us performing at the level of some of South Africa’s best schools, despite our backgrounds.
Almost ten years later, and having graduated salutatorian of my undergraduate class pursuing a BS in Biology at Spelman College in Atlanta; earned a MSc in Medical Anthropology at the University of Oxford in the UK and currently pursuing a medical degree at Stanford University in California, Mr. Luis remains one of the best teachers I have ever had. His love for mathematics (and teaching) remains unmatched. He always finds innovative ways of teaching and making mathematics instinctive. I know I speak for many of my OWLAG peers when I say, he created an engaging and fun learning environment that made an infamously hard subject rather enjoyable. Whether it was to travel the world or be the next world’s best mathematicians, we always left his classes feeling incredibly inspired.
Past Student Of John Luis | mathematics |
https://www.kingethelbert.com/curriculum/subject-information/mathematics | 2023-03-21T00:40:24 | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296943589.10/warc/CC-MAIN-20230321002050-20230321032050-00211.warc.gz | 0.958609 | 1,327 | CC-MAIN-2023-14 | webtext-fineweb__CC-MAIN-2023-14__0__132192220 | en | In the Maths department we aim to embed the whole school curriculum intent, through and beyond our curriculum. We do these in line with the three principles across the school.
|Globally Diverse||Ambitious for the Future||Inquisitive Learners|
In Maths we aim to raise awareness around the following financial topics through the mathematics students learn:
In Maths we also aim to raise awareness of how mathematics can be used to mislead, Teachers identify this through:
Students are introduced to famous mathematicians around the world and their contributions to the mathematics we study today.
In Maths we strive to ensure that all students are numerate by the end of Key Stage 3. We aim to end the phrase ‘I can’t do maths’ by developing confidence and instilling a growth mindset in all our students.
We regularly raise awareness of different professions relating to maths and identifying possible ways where students will require maths in future careers.
We regularly set homework to promote self study and organisation.
We hold regular revision sessions to support independent study. Pupils also have the opportunity to purchase revision resources to help support them in their independent studies.
The mathematics department provides opportunities for students to explore their knowledge and face challenges. Previous opportunities provided include UKMT team challenges, the British Museum, Faraday Challenge and Thorpe Park.
At KS5 pupils are taught the applications and interpretations IB mathematics course; this encourages students to further develop their understanding through investigations and applying these to real life. Students currently have the opportunity to study this at both standard and higher level
There is a large focus in the mathematics curriculum towards problem solving. Staff work with students to develop the resilience and critical thinking skills to break down larger problems into smaller more manageable ones. These are often also taught through real life applications
In all Key Stages students are introduced to different careers in mathematics in lessons and as part of careers week within the school.
The mathematics department are passionate about the subject they teach and want all pupils to share this passion.
Our curriculum develops problem solving skills and provides students with the opportunity to make connections. They will develop their mathematical communication both verbally and in written work. Students will develop resilience, independence and take ownership of their learning through rich open tasks and research based learning.
We want to ensure that students take pride in their work. Presentation is key to showing good mathematics with logic and organised thought. Students will critically evaluate their own work and develop their previous learning through encouragement of reflections, reviewing and correcting.
We want pupils to leave KS4 with the skills to continue studying maths at KS5 and beyond.
Our schemes of learning in all Key Stages develops mastery of skills and will develop links to other subjects. Students will develop a greater depth to their knowledge and be able to apply this to various contexts. They will also better develop their vocabulary with subject specific words.
The mathematics curriculum is a spiralling curriculum allowing students to revisit and build on their knowledge developing the idea that we can always further our knowledge and understanding of different topics. Especially as they mature and their prioritise for studies change depending on their choices for their future.
In key stage 3, we have a mastery curriculum, allowing students to develop both fluency and understanding. They build on their knowledge, developing the idea that we can always further our knowledge and understanding of different topics. We use rich open tasks, developing resilience, independence and ownership of learning. Clear written communication and presentation is promoted which students can use in all aspects of their learning. During ‘Maths Week’, students have the opportunity for self-discovery, particularly in Year 8 when they investigate Pythagoras’ Theorem.
We use rich and open ended tasks which allow students to discover their own insights and apply to the real world. This helps with resilience and problem solving too. We regularly set homework to promote self study and organisation.
The Mathematics department provides opportunities for students to explore their knowledge and face challenges. Previous opportunities provided include UKMT team challenges, the Maths Feast, the British Museum, Bletchley Park, Faraday Challenge and Thorpe Park.
We have an annual ‘Maths Week’ which presents maths in real life and problem solving situations to help students make links between the subject and their everyday life. In addition, Year 7 considers estimating as it is a vital skill in budgeting and financial mathematical fluency.
We teach about best buys through ratio in Year 8, so students can understand value for money. Class discussions give students the opportunity to build listening skills and mutual respect. Investigations ask students to share responsibility with others and work collaboratively. Students are asked to reflect upon their own learning, to further understand and develop their learning journey.
In key stage 4 students study the GCSE Mathematics course, we have designed our curriculum so topics are interwoven and further develop mastery, problem solving and resilience, leading to independent learners who take ownership of their own learning. Students also have the opportunity to make greater connections between subjects and develop their own learning. Statistics GCSE for our most able students gives the opportunity for critical thinking and real life applications for their learning by forcing justification behind answers, spotting misleading information and understanding/arguing different points of view. We teach financial maths such as compound interest, depreciation, loans and mortgages. Through work on representing and analysing data, students begin to think critically about information that is presented to them as well as being exposed to situations where data may be misleading.
Some students also pursue GCSE Statistics which allows students to become better critical learners, looking further than the initial data or information to understand the situation. We continue setting regular homework to promote self study and organisation.
In key stage 5 students can study IB Mathematics Applications and Interpretation, through this course we continue to develop students' independence of study. The introduction of IB mathematics gives more opportunities for application of mathematics and real life scenarios. The Internal Assessment stretches students beyond the outlined curriculum, giving opportunities for personal investigation. The course also encourages students to further develop their understanding through investigations and applying these to real life.
We continue to develop students’ independence with the introduction of the internal assessment. Firm deadlines are introduced which compel students to manage their time. Students are given the opportunity to teach each other, becoming responsible for others' learning as well as their own. In this scenario, students use their presentation and pupil speaking skills as well as ensuring they are prepared in a timely manner. | mathematics |
https://jacobsfoundation.org/fellows/jacobs-foundation-research-fellowship-en/darko-odic/ | 2024-03-04T05:33:26 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476413.82/warc/CC-MAIN-20240304033910-20240304063910-00348.warc.gz | 0.940366 | 567 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__13529914 | en | Darko Odic’s research examines how children acquire abstract cognitive and perceptual representations, including those of number, confidence, and mathematical thought. By examining individual and developmental differences in, for example, how children’s earliest intuitions about number inform their formal math abilities, he seeks to understand why children sometimes learn complex ideas with ease, and sometimes struggle.
My plans for the fellowship period
To learn, we must make mistakes. But mistakes are only useful when they are noticed, evaluated, and corrected. When learning mathematics, a topic particularly challenging for many children around the world, “error monitoring” is especially important: math problems often require one answer in a sea of (literally) infinite possibilities. Unlike learning about gravity through building blocks, math problems do not physically fall down when a mistake is made; unlike learning social skills, math problems don’t flash with moments of anger or joy; unlike reading, math mistakes do not lead to meaningless strings of words.
During the Fellowship period, I will be investigating one potential mechanism for how children catch errors in mathematics: by using their intuitive (but approximate) sense of number. We hypothesize that young children use their intuitive number system to arrive at a probabilistic prediction of the likely answer for a simple equation and therefore catch when they are likely to have made a mistake. We have recently shown that differences in children’s number sense correlate with detecting math mistakes made by others. Over the next 2-4 years my lab plans to: (1) use pupillometric measures to measure the degree of surprise children experience when catching mistakes in mathematics; (2) temporarily enhance or impair children’s intuitive number sense and observe the effects this has on their error monitoring; and (3) train children to actively make predictions about the outcomes of math problems to increase the chance of catching and learning from mistakes. I aim to provide both a mechanistic understanding of how core cognition contributes to formal concepts and to characterize why some children are more successful at learning about math compared to others.
How will my work change children’s and youth’s lives?
My research focuses on children’s early mathematical abilities, which have consistently been shown to predict later school and job success, income level, happiness, and personal health. It will help identify mechanisms that allow children to be more independent, effective, and self-efficacious learners, ultimately informing educators on how children can learn complex topics with minimal external feedback. The current proposal, therefore, helps identify the conditions and skills that children should ideally maximize to deepen their development and ability to contribute to society. And, because the intuitive number sense is present in every child from birth, this work also has important universal implications, and seems to promote education initiatives across traditional cultural and economic divides. | mathematics |
http://draketechnologies.com/LoadQAce.php3?r=qAceGreen&f=/Calculators/Retirement.htm&l= | 2013-05-20T05:20:15 | s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698354227/warc/CC-MAIN-20130516095914-00005-ip-10-60-113-184.ec2.internal.warc.gz | 0.922834 | 175 | CC-MAIN-2013-20 | webtext-fineweb__CC-MAIN-2013-20__0__150047742 | en | Use this calculator to compute how much you would need to have invested in order to withdraw a specified amount each year over the course of a specified period of time. For example, if you want to be able to withdraw $500 during each month of your expected 20-year retirement, this calculator will tell you that if you expect to earn a 10% interest rate you will need to have $51,812.30 saved up by the time you retire. This is often referred to as "Present Value of an Annuity" analysis.
This is a hypothetical example used for illustrative purposes only and does not represent the return of any specific investment. Actual rates of return will vary over time; particularly for long-term investments.
To compute the Present Value of an Annuity, fill in the first three text boxes and then click the "compute" button. | mathematics |
https://oxfordshireteachertraining.co.uk/blog/episode-30-in-this-episode-of-the-oxfordshire-teacher-training-podcast-matthew-coatsworth-discusses-the-wonderful-work-of-the-ncetm-the-national-centre-for-excellence-in-the-teaching-of-mathemati/ | 2022-06-28T23:42:21 | s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103619185.32/warc/CC-MAIN-20220628233925-20220629023925-00286.warc.gz | 0.92192 | 237 | CC-MAIN-2022-27 | webtext-fineweb__CC-MAIN-2022-27__0__40634433 | en | In this episode of the Oxfordshire Teacher Training podcast, Matthew Coatsworth discusses the wonderful work of the NCETM – the National Centre for Excellence in the Teaching of Mathematics – with NCETM Professional Development Leads and Oxfordshire Teacher Training Mentors Claire Shorrock and Crispin Hoad. Claire and Crispin outline some of the key work of the NCETM, the BBO Maths Hub, Teaching for Maths Mastery and the five big ideas, as well as how to cater for the wide variation of mathematical ability within classes and how to adapt teaching effectively.
Please note that this episode was recorded remotely and unfortunately the sound quality from Claire’s device is a little distorted. We hope it does not affect your listening too much!
Links to resources mentioned in the podcast:
(Bucks, Berks and Oxon Maths Hub)
(KS3 Subject Audits) | mathematics |
https://eduebookstore.com/product/a-first-course-in-probability-9th-edition-by-sheldon-ross-isbn-13-978-0321794772-2/ | 2023-03-30T13:49:32 | s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949331.26/warc/CC-MAIN-20230330132508-20230330162508-00228.warc.gz | 0.910797 | 779 | CC-MAIN-2023-14 | webtext-fineweb__CC-MAIN-2023-14__0__170050464 | en | A First Course in Probability 9th Edition by Sheldon Ross, ISBN-13: 978-0321794772
[PDF eBook eTextbook]
- Publisher: Pearson; 9th edition (December 21, 2012)
- Language: English
- 480 pages
- ISBN-10: 032179477X
- ISBN-13: 978-0321794772
This book is intended as an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences (including computer science, biology, the social sciences, and management science) who possess the prerequisite knowledge of elementary calculus. It attempts to present not only the mathematics of probability theory, but also, through numerous examples, the many diverse possible applications of this subject.
Content and Course Planning
Chapter 1 presents the basic principles of combinatorial analysis, which are most useful in computing probabilities.
Chapter 2 handles the axioms of probability theory and shows how they can be applied to compute various probabilities of interest.
Chapter 3 deals with the extremely important subjects of conditional probability and independence of events. By a series of examples, we illustrate how conditional probabilities come into play not only when some partial information is available, but also as a tool to enable us to compute probabilities more easily, even when no partial information is present. This extremely important technique of obtaining probabilities by “conditioning” reappears in Chapter 7, where we use it to obtain expectations.
The concept of random variables is introduced in Chapters 4, 5, and 6. Discrete random variables are dealt with in Chapter 4, continuous random variables in Chapter 5, and jointly distributed random variables in Chapter 6. The important concepts of the expected value and the variance of a random variable are introduced in Chapters 4 and 5, and these quantities are then determined for many of the common types of random variables.
Additional properties of the expected value are considered in Chapter 7. Many examples illustrating the usefulness of the result that the expected value of a sum of random variables is equal to the sum of their expected values are presented. Sections on conditional expectation, including its use in prediction, and on momentgenerating functions are contained in this chapter. In addition, the final section introduces the multivariate normal distribution and presents a simple proof concerning the joint distribution of the sample mean and sample variance of a sample from a normal distribution.
Chapter 8 presents the major theoretical results of probability theory. In particular, we prove the strong law of large numbers and the central limit theorem. Our proof of the strong law is a relatively simple one that assumes that the random variables have a finite fourth moment, and our proof of the central limit theorem assumes Levy’s continuity theorem. This chapter also presents such probability inequalities as Markov’s inequality, Chebyshev’s inequality, and Chernoff bounds. The final section of Chapter 8 gives a bound on the error involved when a probability concerning a sum of independent Bernoulli random variables is approximated by the corresponding probability of a Poisson random variable having the same expected value.
Chapter 9 presents some additional topics, such as Markov chains, the Poisson process, and an introduction to information and coding theory, and Chapter 10 considers simulation.
As in the previous edition, three sets of exercises are given at the end of each chapter. They are designated as Problems, Theoretical Exercises, and Self-Test Problems and Exercises. This last set of exercises, for which complete solutions appear in Solutions to Self-Test Problems and Exercises, is designed to help students test their comprehension and study for exams.
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https://holtville.ech.schoolinsites.com/lyndee_antley | 2022-10-07T22:52:10 | s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030338280.51/warc/CC-MAIN-20221007210452-20221008000452-00077.warc.gz | 0.97502 | 189 | CC-MAIN-2022-40 | webtext-fineweb__CC-MAIN-2022-40__0__138954679 | en | I am a native Slapoutian and a third generation graduate of Holtville High School. I am married to Casey Antley who is also a graduate of Holtville High School. We have a daughter, Scarlett, and three large fur babies. My husband and I both take a lot of pride in our school and our community.
I graduated from Holtville in 2009 and went on to AUM where I graduated in 2014 with my degree in Secondary Education - Mathematics. Recently, I returned to AUM where I completed my Masters in Math Education. After college, I spent a year teaching 7th grade math at Eclectic Middle School before returning "home" to HHS in 2016. I have been teaching math here at HHS ever since. I love math and I hope to pass on my love for the subject to my students.
Please feel free to contact me at anytime if there is anything I can do to help your student succeed! | mathematics |
http://mrsquitt.weebly.com/blog/week-of-may-4-2015 | 2023-12-11T06:50:45 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679103558.93/warc/CC-MAIN-20231211045204-20231211075204-00643.warc.gz | 0.931612 | 394 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__132123025 | en | Summer Curriculum Correspondence
It is already that time of the year to start thinking about the summer. It is vital that each student retains and even improves academic skills during the summer weeks. The jump to third grade is a very significant one.
If your student participates in the Summer Correspondence program, each week for 6 weeks during the summer, your student will receive a packet to help him/her maintain grade level skills. If they finish all of the packets and return the completed cover sheet when school restarts in August, they earn a recognition.
If you would like your student to participate in this summer's Curriculum Correspondence program, please send in six (6) number 10 (that's legal sized) envelopes. Each envelope must have postage affixed. Each envelope must have your mailing address and your student's name. Each envelope should have your mailing address as the return address. Turn the envelopes in to your child's teacher.
We are starting Unit 7, Arrays, Partitioned Rectangles, and Equal Shares, this week. Please see the informational letter sent home on Monday for more specific info.
In this unit, students should be able to arrange items in rectangular arrays and partition rectangles into equal shares. Use the paper Square-Inch Tiles sent home Monday for practice.
Students should be able to:
• easily identify and know the difference between columns and rows
• measure a rectangle and draw lines to partition it into square centimeters or square inches
• partition a rectangular array into halves, thirds, and fourths
• partition a rectangular array by measuring in square centimeters or square inches
• fold a circle to make equal halves and fourths
• fold a rectangle into equal halves, thirds, and fourths in different ways
• solve word problems involving lengths
• use a number line diagram to add and subtract within 100
• calculate the perimeter (distance around) of a shape | mathematics |
https://mehtaplus.medium.com/perpetual-learning-our-journey-with-math-kangaroo-bb77135332b6 | 2023-10-04T06:53:19 | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511361.38/warc/CC-MAIN-20231004052258-20231004082258-00416.warc.gz | 0.982045 | 1,200 | CC-MAIN-2023-40 | webtext-fineweb__CC-MAIN-2023-40__0__165386027 | en | By Haripriya Mehta, Co-founder of MehtA+
When the CEO of Math Kangaroo USA, Ms. Joanna asked if MehtA+ would be interested in sponsoring 3000+ digital kits for the 2021 Math Kangaroo competition, without a moment of hesitation, I said yes.
My brother (and the other co-founder of MehtA+) and I had participated in Math Kangaroo since elementary school. I had placed in the top 10 nationally twice and my brother received 1st place internationally twice in high school with a perfect score besides placing top 10 nationally several other times! And while winning and receiving an award, a certificate and a medal were exciting, there was much greater joy in learning and strengthening our mathematical and logic skills as we prepared for and took the Math Kangaroo test. The skills we learned during Math Kangaroo preparation helped me succeed at MIT and my brother at Stanford where we majored in electrical engineering and computer science.
Even so, we wanted our digital kits to be special for the top 10 winners in grades 1–5, which they would be receiving in addition to a certificate from Math Kangaroo. After all, it had been a difficult year with the ongoing pandemic and we wanted to create something that students would be looking forward to. We didn’t have any budget because all of the instructors in our organization are current university students or recent alumni. But, inspired by Math Kangaroo’s volunteers such as Ms. Grazyna, a longtime volunteer of my hometown’s Math Kangaroo chapter, who have dedicated their lives to facilitating this math competition, MehtA+ instructors were absolutely ready to volunteer their time to design a memorable prize!
Designing a prize was definitely a challenging feat. MehtA+’s target demographic for camps, workshops, tutoring and consulting services are middle and high school students so we were not sure what elementary-aged students would like. We also did not want it to be a completely digital prize because it is often more exciting to play with a physical prize. More importantly, we had heard from a lot of grownups that they did not want their students to be looking at their computer screens any more than they needed to, since students had been looking at screens non-stop throughout the virtual school year.
Then, one fine morning, as I was cleaning my room, inspiration struck. A little kangaroo stuffed animal fell out of my bookshelf. This was a kangaroo I had won in Math Kangaroo as an elementary student. I remember how much I had cherished it and kept it ever since. This is what the elementary students would love. MehtA+ instructors could teach elementary school students how to create their own paper model of a kangaroo, while learning principles of mechanical engineering and design.
I enjoyed the MehtA+ Digital Kit. It was fun to assemble and is a great decoration for my study area!
I hurriedly called our Product Lead and instructor, Ms. Marwa who had completed her undergraduate studies in mechanical engineering at MIT, if she could design such a kit. She gladly agreed despite her busy schedule — she was reaching out to labs for her PhD program in Mechanical Engineering at MIT, which she was to begin a couple of months later. She was also fasting as it was Ramadan!
Ms. Marwa first took the Math Kangaroo logo and vectorized it. She exported the file to DXF format so she could create a 3-D model of the kangaroo by extruding the image in CAD software. She then created the unfolded pattern of the 3-D model. However, it turned out that the design of the 3-D model was larger than A4 paper (normal printer paper)! A design larger than A4 paper would mess with the integrity of the paper structure because there would be individual cutouts split between multiple papers rather than having one continuous pattern. Ms. Marwa spent several more hours trying to modify the structure so that it would fit on an A4 paper and it was easy for students to assemble.
It was important for us that the students could create the kangaroo using materials easily accessible to them. The kit was designed in such a way that students could print out the design on printer paper or cardstock and only needed household items to create it — scissors, Q-tips, and glue/tape was sufficient.
Ms. Marwa also recorded videos that taught students how to fold the kangaroo cutout as well as how to create similar cutouts using software that mechanical engineers use — TinkerCad and Pepakura. We figured that this was a great opportunity for younger students to strengthen their motor skills and practice cutting and coloring. For older students, this was a great way to understand the applications of mathematical concepts that they had learned in preparation for the Math Kangaroo.
Growing up, none of our instructors had this kind of exposure to the applications of the theory we learned in school. While there were many 3-D cutouts of different animals found on the web, no one explained to the students how these cutouts were made using mechanical engineering software. We always strive to introduce new concepts to students, while they are having fun!
The kit was a huge success. 2nd grader Gideon B. from RSM Winchester created, colored and sent us a picture of his beautiful 3-D paper kangaroo. One 4th grade student remarked, “I enjoyed the MehtA+ Digital Kit. It was fun to assemble and is a great decoration for my study area!”
We are excited to announce that we will be sponsoring Math Kangaroo USA again in 2022. For students in grades 1–12, please don’t forget to register for Math Kangaroo by December 15, 2021. Who knows, you might be receiving one of our prizes next year! | mathematics |
https://www.iusmentis.com/technology/encryption/diffie-hellman/ | 2023-10-03T17:49:44 | s3://commoncrawl/crawl-data/CC-MAIN-2023-40/segments/1695233511170.92/warc/CC-MAIN-20231003160453-20231003190453-00373.warc.gz | 0.95287 | 576 | CC-MAIN-2023-40 | webtext-fineweb__CC-MAIN-2023-40__0__290287107 | en | The Diffie-Hellman system
The Diffie-Hellman algorithm is a public key algorithm. It was invented in 1976 by Whitfield Diffie and Martin Hellman (US patent 4,200,770). It allows two parties, commonly called Alice and Bob, to agree on a key that they can use to encrypt messages they want to send to each other. They can to this even when an eavesdropper (Eve) listens in on their entire conversation.
The security of this algorithm depends on the assumption that it is easy to raise a number to a certain power, but difficult to compute which power was used given the number and the outcome.
The Diffie-Hellman system allows Alice and Bob to agree on a key even when Eve is listening to everything they say to each other. Alice and Bob need to agree on a prime number p, which they can do by simply sending it to each other. Eve is allowed to learn this number p. In practice the number p is often simply advertised somewhere public.
Given a prime number p, it is possible to come up with a number g (the so-called generator) with a very interesting property. Every number between 1 and p-1 can be written as a power of g when calculating modulo p. For example, using p = 5 the generator is 2, because
- 20 = 1
- 21 = 2
- 22 = 4
- 23 = 3 (because 8 = 3 mod 5)
Alice and Bob agree in the same way on a generator g for the numbers between 1 and p-1.
The public key
The numbers p and g serve as the public key.
Alice and Bob both choose random numbers (a and b respectively). Alice then computes ga and Bob computes gb. They exchange their results.
The key that Alice and Bob now agree on is simply ga*b. This is all very easy to compute. Alice knows a and gb, and Bob knows b and ga, and
Alice and Bob can use the key ga*b to encrypt messages with any secret key algorithm.
The security of the Diffie-Hellman system depends on the assumption that it is easy to raise a number to a certain power, but difficult to compute which power was used given the number and the outcome. For example, it's easy to compute 210 = 1024, but more difficult to determine that 1024 is the 10th power of 2.
Eve knows ga and gb, but since she does not know a or b itself, she cannot compute the key in a reasonable amount of time. To do that, she has to calculate the g-logarithm of ga (which mathematicians write as logg(ga)). And calculating this logarithm takes a long time. | mathematics |
https://webstat.une.edu.au/unit_materials/c5_inferential_statistics/confidence_interv_hypo.html | 2020-03-30T14:01:15 | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00287.warc.gz | 0.877166 | 245 | CC-MAIN-2020-16 | webtext-fineweb__CC-MAIN-2020-16__0__84224341 | en | Confidence Intervals and
Two basic uses of inferential statistics are possible:
a)interval estimation Ð so-called "confidence intervals"
b)point estimation Ð so-called "hypothesis testing"
Interval estimation ("Confidence Intervals") and point estimation ("Hypothesis Testing") are two different ways of expressing the same information.
Using Confidence Intervals we make statements like the following:
- the probability that the population mean (µ, or the 'true' value of the population mean) lies between 19 and 23 is 0.80;
- the probability that the population correlation value (r, or the 'true' value of the correlation between these two variables) lies between 0.20 and 0.24 is 0.60;
Using Hypothesis testing we say:
- the probability that our sample mean comes from a population with a mean of 21 is greater than 0.95
- the probability that our two sample means come from the one populations is less than 5% (i.e.,0.05).
- the probability that our sample comes from a population in which the true correlation is zero is 0.60. | mathematics |
https://president.williams.edu/in-memoriam/the-passing-of-olga-r-beaver/ | 2023-12-11T08:43:11 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679103810.88/warc/CC-MAIN-20231211080606-20231211110606-00552.warc.gz | 0.98415 | 301 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__213195689 | en | To the Williams Community,
I am very sad to report the death this morning of a true stalwart of our faculty, Professor of Mathematics Ollie Beaver, who taught as recently as this semester despite advancing illness.
Ollie earned her Ph.D., at UMASS Amherst, when that was quite a difficult path for a young mother, and in 1979 joined what was then a much smaller and male-dominated math department than the one she helped it become. From the start she was especially dedicated to women and minority students in math and science. She help found, and for many years directed, the Summer Science Program that has given countless Williams students a strong footing in those subjects. She often mentored those students throughout their four years.
Meanwhile, she pursued her research in measure and probability theory. She was the second person ever to win the Louise Hay Award from the Association for Women in Mathematics, and the phenomenal growth in our math department is attributable in no small part to her.
A college citizen of the highest order, she served also as department chair, as the Gaudino Scholar, and for many years as chair of the Winter Study Committee. In fact, the list of her committee assignments is impressively long. She loved all this work, and set about doing it effectively and without fanfare.
After such a painfully swift loss, our thoughts and hearts will be for a long time with her family, especially her husband Don, professor of history of science. | mathematics |
https://firstpriorityfinancial.com/learning-center/calculators/ | 2020-06-05T21:52:34 | s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348504341.78/warc/CC-MAIN-20200605205507-20200605235507-00360.warc.gz | 0.903792 | 320 | CC-MAIN-2020-24 | webtext-fineweb__CC-MAIN-2020-24__0__9887323 | en | Check out our Calculators
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http://ntades.eu/2021/ntades/accommodation.html | 2022-12-09T18:58:33 | s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711475.44/warc/CC-MAIN-20221209181231-20221209211231-00806.warc.gz | 0.765078 | 95 | CC-MAIN-2022-49 | webtext-fineweb__CC-MAIN-2022-49__0__160960583 | en | Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Eight International Conference
New Trends in the Applications of Differential Equations in Sciences (NTADES 2021)
6-9 September 2021, Sts. Constantine and Helena (Bulgaria)
The conference will be held in the Joliot-Curie International House of Scientists, St. Constantine and Helena, Bulgaria.
Last modified: 2021-01-13 | mathematics |
https://www.cropscience.bayer.us/articles/channel/estimating-soybean-yield-potential | 2024-02-22T04:00:46 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947473690.28/warc/CC-MAIN-20240222030017-20240222060017-00059.warc.gz | 0.915271 | 1,081 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__40095826 | en | Estimating Soybean Yield Potential
Harvest will be quickly upon us, and yield estimates will be occurring across the countryside. Crop yield potential is normally estimated by determining the number of plants in an area, the number of reproductive units, and the weight of those reproductive units.
Potential Yield = plants/acre x seeds/plant x seed weight
Yield potential estimates for most row crops have three yield components, but how those yield component numbers are determined are different for each crop. Before estimating soybean yield potential, a word of caution; estimating soybean yield potential can be tricky. Soybean yield components can vary greatly by soybean product, different parts of the field, and from plant to plant. It is not advised to conduct a yield estimate during early reproductive stages as the plant has not fully determined the number of seeds that it may produce. Soybean yield potential estimates should only occur after the R6 (full seed) growth stage. Yield estimates should be conducted in at least 5 to 10 random places in the field and these random places should be representative of the plants in that area. By sampling in multiple places, a more uniform yield estimate for the entire field can be obtained.
Step 1: Determine number of plants per acre.
- Take time to calculate the number of harvestable plants per acre, as this number could have changed from when stand counts were determined earlier in the season.
- Determine the row width and measure the corresponding row length to achieve 1/1000th of an acre.
- Count the number of plants in the row for 1/1000th of an acre and multiple by 1000, to estimate the number of plants per acre.
- For example, in 30-inch rows, measure 17 feet 5 inches in row length and count the number of plants in that row. If 114 plants were counted in the row, multiply by 1000 to have an estimated 114,000 harvestable plants per acre.
Step 2: Estimate the number of pods per plant.
- To estimate pods per plant, count the number of pods on each plant for 10 consecutive plants in one row.
- Divide the total number of pods by 10 to determine the average number of pods per plant.
- For example, if a total of 350 pods were counted, divide by 10 to reach an average of 35 pods per plant.
Step 3: Estimate number of seeds per pod.
- When determining the number of pods per plant, look at those pods from the 10 consecutive plants from Step 2.
- If there is about an even mix of three and two seeded pods, use the general 2.5 seeds per pod value.
- Typically, a value of 2.5 seeds per pod is used with healthy soybean plants when there is an average growing season. However, in stressful growing conditions, this number may be lower. This is when it would be advised to count the number of three seeded, two seeded, and one seeded pods to determine if a lower value of 2 or 1.5 seeds per pod should be used.
Step 4: Estimate the weight of the seed
- Seed weight is the most difficult yield component to estimate correctly.
- Seed weight can vary by seed product and growing conditions.
- When there is ample rain in August, larger seeds are typically produced which correspond to larger seed weights.
- Stressful conditions of hot and dry usually produce plants with small seeds and lower seed weight.
- A general ‘rule of thumb’ factor for seed weight is 2500 seeds per pound. However, a better indicator is typically what the original seed size was from the seed bag tag at planting. The seed weight factor can be adjusted if the final yield estimate is unusually too high or low.
Step 5: Estimate the final yield (bushel/acre)
Make sure to set up the equation correctly to have the correct units for each portion of the equation. For the equation, the weight of one bushel of soybean (60 pounds) is needed. Using the numbers in the examples above, the hypothetical soybean potential yield estimate from one spot in the field would be:
Potential yield (bu/acre) = (plants/acre) x (pods/plant) x (seeds/pod) ÷ (seeds/lb) ÷ (lb/bu)
bu/acre = 114,000 plants/acre x 35 pods/plant x 2.5 seeds/pod ÷ 2500 seeds/lb ÷ 60 lbs/bu = 66.5 bu/acre
These steps should be repeated at multiple locations across the field to get a representative average of estimated yield potential for the field. A reminder that yield potential estimates are only as good as the numbers used in the equation. Yield estimates made closer to harvest are more reliable than yield estimates taken earlier in the season when pod and seed development are occurring. Contact your local Channel Seedsmen concerning questions and assistance in estimating soybean yield potential.
Knott, C. and Lee, C. 2018. Cultural practices. Chapter 4. A Comprehensive Guide to Soybean Management in Kentucky. ID-249. University of Kentucky College of Agriculture Food and Environment Cooperative Extension Service.
Source verified 6/22/23. 1110_274488 | mathematics |
https://www.housedumonde.com/group/mysite-231-group/discussion/be245823-3bc0-413a-965f-ce8d125dec2b | 2024-04-15T11:56:09 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816977.38/warc/CC-MAIN-20240415111434-20240415141434-00079.warc.gz | 0.946606 | 2,053 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__140882651 | en | In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right.
Various physical systems, such as crystals and the hydrogen atom, and three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also central to public key cryptography.
The early history of group theory dates from the 19th century. One of the most important mathematical achievements of the 20th century was the collaborative effort, taking up more than 10,000 journal pages and mostly published between 1960 and 2004, that culminated in a complete classification of finite simple groups.
Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields. Early results about permutation groups were obtained by Lagrange, Ruffini, and Abel in their quest for general solutions of polynomial equations of high degree. Évariste Galois coined the term "group" and established a connection, now known as Galois theory, between the nascent theory of groups and field theory. In geometry, groups first became important in projective geometry and, later, non-Euclidean geometry. Felix Klein's Erlangen program proclaimed group theory to be the organizing principle of geometry.
Galois, in the 1830s, was the first to employ groups to determine the solvability of polynomial equations. Arthur Cayley and Augustin Louis Cauchy pushed these investigations further by creating the theory of permutation groups. The second historical source for groups stems from geometrical situations. In an attempt to come to grips with possible geometries (such as euclidean, hyperbolic or projective geometry) using group theory, Felix Klein initiated the Erlangen programme. Sophus Lie, in 1884, started using groups (now called Lie groups) attached to analytic problems. Thirdly, groups were, at first implicitly and later explicitly, used in algebraic number theory.
The different scope of these early sources resulted in different notions of groups. The theory of groups was unified starting around 1880. Since then, the impact of group theory has been ever growing, giving rise to the birth of abstract algebra in the early 20th century, representation theory, and many more influential spin-off domains. The classification of finite simple groups is a vast body of work from the mid 20th century, classifying all the finite simple groups.
The range of groups being considered has gradually expanded from finite permutation groups and special examples of matrix groups to abstract groups that may be specified through a presentation by generators and relations.
The theory of transformation groups forms a bridge connecting group theory with differential geometry. A long line of research, originating with Lie and Klein, considers group actions on manifolds by homeomorphisms or diffeomorphisms. The groups themselves may be discrete or continuous.
Most groups considered in the first stage of the development of group theory were "concrete", having been realized through numbers, permutations, or matrices. It was not until the late nineteenth century that the idea of an abstract group as a set with operations satisfying a certain system of axioms began to take hold. A typical way of specifying an abstract group is through a presentation by generators and relations,
A significant source of abstract groups is given by the construction of a factor group, or quotient group, G/H, of a group G by a normal subgroup H. Class groups of algebraic number fields were among the earliest examples of factor groups, of much interest in number theory. If a group G is a permutation group on a set X, the factor group G/H is no longer acting on X; but the idea of an abstract group permits one not to worry about this discrepancy.
The change of perspective from concrete to abstract groups makes it natural to consider properties of groups that are independent of a particular realization, or in modern language, invariant under isomorphism, as well as the classes of group with a given such property: finite groups, periodic groups, simple groups, solvable groups, and so on. Rather than exploring properties of an individual group, one seeks to establish results that apply to a whole class of groups. The new paradigm was of paramount importance for the development of mathematics: it foreshadowed the creation of abstract algebra in the works of Hilbert, Emil Artin, Emmy Noether, and mathematicians of their school.
An important elaboration of the concept of a group occurs if G is endowed with additional structure, notably, of a topological space, differentiable manifold, or algebraic variety. If the group operations m (multiplication) and i (inversion),
are compatible with this structure, that is, they are continuous, smooth or regular (in the sense of algebraic geometry) maps, then G is a topological group, a Lie group, or an algebraic group.
The presence of extra structure relates these types of groups with other mathematical disciplines and means that more tools are available in their study. Topological groups form a natural domain for abstract harmonic analysis, whereas Lie groups (frequently realized as transformation groups) are the mainstays of differential geometry and unitary representation theory. Certain classification questions that cannot be solved in general can be approached and resolved for special subclasses of groups. Thus, compact connected Lie groups have been completely classified. There is a fruitful relation between infinite abstract groups and topological groups: whenever a group Γ can be realized as a lattice in a topological group G, the geometry and analysis pertaining to G yield important results about Γ. A comparatively recent trend in the theory of finite groups exploits their connections with compact topological groups (profinite groups): for example, a single p-adic analytic group G has a family of quotients which are finite p-groups of various orders, and properties of G translate into the properties of its finite quotients.
During the twentieth century, mathematicians investigated some aspects of the theory of finite groups in great depth, especially the local theory of finite groups and the theory of solvable and nilpotent groups. As a consequence, the complete classification of finite simple groups was achieved, meaning that all those simple groups from which all finite groups can be built are now known.
During the second half of the twentieth century, mathematicians such as Chevalley and Steinberg also increased our understanding of finite analogs of classical groups, and other related groups. One such family of groups is the family of general linear groups over finite fields. Finite groups often occur when considering symmetry of mathematical orphysical objects, when those objects admit just a finite number of structure-preserving transformations. The theory of Lie groups,which may be viewed as dealing with "continuous symmetry", is strongly influenced by the associated Weyl groups. These are finite groups generated by reflections which act on a finite-dimensional Euclidean space. The properties of finite groups can thus play a role in subjects such as theoretical physics and chemistry.
This definition can be understood in two directions, both of which give rise to whole new domains of mathematics. On the one hand, it may yield new information about the group G: often, the group operation in G is abstractly given, but via ρ, it corresponds to the multiplication of matrices, which is very explicit. On the other hand, given a well-understood group acting on a complicated object, this simplifies the study of the object in question. For example, if G is finite, it is known that V above decomposes into irreducible parts (see Maschke's theorem). These parts, in turn, are much more easily manageable than the whole V (via Schur's lemma).
Given a group G, representation theory then asks what representations of G exist. There are several settings, and the employed methods and obtained results are rather different in every case: representation theory of finite groups and representations of Lie groups are two main subdomains of the theory. The totality of representations is governed by the group's characters. For example, Fourier polynomials can be interpreted as the characters of U(1), the group of complex numbers of absolute value 1, acting on the L2-space of periodic functions.
A Lie group is a group that is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups are named after Sophus Lie, who laid the foundations of the theory of continuous transformation groups. The term groupes de Lie first appeared in French in 1893 in the thesis of Lie's student Arthur Tresse, page 3.
Lie groups represent the best-developed theory of continuous symmetry of mathematical objects and structures, which makes them indispensable tools for many parts of contemporary mathematics, as well as for modern theoretical physics. They provide a natural framework for analysing the continuous symmetries of differential equations (differential Galois theory), in much the same way as permutation groups are used in Galois theory for analysing the discrete symmetries of algebraic equations. An extension of Galois theory to the case of continuous symmetry groups was one of Lie's principal motivations. 350c69d7ab
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http://stivoschool.org/page/exam-results | 2018-08-20T03:10:14 | s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221215523.56/warc/CC-MAIN-20180820023141-20180820043141-00051.warc.gz | 0.977242 | 358 | CC-MAIN-2018-34 | webtext-fineweb__CC-MAIN-2018-34__0__45989367 | en | Overview of exam results
GCSE results 2017
66% of students gained a grade 4 or higher in both English and Maths.
In English 74% of students gained a 4 or higher.
In maths 76% of students gained a 4 or higher.
20% of all GCSE grades were awarded at A*/A.
In Chemistry 66% of grades were at A*/A. In Art 42% of grades were at A*/A.
There were some notable high achievers in this year’s results. Abbey gained the equivalent of 10 A* grades closely followed by Mahil and Robert with 8 A*s and Jenna with 7 grades at A*.
Headteacher Sam Griffin said “These are an impressive set of results for this year group. I am delighted to see so many students doing so well. I would like to congratulate all of students on their achievements and to thank their staff and parents for their ongoing support. We are looking forward to welcoming students back into our Sixth Form at the start of term.”
The latest official DfE performance tables for the school's GCSE results can be found here.
A level results 2018
We are delighted to have received another strong set of A Level results, particularly with over half of all grades at A*, A and B, and a quarter of grades at A*A! These results have enabled the vast majority of our students to progress to the university courses of their choice. Individual successes at the school include 12 students with straight A*A grades (or equivalent), with two of these students being awarded straight A* grades. Maths, Chemistry and Sport students have also performed particularly well, with over 50% of grades in these subjects at A*A or equivalent. | mathematics |
https://www.coffeyvillepl.org/2012/08/23/homework-help-the-library/ | 2019-03-22T00:00:09 | s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202588.97/warc/CC-MAIN-20190321234128-20190322020128-00020.warc.gz | 0.946689 | 183 | CC-MAIN-2019-13 | webtext-fineweb__CC-MAIN-2019-13__0__117788939 | en | Elementary school children who need a little extra help with their homework have a new resource at the library. Brittini Trytek, a teacher at Holy Name, will be available at the library from 5-8 on Monday, Wednesday and Thursday and all day on Saturday to assist children who need help in getting their homework done.
The children should bring their books and their homework assignment with them to the library. Brittini will help them understand how to do the assignment. She will not do the assignment for the children. With Learning Express, an online database, and other library resources, Brittini and the children can do extra practice in math and reading.
Brittini can help children research material for projects using the books in the library and trusted Internet sources. She will teach the children how to find accurate online information using the Student Research Center, Learning Express, Ebsco Digital Books and Kids.gov. | mathematics |
https://www.promohub.ng/how-to-use-fibonacci-numbers-in-forex-trading/ | 2023-12-03T21:15:20 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100508.53/warc/CC-MAIN-20231203193127-20231203223127-00839.warc.gz | 0.897882 | 5,363 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__164827521 | en | Are you looking to level up your forex trading game to maximize your profits? One of the most popular and effective techniques is the use of Fibonacci numbers. This powerful tool can help traders predict market trends and identify the best entry and exit points. Whether you’re a beginner or an experienced trader, mastering the Fibonacci sequence can give you the edge you need to succeed in the ever-evolving world of forex trading.
The Fibonacci numbers, named after an Italian mathematician, are a sequence of numbers generated by adding the two preceding numbers to create the next number in the sequence. The pattern goes 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. Traders use these numbers to plot key levels of support and resistance on a price chart. By identifying these levels, they can make informed decisions about when to buy or sell a currency pair. This strategy works particularly well in volatile markets, where prices tend to move in repetitive cycles.
But how exactly does one use Fibonacci numbers in forex trading? It all starts by identifying the highs and lows of a price chart. From there, traders can use the Fibonacci ratios to identify key levels to watch for a potential breakout. By setting stop-loss orders just below these levels, traders can minimize their risk and increase their chances of success. With practice and persistence, even beginner traders can master this powerful tool and start making more informed and profitable trades.
What are Fibonacci numbers and ratios?
Fibonacci numbers are a series of numbers where each number is the sum of the two preceding numbers. The series starts with 0, 1, 1, 2, 3, 5, 8, 13, and continues infinitely. These numbers were first introduced in the book Liber Abaci by Italian mathematician Leonardo Fibonacci in the 13th century, which described various problems involving arithmetic, algebra, and geometry.
Fibonacci ratios are the values that are derived from the series of Fibonacci numbers. These ratios are used for technical analysis in various financial markets, including forex trading. The most popular ratios are 0.236, 0.382, 0.500, 0.618, and 0.786. The inverse of these ratios, which are 1.618, 2.618, and 4.236, are also commonly used in forex trading.
Fibonacci retracements as a trading tool
One of the most popular ways to use Fibonacci numbers in forex trading is through the use of Fibonacci retracements. These retracements are based on the idea that after a significant price move in one direction, the price will often retrace a certain percentage of that move before continuing in the original direction.
Fibonacci retracements are calculated by taking two extreme points on a price chart, typically a swing high and a swing low, and dividing the vertical distance between them by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8%, and 100%. These ratios are based on the Fibonacci sequence, which states that each number in the sequence is the sum of the two preceding numbers (i.e. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc.).
Using Fibonacci retracements in forex trading
- Identifying potential support and resistance levels: By plotting Fibonacci retracements on a price chart, traders can identify potential levels of support and resistance where the price is likely to stall or reverse. For example, the 38.2% and 61.8% retracement levels are often considered key levels to watch, as the price will often test these levels before continuing in the original direction.
- Setting profit targets and stop loss levels: Fibonacci retracements can also be used to set profit targets and stop loss levels. For example, a trader might set a profit target at the 61.8% retracement level, where there is a higher likelihood that the price will stall or reverse. Likewise, a trader might set a stop loss at the 38.2% retracement level, which would indicate that the trade is likely to be unsuccessful.
- Confirming other technical analysis: Fibonacci retracements can also be used to confirm other technical analysis indicators, such as trend lines or moving averages. If a Fibonacci retracement level coincides with a trend line or moving average, it is more likely to serve as a significant support or resistance level.
Fibonacci retracement levels table
Overall, Fibonacci retracements are a powerful tool for forex traders looking to identify potential levels of support and resistance, set profit targets and stop loss levels, and confirm other technical analysis indicators. With the help of these retracements, traders can more effectively navigate the complex world of forex trading and increase their chances of success.
How to Draw Fibonacci Retracement Levels on a Trading Chart
Fibonacci retracement levels are used in forex trading to identify potential support and resistance levels. These levels are based on the Fibonacci sequence of numbers and are widely used by traders to determine entry and exit points for currency trades.
Drawing Fibonacci retracement levels on a trading chart is a simple process that traders can easily learn and apply. Here are the steps to follow:
- Step 1: Identify the trend – Before drawing the Fibonacci retracement levels, you need to identify the trend of the currency pair you are trading. You can do this by analyzing the price movement over a period of time and looking for the direction of the trend.
- Step 2: Select the swing high and swing low – Once you have identified the trend, you need to select the swing high and swing low points. The swing high is the highest point reached by the currency pair during an uptrend, while the swing low is the lowest point reached during a downtrend
- Step 3: Draw the retracement levels – To draw the Fibonacci retracement levels, you need to use a Fibonacci retracement tool. This tool is usually available on most trading platforms. Click on the tool and then click on the swing low and drag it to the swing high point. The tool will automatically draw the retracement levels for you.
The Key Fibonacci Retracement Levels
The retracement levels that traders commonly use are 38.2%, 50%, and 61.8%. Traders also use the 23.6% and 78.6% levels, although they are not as significant as the three key levels. Here is how to interpret the retracement levels:
|38.2%||This is the first retracement level and is considered to be a shallow retracement. If the price retraces to this level, it is a sign that the trend is still strong and is likely to continue in the same direction.|
|50%||This is the second retracement level and is considered to be a moderate retracement. If the price retraces to this level, it is a sign that the trend is likely to continue, but may be losing momentum.|
|61.8%||This is the third and final retracement level and is considered to be a deep retracement. If the price retraces to this level, it is a sign that the trend is losing momentum and may be reversing.|
Tips and Tricks for Using Fibonacci Retracement Levels
Here are some tips and tricks for using Fibonacci retracement levels in forex trading:
- Don’t rely solely on Fibonacci retracement levels. They are just one tool that traders use and should be used in conjunction with other indicators and analysis.
- Use Fibonacci retracement levels in combination with support and resistance levels. This will help you identify potential entry and exit points for your trades.
- Practice drawing Fibonacci retracement levels on a demo trading account to get comfortable with the process before you begin trading with real money.
By following these steps and tips, traders can effectively use Fibonacci retracement levels to identify potential support and resistance levels for their forex trades. Remember to always practice risk management and never risk more than you can afford to lose.
Fibonacci extensions and their use in trading
Fibonacci extensions are another powerful tool in forex trading. They are used to help traders identify potential profit targets on trades. Once a trader has identified a trend, they can use Fibonacci extensions to predict where the price may move in the future.
- First, the trader identifies the swing high and swing low points of the trend.
- Then, they apply Fibonacci extensions levels to the chart.
- The levels indicate where the price may potentially reach, based on the length of the trend.
There are different levels of Fibonacci extensions, including 127.2%, 161.8%, and 261.8%. These levels can be used as potential exit points for traders, as the price may encounter resistance or support at these levels.
Fibonacci extensions can also be used in conjunction with other technical analysis tools, such as trend lines and moving averages, to confirm potential price targets.
Example of Fibonacci extensions in trading
|Date||Swing High||Swing Low||Price Target|
|January 1st||1.2000||1.1000||1.2720 (127.2% extension)|
|January 15th||1.4000||1.2500||1.6170 (161.8% extension)|
|February 1st||1.8000||1.6000||2.0860 (261.8% extension)|
In this example, the trader has identified the swing high and swing low points of three different trends. They have then applied Fibonacci extensions levels to the chart, with the levels indicating where the price may potentially reach. The trader can use these levels as potential profit targets, or as points to exit the trade.
Common Fibonacci levels used by traders
Fibonacci levels are widely used by traders in forex trading to identify potential support and resistance levels. Understanding these levels is crucial for traders to make informed decisions when it comes to placing trades. The most commonly used Fibonacci levels in trading are:
The Number 5
The number 5 is an important Fibonacci level that is used in trading. This level is not directly related to the actual Fibonacci sequence, but it is still important for traders to understand its significance. The number 5 is derived from the relationship between adjacent numbers in the Fibonacci sequence. The ratio of any two adjacent numbers in the Fibonacci sequence approaches the golden ratio of 1.618. When we add two adjacent Fibonacci numbers together, we get the next number in the sequence. For example, 3 + 2 = 5, and 5 + 3 = 8.
Traders use the 5 level as a potential reversal point. When prices break above or below this level, it often indicates a potential reversal in the direction of the trend. This level is also used in combination with other Fibonacci levels to identify potential support and resistance levels. For example, the 50% level is often used in combination with the 5 level to identify a potential reversal point.
In addition to its use in Fibonacci retracements, the number 5 is also important in other aspects of trading. For example, some traders use a 5-period moving average to identify short-term trends in the market. This moving average is calculated by taking the average closing price of the last 5 periods.
Overall, understanding the significance of the number 5 in trading can help traders make more informed decisions when it comes to placing trades. By combining this level with other Fibonacci levels, traders can identify potential support and resistance levels and make more accurate predictions about future price movements.
Identifying support and resistance levels with Fibonacci
One of the most popular ways to use Fibonacci numbers in forex trading is to identify support and resistance levels. Support levels are price points that a currency pair tends to bottom out at, while resistance levels are price points that a currency pair tends to peak at. By identifying these levels, traders can use them as indicators of potential future price movements and make more informed trading decisions.
- To use Fibonacci levels to identify support and resistance, traders first need to locate the most recent high and low points on a chart. These points will be used to draw Fibonacci retracement levels. These levels are drawn by placing horizontal lines at the appropriate Fibonacci ratios.
- Once the retracement levels are drawn, traders can look for support or resistance at these levels. Price action that shows a strong bounce off of a Fibonacci level can suggest that the level is acting as support or resistance.
- Traders should also be on the lookout for multiple Fibonacci levels that occur close to each other. This confluence can provide additional evidence that a particular level is acting as support or resistance.
For example, suppose a currency pair has recently been trending upwards and has reached a high point of 1.4500. The pair then begins to retrace downwards, with a low point of 1.4000. To draw Fibonacci levels, traders would draw a horizontal line between these two points and place horizontal lines at the appropriate Fibonacci ratios, such as 38.2%, 50%, and 61.8%.
If the currency pair bounces strongly off the 38.2% level, traders might expect that level to act as support in the future. Similarly, if the currency pair encounters strong resistance at the 61.8% level, traders might expect that level to act as resistance in the future.
Overall, using Fibonacci numbers to identify support and resistance levels can be a useful tool in forex trading. By paying attention to these levels and the price action surrounding them, traders can gain valuable insights into potential future price movements and make more informed trading decisions.
Fibonacci and Elliot Wave Theory in Forex Trading
Fibonacci retracements are a widely-used technical analysis tool in forex trading. They are based on the sequence of numbers known as the Fibonacci sequence, which is derived from the mathematical discoveries of Leonardo Fibonacci in the 13th century. Elliot Wave Theory, on the other hand, is a technical analysis approach developed by Ralph Nelson Elliot in the 1930s that identifies waves in financial markets.
Using Fibonacci Numbers in Forex Trading
- Fibonacci retracements are used to identify potential levels of support and resistance in a market. Traders use Fibonacci retracements to identify potential entry and exit points for their trades.
- The most common retracement levels are 23.6%, 38.2%, 50%, 61.8%, and 78.6%. These levels are calculated by taking the high and low points of a price movement and applying Fibonacci ratios to determine where the price is likely to retrace to.
- Fibonacci retracements are often used in conjunction with other technical indicators, such as moving averages, to confirm potential entry and exit points.
The Relationship between Fibonacci and Elliot Wave Theory
Elliot Wave Theory identifies trends in the market as a series of impulsive and corrective waves. Fibonacci retracements are often used by Elliot Wave analysts to identify potential levels of support and resistance within these waves.
For example, an Elliot Wave analyst may identify a wave as being in an impulsive phase, and use Fibonacci retracements to identify potential levels of support for buying opportunities.
Fibonacci Retracement Levels
Overall, the use of Fibonacci retracements in forex trading can be a useful tool for identifying potential entry and exit points for traders. When used in conjunction with other technical indicators, such as Elliot Wave Theory, Fibonacci retracements can help traders gain a better understanding of market trends and make more informed trading decisions.
Combining Fibonacci with other technical analysis indicators
Fibonacci retracement is just one of several technical analysis tools used in trading. However, it is commonly used alongside other indicators to confirm a trend, support or resistance level, or possible reversal points. Below are ways on how to combine Fibonacci with other technical analysis indicators:
- Moving Averages: Moving averages can help validate potential Fibonacci retracement levels. For instance, traders may be more inclined to look for retracements near key moving averages; the 50, 100, and 200 SMA. Similarly, if a retracement level coincides with a moving average, this may provide more emphasis on the level.
- Relative Strength Index (RSI): RSI is a momentum indicator used to determine if a currency is overbought or oversold. If the RSI is over 70, the currency may be overbought, and if the RSI is below 30, the currency may be oversold. Fibonacci levels can confirm RSI signals. For example, if the RSI becomes oversold at a Fibonacci retracement level, it may indicate a possible reversal of the downtrend.
- MACD: Moving Average Convergence Divergence (MACD) is a trend-following momentum indicator. This indicator is used to show the relationship between two moving averages. Similar to the RSI, traders combine it with Fibonacci retracements to confirm trend or reversal. If prices pull back to a Fibonacci level and the MACD is showing a bullish crossover, that could signal a potential bullish trend reversal.
Retracement Trading Strategies
There are different trading strategies that traders use to apply Fibonacci retracements alongside other indicators. One strategy is the “Fibonacci Fan” strategy. This involves drawing diagonal trend lines to connect significant price points and form a fan-like pattern.
Another popular Fibonacci strategy is known as the “Fibonacci extension” strategy. This technique uses Fibonacci retracements and extensions to determine price targets. Extensions are calculated by projecting the price level of a retracement from the previous trend wave. A trader can enter a position near a key Fibonacci retracement level and place a stop loss underneath. Then, they can use a Fibonacci extension level as a profit-taking target to exit the trade.
Fibonacci Retracement Levels Table
In conclusion, combining Fibonacci retracements with technical indicators can provide traders with additional confirmation of trend, support and resistance levels, or potential reversals. It is essential to have a solid understanding of both the tools and the market before applying any strategy to ensure positive trading outcomes.
Pros and cons of using Fibonacci in forex trading
Using Fibonacci in forex trading is a popular technique among traders. Fibonacci numbers are a mathematical sequence that appears in many natural phenomena. In forex trading, these numbers are used to identify potential price movements and support/resistance levels.
- The Fibonacci sequence can help traders identify possible price movements based on past trends and patterns.
- It can serve as a guideline for where to enter or exit the market.
- Fibonacci retracements can provide support and resistance levels that traders can use to set stop-loss or take-profit orders.
- It can help traders manage risk by identifying potential entry and exit points.
- The use of Fibonacci requires a certain level of technical analysis knowledge and expertise.
- The accuracy of Fibonacci levels is not guaranteed, and they should not be used as the sole basis for trading decisions.
- The strategy can be subjective and open to interpretation, leading to different outcomes.
- It can be easy to get caught up in the patterns and forget about other important factors that may affect the market.
Despite its advantages and disadvantages, the Fibonacci sequence is still a widely used tool in forex trading. Traders should always exercise caution and use it as part of a comprehensive trading plan that takes into account various factors, such as market conditions, news events and economic data.
One of the key Fibonacci numbers used in forex trading is 9. This number is often used in conjunction with the 38.2% and 61.8% retracement levels to identify potential support and resistance zones. The table below illustrates how the 9 Fibonacci number can be used in trading:
Traders can use the above table to determine potential levels for entry, stop loss and take profit orders based on the 9 Fibonacci number and the corresponding retracement and extension levels. However, it is important to keep in mind that this is not a foolproof method and should be used in conjunction with other strategies and analysis.
Real-life examples of successful Fibonacci trading strategies
There are many trading strategies that incorporate Fibonacci retracements and extensions. Here, we will explore some real-life examples of successful Fibonacci trading strategies.
- Retracement Strategy: This strategy involves identifying a trend, drawing a Fibonacci retracement from swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend), and entering a trade at a retracement level. For example, if the retracement level is 50%, the trader would enter a buy (in an uptrend) or sell (in a downtrend) order at that level. If price bounces off the retracement level and continues in the direction of the trend, the trade is successful.
- Extension Strategy: This strategy involves identifying a trend, drawing a Fibonacci extension from swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend), and placing buy (in an uptrend) or sell (in a downtrend) orders at the extension levels. For example, if the extension levels are 127.2%, 161.8%, and 261.8%, the trader would place buy (in an uptrend) or sell (in a downtrend) orders at these levels. If price reaches these levels and bounces, the trade is successful.
- Fibonacci Fan Strategy: This strategy involves drawing a Fibonacci fan from a swing low to swing high (in an uptrend) or swing high to swing low (in a downtrend). The fan creates diagonal support and resistance levels. Traders can use these levels to enter trades or take profit. For example, if price is in an uptrend and approaching a fan level, traders can enter a buy order at that level. If price bounces off the level and continues in the direction of the trend, the trade is successful.
Overall, Fibonacci retracements and extensions can be powerful tools when used in conjunction with other technical analysis tools and market knowledge. However, traders should always use proper risk management and consider the possibility of false signals or market manipulation.
Below is a table of common Fibonacci retracement and extension levels:
Remember that Fibonacci levels are not always foolproof, and it’s essential to use other technical analysis indicators and market knowledge in combination with Fibonacci tools. When used properly, Fibonacci retracements and extensions can give traders an edge in analyzing market movements and making informed trading decisions.
FAQs about How to Use Fibonacci Numbers in Forex Trading
1. What are Fibonacci numbers in forex trading?
Fibonacci numbers are a series of numbers used by traders in financial markets to predict future price movements.
2. How are Fibonacci numbers used in forex trading?
Fibonacci retracement levels are used by forex traders to identify potential levels of support and resistance in the market. Traders plot these levels on their charts to help them identify potential buy and sell points.
3. What is Fibonacci retracement level?
Fibonacci retracement level is the percentage of a price move that retraces before continuing in the original direction. These levels are drawn from the highest point to the lowest point, or vice versa, in a given price move.
4. Can Fibonacci numbers be used to predict future forex market trends?
Fibonacci numbers and retracement levels cannot predict future market trends with certainty. In fact, traders should always consider other technical and fundamental indicators before they make trading decisions.
5. How do I add a Fibonacci retracement level to my chart?
Most forex trading platforms have built-in Fibonacci tools that you can use to add retracement levels to your chart. Look for the Fibonacci Retracement option in your platform’s charting tools.
6. How do I interpret the Fibonacci retracement levels on my chart?
The retracement levels help traders identify areas of support and resistance in the market. These levels can be used to determine potential entry and exit points, as well as stop-loss and take-profit levels.
7. Are there any downsides to using Fibonacci numbers in forex trading?
Some critics argue that Fibonacci numbers and retracement levels are not based on any sound mathematical or statistical principles. However, many traders have found success using these tools in their trading.
Closing Title: Thanks for Reading Our Guide on How to Use Fibonacci Numbers in Forex Trading
We hope this guide has been helpful in gaining a better understanding of how to use Fibonacci numbers and retracement levels in forex trading. Remember that Fibonacci numbers are just one tool in your trading arsenal, and it should always complement your trading strategy. Thanks for reading and be sure to visit us again for more useful trading tips and information. | mathematics |
https://flhespectator.com/how-much-math-do-you-need-for-computer-science/ | 2024-03-04T02:26:58 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476409.38/warc/CC-MAIN-20240304002142-20240304032142-00692.warc.gz | 0.911874 | 2,237 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__162586102 | en | How Much Math Do You Need for Computer Science?
Mathematics is an essential element in the field of computer science and plays a vital role in various areas within the discipline. Whether you are interested in coding, algorithms, data analysis, or artificial intelligence, a solid understanding of math concepts is crucial for success.
Foundational Math Skills
At the very least, computer science students should have a strong foundation in basic math skills. This includes a solid understanding of arithmetic, algebra, and geometry. These fundamental areas of math provide the building blocks for more advanced concepts, making them essential for any aspiring computer scientist.
Arithmetic (basic calculations like addition, subtraction, multiplication, and division) is essential for understanding the basics of coding and algorithms. Algebra helps students develop problem-solving skills and logical thinking, which are crucial for writing efficient and optimized code. Geometry, on the other hand, is necessary for understanding concepts related to geometric algorithms, computer graphics, and visualization.
Discrete mathematics is an area of math that focuses on countable and distinct elements, and it is highly relevant to computer science. It covers topics such as set theory, logic, graph theory, combinatorics, and probability theory. These concepts help computer scientists understand and analyze algorithms, data structures, and cryptography.
Set theory provides a foundation for understanding data structures like sets, arrays, and trees. Logic is essential for designing and analyzing the correctness of algorithms. Graph theory helps in understanding and optimizing network algorithms and data relationships. Combinatorics plays a role in analyzing the efficiency of searching and sorting algorithms. Probability theory is crucial for machine learning algorithms and artificial intelligence tasks that involve uncertainty and randomness.
Calculus and Continuous Mathematics
While not every computer science student may need to delve deeply into calculus, having a basic understanding of calculus and continuous mathematics can be beneficial, especially for certain areas within computer science.
Calculus helps computer scientists understand concepts such as optimization, approximation, and continuous change over time. It is particularly important in areas like machine learning, data analysis, and computer graphics. A solid foundation in calculus allows computer scientists to develop and optimize algorithms for complex computational problems.
Linear algebra is another important branch of math that is highly applicable to computer science. It deals with systems of linear equations, vectors, and matrices. Linear algebra is widely used in diverse areas such as computer graphics, cryptography, data compression, and machine learning.
Understanding linear algebra allows computer scientists to manipulate and analyze large data sets, apply transformations to graphical objects, optimize algorithms, and solve systems of equations efficiently.
Mathematics forms a strong foundation for computer science and is integral to many areas within the field. While the level of math required may vary depending on the specific area of focus, having a solid understanding of arithmetic, algebra, discrete mathematics, calculus, and linear algebra is crucial for success in computer science.
By mastering these math concepts, computer scientists can develop efficient algorithms, design robust systems, analyze data effectively, and explore the frontiers of artificial intelligence. So, embrace math as you embark on your computer science journey and unlock the immense possibilities it offers.
Foundational Mathematical Concepts
A solid foundation in discrete mathematics, including sets, logic, and algorithms, is essential for tackling computer science problems effectively. Discrete mathematics provides the logical framework and tools required to understand the fundamental principles of computer science and programming.
One of the key components of discrete mathematics is understanding sets. In computer science, sets are used to organize and categorize data. They are particularly useful when dealing with large amounts of information. For example, in a database, sets can be used to represent a collection of records or entities. Understanding concepts such as unions, intersections, and complements of sets is crucial for efficiently manipulating and analyzing data.
Logic is another important aspect of discrete mathematics. It provides the foundation for creating and evaluating logical statements, which are fundamental in computer science. Logic helps identify patterns, make deductions, and reason through complex problems. It allows computer scientists to construct solid and reliable arguments, which are essential for designing algorithms and creating robust software.
Algorithms form the backbone of computer science. These step-by-step procedures are used to solve problems and perform computations. To effectively design and analyze algorithms, a strong understanding of mathematical concepts is necessary. This includes grasping concepts such as efficiency and complexity, which are directly related to the mathematical representation and analysis of algorithms. By understanding these concepts, computer scientists can create efficient and optimized algorithms to solve problems in the most effective manner.
Additionally, a strong foundation in discrete mathematics helps develop critical thinking skills, which are essential in computer science. The ability to break down a problem, analyze its components, and devise a solution is crucial when working with complex algorithms and systems. Discrete mathematics provides the necessary tools and techniques to approach problems logically and systematically.
In summary, a solid understanding of the foundational mathematical concepts in discrete mathematics is crucial for computer scientists. Sets, logic, and algorithms are at the heart of computer science, and a strong foundation in these areas is necessary for tackling complex problems and creating efficient solutions. By developing a solid mathematical foundation, computer scientists can effectively navigate the ever-changing landscape of technology and contribute to advancements in the field.
Calculus and Analysis
A basic understanding of calculus, particularly differential calculus and sequences, is useful for analyzing algorithms and computational complexity. Calculus is a branch of mathematics that deals with the study of change, particularly of functions and their rates of change. It helps in understanding how quantities change over time or space.
In computer science, calculus is particularly important for analyzing algorithms and computational complexity. Algorithms are step-by-step procedures used for solving a problem, and understanding their efficiency is crucial for developing efficient programs. Computational complexity, on the other hand, deals with measuring the resources required to execute an algorithm, such as time and memory.
Differential calculus, which focuses on the concept of derivatives, is especially relevant in computer science. Derivatives measure the instantaneous rate of change of a function and have applications in optimization and approximation algorithms. For example, in machine learning, derivatives are used to optimize the parameters of a model to minimize the error between predicted and actual outcomes.
Sequences, another topic within calculus, are important for understanding the behavior of algorithms. In computer science, algorithms often deal with sequences of data, such as arrays or linked lists. Understanding the properties and behavior of these sequences helps in analyzing and designing efficient algorithms.
Overall, a basic understanding of calculus, particularly differential calculus and sequences, provides essential tools for analyzing algorithms and computational complexity in computer science. It helps in optimizing algorithms and understanding their efficiency in terms of time and memory consumption.
Linear Algebra and Matrices
In computer science, a strong foundation in linear algebra and matrices is essential. These mathematical concepts play a crucial role in various applications such as graphics, machine learning, and cryptography.
Linear algebra deals with vector spaces and linear transformations. It provides the tools and techniques to solve systems of linear equations, analyze geometric transformations, and understand the properties of vectors and matrices. Matrices are a fundamental component of linear algebra, representing linear transformations and assisting in solving complex problems efficiently.
One significant area where linear algebra is utilized in computer science is graphics. Graphics involve creating and manipulating images, animations, and visual effects using computer algorithms. Techniques such as 3D modeling, rendering, and image processing heavily rely on linear transformations and matrix operations. For instance, rotating and scaling objects in computer graphics involve applying linear transformations to vectors, and matrices are used to represent these transformations.
Another important application of linear algebra in computer science is machine learning. Machine learning algorithms train models to make predictions or decisions without being explicitly programmed. Linear algebra is used to represent and manipulate data in these models. For example, in linear regression, a popular machine learning algorithm, linear algebra is used to estimate the coefficients of a linear equation that best fits the given data.
Cryptography, the study of secure communication, also heavily relies on linear algebra. Cryptographic algorithms, like the widely used RSA algorithm, involve modular arithmetic operations that can be represented using matrices. Linear algebra techniques, such as matrix multiplication, inversion, and exponentiation, are fundamental in implementing and analyzing these cryptographic algorithms.
Having a strong understanding of linear algebra and matrices allows computer scientists to develop efficient and optimized algorithms, understand the mathematical foundations of various computer science applications, and tackle complex problems in the field.
Probability and Statistics
Probability and statistics are essential concepts in computer science, as they provide the foundation for understanding and analyzing data. Whether you’re working on data analysis, machine learning, or network modeling, a strong grasp of probability and statistics is crucial.
Probability is the study of chance and uncertainty. It allows us to quantify the likelihood of an event happening. In computer science, probability is used to analyze data and make predictions. For example, in machine learning algorithms, probability is used to determine the likelihood of a certain outcome based on patterns found in the data.
Statistics, on the other hand, involves the collection, analysis, interpretation, presentation, and organization of data. It helps us make sense of the information we gather and draw valuable insights. In computer science, statistics is used to analyze large datasets and make informed decisions.
One area of computer science where probability and statistics are extensively used is data analysis. Data analysis involves sorting, cleaning, and analyzing large sets of data to uncover meaningful patterns and insights. By applying statistical techniques, such as hypothesis testing and regression analysis, computer scientists can draw valuable conclusions from the data.
Machine learning, a subset of artificial intelligence, also heavily relies on probability and statistics. Machine learning algorithms learn from past data and use that knowledge to make predictions or decisions. Probability is used to find the most likely outcome, while statistical models help in training and evaluating machine learning algorithms.
For example, in image recognition tasks, probability and statistics are used to classify images into different categories. The algorithm compares the features of the image with the probabilities of each category to determine the most likely classification. Statistical models are then used to optimize and improve the accuracy of the algorithm.
Network modeling is another area of computer science where probability and statistics come into play. Networks, such as social networks or computer networks, are complex systems with interconnected entities. Probability is used to model the behavior of these networks and predict outcomes.
For example, in network security, probability is used to analyze the likelihood of a cyber-attack happening and the potential impact it could have. By understanding the probabilities, computer scientists can develop strategies to protect the network and mitigate the risks.
In conclusion, probability and statistics are vital for computer science. They provide the necessary tools to analyze data, make predictions, and understand complex systems. Whether you’re working on data analysis, machine learning, or network modeling, a solid understanding of probability and statistics is essential for success. | mathematics |
https://slow.mathewkiang.com/2013/12/20/shiny-desolve-interactive-ode-models/ | 2024-04-14T14:37:49 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816879.72/warc/CC-MAIN-20240414130604-20240414160604-00585.warc.gz | 0.917228 | 402 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__23662601 | en | While taking a disease dynamics course, I thought it would be a good opportunity to learn how to use the
Shiny package in
R and create an interactive interface for some of my problem sets. After a few trial runs with smaller, simpler setups, I have wrapped up the side project (for now). You can see it in action here 1 and you can view the final code on my Git.
At some point, I’d like to make an analogous version of these models using network-based approaches. However, all my work in network models has been done using Python so it might take a while.
If you’re unfamiliar with compartmental models, they are deterministic models that use differential equations to describe the spread of an epidemic through a population. The Wikipedia page on them is a pretty good place to start. The parameters on the page are described below—note that certain parameters are only shown when they are applicable.
- Probability of transmission: the probability that an infectious person will infect a susceptible person at any one contact.
- Average contacts: the number of people an infected person will run into (per week).
- Disease properties:
- No recovery: when checked, if somebody becomes infected, they will be infectious forever—never recovering.
- Duration: how long an infected person remains infected
- Latent period: the time between being infected and being infectious (at which point they are neither susceptible nor infected, but are “exposed”).
- Seasonal fluctuations: a cosine function that emulates seasonal fluctuations in contact rates.
- Vital dynamics:
- Birth and death rate: Self-explanatory. In these model, kept equal to each other.
- Proportion of vaccinated a birth: assumes vaccination occurs immediately at birth (therefore, this is the proportion of new births who never enter a susceptible stage).
- Vaccine effectiveness: probability of a vaccine actually working. | mathematics |
http://rovaa.sk/library/mathematical-analysis-i-unitext-volume-84-2-nd-edition | 2018-05-23T11:08:00 | s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794865595.47/warc/CC-MAIN-20180523102355-20180523122355-00261.warc.gz | 0.895331 | 1,478 | CC-MAIN-2018-22 | webtext-fineweb__CC-MAIN-2018-22__0__132207077 | en | The aim of the quantity is to supply a aid for a primary path in arithmetic. The contents are organised to charm particularly to Engineering, Physics and computing device technology scholars, all components within which mathematical instruments play a vital position. easy notions and techniques of differential and vital calculus for services of 1 actual variable are offered in a fashion that elicits severe examining and activates a hands-on method of concrete purposes. The format has a specifically-designed modular nature, permitting the teacher to make versatile didactical offerings whilst making plans an introductory lecture path. The e-book could in reality be hired at 3 degrees of intensity. on the effortless point the scholar is meant to understand the very crucial principles and familiarise with the corresponding key ideas. Proofs to the most effects befit the intermediate point, including numerous feedback and complementary notes improving the treatise. The final, and farthest-reaching, point calls for the extra research of the cloth inside the appendices, which permit the strongly prompted reader to discover additional into the topic. Definitions and houses are offered with large examples to stimulate the training approach. Over 350 solved routines whole the textual content, a minimum of half which advisor the reader to the answer. This re-creation beneficial properties extra fabric with the purpose of matching the widest diversity of academic offerings for a primary process arithmetic.
Read or Download Mathematical Analysis I (UNITEXT) PDF
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Additional info for Mathematical Analysis I (UNITEXT)
Then: a) If f expanding on I, then f′(x) ≥ zero for all x ∈ I. b1) If f′(x) ≥ zero for any x ∈ I, then f is expanding on I; b2) if f′(x) > zero for all x ∈ I, then f is exactly expanding on I. evidence. allow f be the map. consider first f is continuous, for this reason for each x zero ∈ I, the variation quotient , with x ∈ I, x ≠ x zero, is 0. Then f‱(x zero) = zero via definition of by-product. Vice versa, consider f has 0 spinoff on I and allow us to end up that f is continuing on I. this may be resembling challenging Take x 1, x 2 ∈ I and use formulation (6. thirteen) on f. For an appropriate among x 1,x 2, we now have therefore f(x 1) = f(x 2). □ 6. 7 6. 7 Monotone maps within the mild of the consequences on differentiability, we take on the problem of monotonicity. evidence. allow us to turn out declare a). believe f expanding on I and think about an inside aspect x zero of I. For all x ∈ I such that x < x zero, we now have therefore, the adaptation quotient among x zero and x is non-negative. nevertheless, for any x ∈ I with x > x zero. the following too the adaptation quotient among x zero and x is confident or 0. Altogether, Corollary four. three on yields f′(x zero) ≥ zero. As for the potential extremum issues in I, we arrive on the comparable end via contemplating one-sided limits of the variation quotient, that's constantly ≥ zero. Now to the results in elements b). Take f with f′(x) ≥ zero for all x ∈ I. the assumption is to mend issues x 1 < x 2 in I and turn out that f(x 1) ≤ f(x 2). For that we use (6. thirteen) and notice that through assumption. yet because x 2 − x 1 > zero, now we have proving b1). contemplating f such that f′(x) > zero for all x ∈ I as an alternative, (6. thirteen) implies f(x 2) − f(x 1) > zero, accordingly additionally b2) holds. □ the theory asserts that if f is differentiable on I, the next common sense equivalence holds: additionally, The latter implication isn't really reversible: f strictly expanding on I doesn't suggest f′(x) > zero for all x ∈ I. we have now somewhere else saw that f(x) = x three is in all places strictly expanding, regardless of having vanishing spinoff on the foundation. an identical assertion to the above holds if we modify the observe ‘increasing’ with ‘decreasing’ and the symbols ≥, > with ≤, <. Corollary 6. 28 permit f be differentiable on I and x zero an inside severe aspect. If f′(x) ≥ zero on the left of x zero and f′(x) ≤ zero at its correct, then x zero is a greatest element for f. equally, f′(x) ≤ zero on the left, and ≥ zero on the correct of x zero implies x zero is a minimal element. Theorem 6. 27 and Corollary 6. 28 justify the hunt for extrema one of the zeroes of f′, and clarify why the derivative's signal impacts monotonicity periods. instance 6. 29 The map f : ℝ → ℝ, f(x) = xe2x differentiates to f′(x) = (2x + 1)e2x , whence is the only serious element. As f′(x) > zero if and provided that is an absolute minimal. The functionality is exactly reducing on and strictly expanding on . □ 6. eight 6. eight Higher-order derivatives enable f be differentiable round x zero and permit its first by-product f′ be additionally outlined round x zero. Definition 6. 30 If f′ is a differentiable functionality at x zero, one says f is two times differentiable at x zero. The expression is termed moment spinoff of f at x zero. | mathematics |
https://online.engineering.arizona.edu/faculty/Fan/ | 2022-08-12T20:16:26 | s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571758.42/warc/CC-MAIN-20220812200804-20220812230804-00660.warc.gz | 0.913721 | 364 | CC-MAIN-2022-33 | webtext-fineweb__CC-MAIN-2022-33__0__135322737 | en | Neng Fan is an associate professor in the Systems and Industrial Engineering Department at the University of Arizona. He obtained his bachelor’s degree in computational mathematics from Wuhan University in 2004 and master’s degree in applied mathematics from Nankai University in 2007. He obtained his master’s and PhD degrees from the Industrial and Systems Engineering Department at the University of Florida in 2009 and 2011, respectively.
Fan’s research interests include integer programming, stochastic and robust optimization methods, and their applications in data mining, combinatorial optimization, energy systems, water systems, and health care. He has been involved in organizing several conferences in the areas of optimization, smart grids, and health care, and also served as a reviewer for many journals. Currently, he is the associate editor for two journals, Optimization Letters and Energy Systems, published by Springer.
Fan is a member of the Institute for Operations Research and Management Sciences (INFORMS) and the Institute of Industrial Engineering (IIE).
- PhD Industrial and Systems Engineering - University of Florida, 2011
- MS Industrial and Systems Engineering - University of Florida, 2009
- MS Applied Mathematics - Nankai University, 2007
- BS Computational Mathematics - Wuhan University, 2004
Teaching Interests: Optimization, operations research, probability, statistics, data analytics, and machine learning
Research Interests: Methodologies in optimization: integer programming, combinatorial optimization, stochastic programming, robust optimization, multilevel programming, and large-scale optimization; applied operations research: energy systems, water systems, renewable energy integration, interdependent infrastructures, healthcare and sustainable agriculture; data analytics: data mining, machine learning, and high-dimensional data with uncertainties | mathematics |
https://numathsapp.com/2016/11/11/south-african-learners-have-the-lowest-performance-in-the-international-mathematics-and-science-study/ | 2021-09-24T00:56:00 | s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057479.26/warc/CC-MAIN-20210923225758-20210924015758-00051.warc.gz | 0.967682 | 519 | CC-MAIN-2021-39 | webtext-fineweb__CC-MAIN-2021-39__0__15567660 | en | In 2011, the Trends in International Mathematics and Science Study (TIMSS) showed that South African learners have the lowest performance among all 21 middle-income countries that participated. South Africa’s development as a knowledge economy depends partly on improving the teaching of mathematics and numeracy. Furthermore, South Africa’s extremely high youth unemployment, which is currently at 50%, is closely linked to the quality of schooling; numeracy and mathematics competency in particular. We have looked at the education Stats for 2013 and 2014 as shown on department of education website, and the results show that we still have a long way to go in terms of improving the situation for the future of this country.
Nubian Smarts believes that building a solid math foundation is vital for children to succeed. Hence our interest in creating applications for primary school children. Studies have shown that students with weak basic math skills find the subject increasingly difficult and confusing thus leading them to get poor results. This often leads to math anxiety and the belief that mathematics is hard and not fun, which is how most people feel when asked about their experiences with regards to maths.
So in essence when a child develops a solid math foundation, you notice that the stress caused by poor math skills disappears, and you might notice the child even saying that maths is fun. We at Nubian Smarts believe that this is not an unattainable goal and that the key to improving these statistics is by creating mobile applications that focus on creating a lifelong love of mathematics. These mobile applications are not intended to be a unique educational method but rather to complement the other areas of the educational programme.
Studies conducted have reported that mobile apps are not only engaging, but educational, for children as young as preschool. PBS Kids, in partnership with the US Department of Education, found that the vocabulary of kids’ age’s three to seven who played its Martha Speaks mobile app improved up to 31%. Abilene Christian University conducted research around the same time that found math students who used the iOS app “Statistics 1” saw improvement in their final grades. They were also more motivated to finish lessons on mobile devices than through traditional textbooks and workbooks.
More recently, two studies that separately followed fifth and eighth graders who used tablets for learning in class and at home found that learning experiences improved across the board. 35% of the 8th graders said that they were more interested in their teachers’ lessons or activities when they used their tablet, and the students exceeded teachers’ academic expectations when using the devices. | mathematics |
https://differencify.com/feet-vs-square-feet/ | 2024-03-03T20:24:27 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947476397.24/warc/CC-MAIN-20240303174631-20240303204631-00678.warc.gz | 0.935509 | 1,143 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__49984305 | en | Are you ready to take a step towards understanding the fundamental difference between feet and square feet? Whether you’re a novice in the world of measurement or simply curious about how these terms are used, this blog post will unravel the mystery for you. From finding the perfect shoe fit to calculating your living space, we’ll explore why it’s essential to distinguish between regular feet and their squared counterpart. Get ready to put your best foot forward as we dive into this fascinating topic!
Feet Vs Square Feet (Comparison Table)
|The term “foot” refers to a unit of measurement equal to 12 inches (30.48 cm) in length.
|The term “square foot” refers to a unit of area measuring equal to one foot by one foot (1 sq ft = 12 in x 12 in = 144 sq in).
|The unit symbol for the foot is “ft”.
|The unit symbol for square feet is “sq ft”.
|The Foot is used to measure lengths, such as heights and distances.
|Square feet are used to measure area, often for rooms or land parcels.
|You cannot directly convert feet to square feet due to the different measurement types.
|To convert from feet to square feet, calculate the area in square inches and then convert it using the appropriate factor.
|Feet are measured in linear units.
|Square feet are measured in terms of area units.
|The term “foot” is derived from the Latin word “pedem,” meaning foot.
|The term “square foot” combines “square” and “foot” to denote an area defined by one-foot sides of a square.
Feet (plural of foot) is the non-SI unit for measuring length. It is used mainly in the Imperial and U.S. customary systems of measurement and is equal to 12 inches or 30.48 centimeters. We often use feet to measure the height of something or the distance between two points.
Examples of Feet
- The height of a basketball hoop is 10 feet.
- The length of a soccer field is 120 feet.
- The depth of an Olympic-size swimming pool is 10 feet.
What is Square Feet?
Square feet, on the other hand, is a unit of measurement used in the imperial and US customary systems to measure area. It is equal to one square foot, which is defined as an area with sides of one foot in length. One square foot is equal to 144 square inches and 0.09290304 square meters.
Examples of Square Feet:
- The average size of a two-bedroom apartment is 1,000 square feet.
- The size of an Olympic-size swimming pool is 7,600 square feet.
- A standard bowling alley lane measures 41 ½ feet long by 12 ½ feet wide, for a total area of 518 ¾ square feet.
Key Differences Between Feet and Square Feet Explained
- Meaning: The term “foot” refers to a unit of measurement that is equal to 12 inches (30.48 cm), while the term “square foot” refers to a unit of area measure equal to one foot by one foot (1 sq ft = 12 in x 12 in = 144 sq in).
- Unit Symbol: The unit symbol for the foot is simply “ft”, while the unit symbol for square feet is “sq ft”.
- Conversion: It is not possible to directly convert from feet into square feet because they are different units of measure; however, it is possible to calculate the area of an object or space given its dimensions in feet and then convert this area into square feet using the appropriate conversion factor.
- Measurement: The measurement of feet is taken in linear units while the measurement of square feet is taken in terms of area.
How to Convert Feet to Square Feet
There are 12 inches in a foot, so to convert feet to square feet, you need to multiply the number of feet by 12. For example, if you have a room that is 10 feet wide and 20 feet long, the area of the room would be 200 square feet. Mathematical derivation is as follows:
Area = Length x Width
Area = 10 feet x 20 feet
Area = 200 square feet
Common Mistakes Made When Measuring with Square Feet
When it comes to measuring square feet, there are a few common mistakes that are made.
First, when measuring square footage, you should always use a tape measure. Measuring with a ruler will not give you an accurate measurement.
Second, when measuring the length and width of a room, make sure to measure from the outside edges of the room.
Third, make sure to include all areas of the room when measuring square footage. This includes closets, hallways, and any other areas that are part of the room. Don’t forget to convert your measurements into square feet. To do this, simply multiply the length by the width.
We hope that this article has helped you understand the fundamental difference between feet and square feet. Knowing the unit of measurement for each can be important when planning projects or taking measurements. It is also a useful tool to know when shopping for items that require precise measurements, such as flooring, appliances, furniture, etc.
In addition to understanding these units of measure, it is important to have the right tools in order to make sure your project turns out perfectly! | mathematics |
https://www.gamesforyoungminds.com/blog/2018/7/17/nim-a-devilishly-difficult-game | 2019-08-21T19:00:38 | s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316150.53/warc/CC-MAIN-20190821174152-20190821200152-00468.warc.gz | 0.967154 | 1,356 | CC-MAIN-2019-35 | webtext-fineweb__CC-MAIN-2019-35__0__124257564 | en | Nim - A Devilishly Difficult Game
Ages: 7 and up
Math Ideas: Subtraction, deductive reasoning, mathematical proof
Questions to Ask:
Want to figure out a strategy to always win?
Do you want to go first or second this time?
If you make that move, what do you think I will do?
Years ago, a teacher friend sent me an online version of the game Nim. "Try it out!" they said innocently enough, "See if you can figure out the strategy!"
The game seemed simple enough, basically just a set of three rows of objects. So I gave it a shot, and I lost. And then I lost again, and again. I finally walked away from my computer, a broken man.
In the years since then, I've moved cities and schools, had three kids, and STILL CANNOT BEAT THIS GAME.
In preparation for this newsletter, I finally gave in and looked up the solution. And having seen a lovely explanation from one of my favorite mathematicians, James Tanton, I think I can provide a way to turn this maddening little game into a meaningful mathematical exploration for you and your child.
How to Play
Nim is an ancient game with many variations, but each version is based on the same idea: rows of stones.
The original version I played had three rows of stones, as pictured. But you can have as many rows of stones as you want, and each row can contain as many stones as you like.
You and your opponent take turns choosing a single row of stones and then removing as many stones from that row as you want. You can remove a single stone, a few stones, or even the entire row. The person to take the last stone wins.
You can play an online version of the game with four rows here. The version I played has been lost to the sands of time (Good riddance).
Playing Nim with your Child
Have you played the version above a couple of times? Have you lost every time, just like me? Great, you're ready to explore this game with your child!
I don't usually get this prescriptive with my advice, but I think that Nim provides a great opportunity to show your child one of the greatest problem-solving skills of a mathematician: solving a simpler problem.
Introduce the game to your child, then play a couple of versions of Nim that start with two rows. Then ask them "Do you want to figure out a strategy to always win?" Kids love nothing so much as winning, so hopefully they'll be on board!
Start with a very simple version of Nim: a one-row version of the game. Lay out a row of stones and ask your child "Do you want to go first or second?" Hopefully, they choose to go first and snatch up all the stones! If not, snatch all the stones yourself on your turn, then set up the game again and ask if they want to go first or second.
This version of the game isn't very fun, but it does teach you and your child an important principle of the game: if there is only one row left on your turn, you win!
Now you're ready to play the two-row version of the game. Again, though, you want to start with a simplified version: one stone in each row. Again, ask your child "Do you want to go first or second?"
This time, going first is a guaranteed loser! No matter which stone you choose, your opponent can take the other stone to win. So now you and your child have another piece of strategy about the game: if you can get the stones down to a single stone in each row on your opponent's turn, you win!
One last mini-game before the final reveal: set up a game with two stones in each row and ask your child "Do you want to go first or second?"
Now you can start to discuss all the possible ways the game can go: If you choose to go first, you can either take a single stone from one row, or you can take both stones from one row. But taking both stones is a bad move, since your opponent will just snatch up both stones from the other row and win!
So you have to take a single stone from one row. But wait! Your opponent can take a single stone from the other row, leaving you with one stone in each row, a situation we know is hopeless! So two rows of two stones are equally as hopeless as two rows of one stone. In fact, two equal rows of stones are a guaranteed loser, no matter how many stones are in each row.
And now the strategy becomes clear: On your turn, take stones from the bigger row until both rows are equal. That way, you force your opponent to make the rows unequal on their next turn, and you can make the rows evenly matched again on your turn. Eventually you will winnow down the rows until each row has exactly one stone, and your opponent is doomed!
The beauty of this game is that this strategy works no matter how many stones are in each row. Once you know the goal of making the two rows equal, you can play any variation on the two-row version of Nim. And what if the two rows start out equal? Simple, just ask your opponent to go first! She'll break up the evenness of the rows, and you are back on track to victory.
I think for most kids in elementary school, the two-row version of Nim is perfect. They get the feeling of accomplishment that they know how to beat the game, and they're sure to teach their friends how to play, simply to show off their prowess.
More importantly, though, they have gone through the experience of solving a game by solving simpler versions of a complicated problem. This is a tool that I teach my students to use in middle school, and it's a tool I use as an adult to solve mathematical problems that I've never encountered before. By modeling this process, you are giving your child an opportunity to experience the joy of mathematical discovery.
But wait - we haven't solved the three- and four-row versions of Nim, the ones that drove me crazy for years! That's true. But we have learned something valuable about the structure of Nim, which is that keeping the rows even somehow is a good strategy. In order to see how you can keep three or four rows even, you'll have to watch that lovely video from James Tanton that I mentioned earlier. | mathematics |
http://homeschooljournal.net/category/math/ | 2015-05-24T08:54:43 | s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927863.72/warc/CC-MAIN-20150521113207-00104-ip-10-180-206-219.ec2.internal.warc.gz | 0.923482 | 218 | CC-MAIN-2015-22 | webtext-fineweb__CC-MAIN-2015-22__0__191812568 | en | So, tomorrow is the great Pi day of the century. At 9:26:53 you will have the first ten digits of Pi with the day/month/year – 3.141592653.
Do you celebrate Pi day? If you don’t, you can use the following info for other days as just math lessons, but if you do there are a lot of cute ideas. One that we did was giving each number 0-9 a color and making a Pi chain. We also did Buffon’s needle (virtual and in real life) and got pretty close to 3.14.
Pi stuff, jewelry, belts, a few crafts, here.
Books – Sir Cumference and the Dragon of Pi, Why Pi?, A History of Pi, Joy of Pi.
Lots of Pi related ideas, crafts and games here.
Vi Hart shares her anti-Pi day message (she is pro-Tau) here.
And don’t forget to eat some pie (whether that it pizza or just pie) tomorrow! | mathematics |
https://musictherapyconnections.org/2017/02/sign-language-music-number-signs-1-10/ | 2024-04-18T04:52:50 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296817187.10/warc/CC-MAIN-20240418030928-20240418060928-00092.warc.gz | 0.942046 | 178 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__31850170 | en | This week in Sign Language & Music we explored numbers 1-10 in sign language. I mentioned that I often use number signs 1-31 in calendar time for many of my sessions. The numbers 1-10 are a great start to learning all of those number signs!
So heres the big question… Do I use signed numbers, or standard finger counting?
This really depends on what your classroom, students, or clients are using. If they have been using and gaining understanding with standard counting then that might be the most appropriate counting measure to use. Many of my classrooms use signed numbers so I use those to reiterate the method that is already being used in the classroom. At the end of the day I am always in search of the most efficient and effective means to the end. Check out this weeks video below, and have a wonderful week! | mathematics |
https://professorglobal.com.br/from-blackboard-to-bedsidehigh-dimensional-geometry-istransforming-the-mri-industry/ | 2024-04-23T01:46:59 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818452.78/warc/CC-MAIN-20240423002028-20240423032028-00202.warc.gz | 0.934857 | 3,966 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__119387454 | en | Twice per year, the American Mathematical Society (AMS) and the Mathematical Sciences Research Institute (MSRI) jointly sponsor a Congressional briefing.
These briefings provide an opportunity for communicating information to policymakers and, in particular, for the mathematics community to tell compelling stories of how our federal investment in basic research in mathematics and the sciences pays off for American taxpayers and helps our nation maintain its place as the world leader in innovation. Attendees on 28 June 2017 included Congressional staffers and representatives from the NSF Division of Mathematical Sciences, and Senate Minority Leader Charles Schumer and House Minority Leader Nancy Pelosi dropped in. David Eisenbud (MSRI), Karen Saxe (AMS), Anita Benjamin (AMS), and Kirsten Bohl (MSRI) organized this event. Presenter David Donoho has kindly shared these notes for his Congressional briefing. It is notable that the mathematicians had little interest in applications, yet the math inspired original MRI research and applications.
—Karen Saxe, Director, AMS Washington Office, and David Eisenbud, Director, MSRI
MRI scans are crucial tools in modern medicine: 40 million scans are performed yearly in the US. Individual 2-D MR images portray soft tissues that X-ray CT can’t resolve, without the radiation damage that X-rays produce. MRIs are essential in some fields, for example to neurologists seeking to pinpoint brain tumors or study demyelinating diseases and dementia.
MRI technology is remarkably flexible, constantly spawning new applications. Dynamic MRIs allow cardiologists to view movies showing muscular contractions of the beating heart. 3-D head MRIs allow neurosurgeons to meticulously plan life-and-death brain surgeries, in effect to conduct virtual fly-throughs ahead of time.
Traditionally MRIs required lengthy patient immobilization—in some cases hours. Long scan times limit the number of patients who can benefit from MRI, and increase the cost of individual MRIs. Long scan times also make it difficult to serve fidgety children. Ambitious variations of MR imaging—such as dynamic cardiac imaging and 3-D MRI—require far longer scan times than simple 2-D imaging; such long scan times have typically been awkward or even prohibitive. Yet patients with arrhythmias and afib could get better treatment based on dynamic cardiac imaging; patients with aggressive prostate cancer could get much more accurate biopsies under 3-D MRI guidance; and many neurosurgeries could be much safer and more effective if surgeons could plan surgeries with 3-D MRIbased fly-throughs beforehand.
Help is on the way: inspired by federally funded mathematical sciences research, patients everywhere will soon complete traditional clinical MRI scans much more rapidly. Ambitious but previously rarely available MRI applications will go mainstream.
2. Accelerated Imaging by Compressed Sensing
In 2017, the FDA approved two new MRI devices, which dramatically speed up important MRI applications from 8x to 16x. Siemens’ technology (CS Cardiac Cine) allows movies of the beating heart; GE’s technology (HyperSense) allows rapid 3-D imaging, for example of the brain. Both manufacturers say their product is using Compressed Sensing (CS), a technology that first arose in the academic literature of applied mathematics and information theory.
Roughly ten years ago, mathematicians, in-
cluding Emmanuel Can-dès, now at Stanford, Terence Tao of UCLA, and me, put forward theorems showing that compressed sensing could reduce the number of measurements needed to reconstruct certain signals and images. Partly inspired by these new mathematical results, MRI researchers such as Michael Lustig (now at Berkeley) and collaborators in John Pauly’s lab at Stanford began to work intensively on new scanning protocols and algorithms. Compressed-sensing-inspired imaging became in the next few years a leading theme at international conferences of MRI researchers. Convincing clinical evidence soon emerged. Shreyas Vasanawala at Lucille Packard Children’s Hospital (Stanford) and co-authors (including Lustig and Pauly) showed in 2009 that pediatric MRI scan times could be reduced in representative tasks from 8 minutes to 70 seconds, while preserving the diagnostic quality of images. Fidgety children could thus be imaged successfully and comfortably with far less frequent use of sedation. Other researchers demonstrated impressive speedups in dynamic heart imaging in the clinical setting. Manufacturers ultimately became convinced; serious commercial development followed, leading to 2017’s FDA bioequivalence approvals.
Researchers at GE and Siemens tell me that accelerated imaging can be expected to spread broadly to many other MRI settings. The industry welcomes the new approach to accelerate MRI scans, and is seeking to deploy it where possible.
Transforming the MR industry takes time. In each proposed application, the FDA must first certify that accelerated imaging is bioequivalent to traditional imaging: that it really can produce diagnostic quality images in less scan time. Seeking FDA approval demands a rigorous multi-step evaluation taking years. From this viewpoint, it seems stunning that compressed-sensing inspired products are now on the market, only about a decade after the initial academic journal articles. This is certainly a testament to the energy and talents of MRI researchers and developers, and also a sign that the underlying mathematics was solid, reliable, and applicable.
The technology remains to be deployed into hospitals and clinics. More than 5 billion USD in MR scanners are sold annually; service and maintenance costs add billions more. There are tens of thousands of MRI scanners installed in the US currently, and many more worldwide. Improving MRI, by whatever means—mathematical ideas like compressed sensing, or physical ingredients like more powerful magnets—is always a gradual process of getting new equipment into the marketplace or retrofitting existing scanners.
For patients, such improvements can’t come soon enough. My own son is a neurosurgery resident at a large county hospital that serves many indigent and uninsured patients. He treats dramatic injuries to the head, from gunshot wounds, blunt force trauma, and car wrecks; but also less dramatic yet serious problems like aneurysms and brain tumors. In his hospital, which does not yet have the accelerated MRI technology I’ve been speaking about, lengthy delays for MRIs are common; sometimes he must open the patient’s cranium without any MRI at all. In other cases, he only can inspect a few 2-D slices, rather than a full 3-D image.
My son’s comment about accelerating MRIs: “Faster, please.”
3. The Role of Mathematics Research
NSF-funded Mathematical Sciences research, and NIH funding of cognate disciplines played a key role in these developments.
First: how can mathematics be helpful? Don’t the MRI researchers have all the equipment they need to simply do whatever they need, and then see experimentally if it works?
The answer is interesting. Mathematicians build formal models of systems and then derive logical consequences of those formal models. Whatever mathematicians discover about such models is logically certain. In everyday experience, almost anything can be doubted, nothing is as it seems, whatever can go In mathematics, wrong will go wrong. In mathematics, a true statement ment is true, full stop. If a mathematical theorem says something surprising or impressive, you don’t waste time doubting the messenger—you just read the proof and (if you have the background) you will see why the theorem is true.
Mathematical results can be transformative when applied to a phenomenon in the real world that is poorly understood and as a result controversial. And in the case of accelerated scanning, that was the case. Prior to the mathematical work I mentioned above, isolated projects had observed experimentally that in special circumstances, researchers obtained impressive speed improvements over traditional MRI scanning. However, the MRI community as a whole was uncertain about the scope of such isolated results, and the impact of the published experimental evidence was therefore limited.
Mathematical research can go farther and deeper than experiments ever will go. It can give guarantees that certain outcomes will always result or that certain outcomes will never result. When you first hear of such a guarantee, it can rock your world.
Early mathematical results about compressed sensing guaranteed imaging speedups under certain conditions. This got the attention of MRI researchers and inspired some, such as Michael Lustig, to go all in on compressed sensing. Eventually, the mathematical certainty offered by the guarantees and their breadth broke the apparent ‘logjam’ of hesitation and suspicion that would have otherwise greeted MRI. Compressed sensing became a hot topic in MRI research.
Mathematics can also be a floodlight illuminating clearly the poorly understood path ahead. MRI researchers have always wanted to accelerate MRI; they just didn’t see how to do it. Mathematicians proposed new algorithms and gave persuasive guarantees based on illuminating principles.
4. Some Mathematics
I’ll mention very briefly some mathematical ideas that were mobilized to study compressed sensing.
At its heart, compressed sensing (CS) proposes that we take seemingly too few measurements of an object— so from the given data there are many possible reconstructions. CS selects from among the many possible candidates the one minimizing the so-called Manhattan distance. Mathematics guarantees that the optimizing reconstruction (under conditions) is exactly the one we want.
The bridge between imaging and mathematics is produced by mathematical analysis of convex optimization algorithms that shows that the following statements are equivalent.
• Consider 100,000 random measurements of a 1000 by 1000 image. Suppose the underlying image has only 10,000 nonzero wavelet coefficients. With overwhelming probability this image can be reconstructed by minimizing the Manhattan distance of its wavelet coefficients.
• Consider a random 900,000-dimensional linear subspace of 1,000,000-dimensional Euclidean space. The chance that this slices into a certain regular simplicial cone with 10,000-dimensional apex is negligible.
The mathematical heart of the matter is thus the following geometric probability problem. We are in an N-dimensional Euclidean space, N large. We consider a convex cone K with its apex at zero, and sample an M-dimensional random linear subspace L. What is the probability that L intersects K? (See Figure 1.)
Want to add a caption to this image? Click the Settings icon.
Figure 1. The underlying mathematics asks for the probability that a high-dimensional cone intersects a high-dimensional plane.
As it turns out, this probability depends on the cone K, and on the dimensions M and N—let’s denote it P(K; M,N). The central surprise of compressed sensing is that, for the cones K we are interested in, we can have P(K; M,N) essentially zero, even when M <1, for the regions in question.
In the 1960s two papers by federally-funded US university professors invented key tools to attack our problem. Harold Ruben, then at Columbia, generalized Gauss’s formula for spherical triangles in dimension 3 to all higher dimensions, obtaining general formulas for the spherical volume of high-dimensional spherical simplices. Branko Grünbaum at University of Washington formalized the
cone intersection probability P(K; M,N) in the case K>1 and developed some fundamental formulas for P(K; N,M).
Figure 2. The probability that a line intersects a cone is given by the area of the corresponding region on the surface of the sphere. When R is a spherical triangle, the great mathematician Gauss found a beautiful formula for area: simply the sum of the three internal angles, minus π. This formula is easy to understand but conceals a surprising wealth of intellectual meaning.
In the 1990s, German geometric probabilist Rolf Schneider and Russian probabilist Anatoly Vershik showed how to use Ruben’s and Grünbaum’s formulas to compute P(K’; M,N) for some interesting cones K’. In effect, they showed that (Ruben’s generalization of) Gauss’s charming formula was the heart of the matter; everything reduced to the computation of volumes of spherical simplices.
By the mid 2000s several approaches were developed to show that the central miracle of compressed sensing extended over a wide range of combinations of M and N; Candès and Tao (mentioned above) had developed by other means upper bounds on P(K; M,N), establishing that there was a useful such range. NSF-funded postdoc Jared Tanner (now at Oxford) worked with me to apply geometric tools of Schneider, Vershik, and Ruben to the cones K of interest. We developed precise formulas revealing the precise number of measurements needed for exact reconstruction.
Since then, slick machinery was developed by two teams at Caltech, Oymak/Hassibi and Amelunxen/McCoy/Tropp, to get these and many other results.
5. The Role of Federal Funding
The success story of compressed sensing is a testament to federal funding. Federal funding of pure and applied science has endowed the United States with research universities that are the envy of the world. Federal funding of mathematical sciences has led to amazing collections of sophisticated mathematical talent within those great universities, housed in departments of mathematics, applied mathematics and statistics, electrical and systems engineering and computer science, and even biology and chemistry.
These great institutions attract terrifically talented young people from around the world to come here to learn and become part of our technical infrastructure, strengthening the next generation of US science and industry.
Federal funding enabled the breakthroughs of compressed sensing along three paths:
• Federal funding enabled basic research in high-dimensional geometry, which is at the heart of compressed sensing. Harold Ruben and Branko Grünbaum were housed in statistics and mathematics departments at US universities when they did their foundational work.
• Federal funding enabled cross-disciplinary work that identified the key questions for mathematicians to resolve. In the late 1990s, NSF funded a joint project between optimization specialists Stephen Boyd and Michael Saunders and myself at Stanford, which studied the Manhattan metric for important data processing problems. Prior to this project, most scientists used the Crow Flight metric instead of the Manhattan metric. That project and its sequels funded work by Xiaoming Huo (now at The Georgia Technical Institute), Michael Elad (now at Technion), and myself that proved mathematically that the Manhattan metric could pick out the unique correct answer—when the answer we are seeking had a very strong mathematical sparsity property.
• Federal funding enabled focused research to go far deeper into this surprising area and dramatically weaken the required sparsity, for example by using random measurements. Researchers Emmanuel Candès (then at California Institute of Technology) and Terry Tao (University of California—Los Angeles), and myself and many others all were supported in some way by NSF to intensively study random measurements.
This is above all a case where the federal research funding system has worked. NSF support of mathematics and statistics and NIH support of electrical engineering and radiology have really delivered. The research universities, such as Stanford University, California Technical Institute, University of California—Los Angeles, and University of California—Berkeley, to mention only a few, have really delivered. As we have seen, industrial research groups at Siemens and GE have responded enthusiastically to the initial academic research breakthroughs.
Enabling the rapid transition were the great students and facilities available at Stanford University, produced by decades of patient federal support and also visionary campus planning and generous private donations. When Michael Lustig came to campus in the early 2000s as a graduate student of electrical engineering professor John Pauly, his office in Packard was less than a hundred yards away from the statistics department in Sequoia Hall, maybe 100 yards away from a GE-donated high-field MR research scanner, and maybe 300 yards away from a medical MRI research facility at Stanford Medical school. In a few hours, Lustig could literally engage in impromptu conversations about high-dimensional geometry with mathematical scientists, about specific MR pulse sequences with electrical engineers, and about specific possible clinical trials with doctors at Stanford Hospital. This tremendous concentration of resources allowed him in his thesis to produce results that inspired many MRI researchers to pursue compressed sensing-inspired research programs. Today’s Federal Funding model supported the development of such concentrated facilities and
talent over decades of patient investment; the model has delivered.
The cost-benefit ratio of mathematical research has been off-scale. The federal government spends about $250 million per year on mathematics research. Yet in the US there are 40 million MRI scans per year, incurring tens of billions in Medicaid, Medicare, and other federal costs. The financial benefits of the roughly 10-to-1 productivity improvements now being seen in MRI could soon far exceed the annual NSF budget for mathematics research.
ACKNOWLEDGMENT. There are by now literally thousands of papers in some way concerned with compressed sensing. It’s impossible to mention all the contributions that deserve note. I’ve mentioned here a select few that I could tie into the theme of a Congressional Lunch on June 28, 2017.
Thanks to Michael Lustig, PhD (University of California—Berkeley), Edgar Mueller (Siemens Healthineers), Jason Polzin, PhD (GE Global Research), and Shreyas Vasanawala MD (Stanford University), for patient instruction and clarifying explanation about MRI applications. Thanks to Ron Avitzur and Andrew Donoho for help with Pacific Tech Graphing Calculator Scripts used for the above figures and for movies that were used in the briefing. Thanks to Emmanuel Candès (Stanford University) and David Eisenbud (MSRI) for helpful guidance.
See the first item of “Inside the AMS” in the September 2017 Notices.
Here we really mean l1 norm. I figured that since Senator Charles Schumer would be present, we really should have a way to connect the proceedings to New York State!
Actually many other ways have arisen to understand these results, using sophisticated ideas from metric geometry to information theory. I would mention for example work of Roman Vershynin, Ben Recht and collaborators, and of Mihailo Stojnic. But in a brief presentation for Congressional staffers, I couldn’t mention all the great work being done.
Of course Crow Flight metric means standard Euclidean or l2 distance.
Lustig credits many other MRI researchers with decisive contributions in bringing CS into MR Imaging. He says: “I would emphasize the contributions of Tobias Block pubmed/17534903 and Ricardo Otazo (with Daniel Sodickson) pubmed/20535813. These guys have taken the clinical translation of Compressed Sensing orders of magnitude forward.” He also mentions key contributions of Zhi-Pei Lian of UIUC, Joshua Trzasko of Mayo Clinic, and of Alexey Samsonov and Julia Velikina of UW Madison. It seems that federal funding was important in each case. | mathematics |
http://iltp.de/ARQNL-2016/ | 2017-04-24T09:10:41 | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917119225.38/warc/CC-MAIN-20170423031159-00113-ip-10-145-167-34.ec2.internal.warc.gz | 0.824984 | 464 | CC-MAIN-2017-17 | webtext-fineweb__CC-MAIN-2017-17__0__210347323 | en | Non-classical logics – such as modal logics, conditional logics, intuitionistic logic, description logics, temporal logics, linear logic, dynamic logic, fuzzy logic, paraconsistent logic, relevance logic – have many applications in AI, Computer Science, Philosophy, Linguistics and Mathematics. Hence, the automation of proof search in these logics is a crucial task.
Aims and Scope
The ARQNL workshop aims at fostering the development of proof calculi, automated theorem proving systems and model finders for all sorts of quantified non-classical logics. The workshop will provide a forum for researchers to present and discuss recent developments in this area. The contributions may range from theory to system descriptions and implementations. Contributions may also outline relevant applications, describe problem formalizations, example problems, and benchmarks. We welcome contributions from computer scientists, linguists, philosophers, and mathematicians.
Topics of the ARQNL workshop will cover all aspects related to the mechanization and automation of quantified non-classical logics, including but not limited to:
- Proof theory, semantics, meta theory, and cut-elimination
- Proof search calculi, including sequent calculi, tableau calculi, connection calculi, resolution calculi, and instance-based calculi
- Modal logic, conditional logic, intuitionistic logic, description logic, temporal logic, linear logic, multivalued logic, dynamic logic, fuzzy logic, paraconsistent logic, relevance logic, free logic, and natural logic
- Techniques, strategies and heuristics to deal with first-order or higher-order quantification
- Implementation of theorem provers and experimental evaluations
- Problem libraries and benchmarking for theorem provers
- Applications, formalizations, and example problems
- User interfaces, proof representation, and syntax issues
ARQNL 2016 will be part of the International Joint Conference on Automated Reasoning IJCAR 2016 in Coimbra, Portugal.
23 July 2014, Vienna, Austria
(part of IJCAR 2014).
Proceedings: ARQNL 2014. Automated Reasoning in Quantified Non-Classical Logics. EPiC Series in Computing, Volume 33, EasyChair, 2015. | mathematics |
https://tcchan.wordpress.com/2010/06/13/the-smooth-and-the-striated/ | 2017-04-28T14:02:40 | s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122992.88/warc/CC-MAIN-20170423031202-00164-ip-10-145-167-34.ec2.internal.warc.gz | 0.947637 | 193 | CC-MAIN-2017-17 | webtext-fineweb__CC-MAIN-2017-17__0__4868825 | en | The Smooth and the Striated
Sierpensky’s sponge: more than a surface, less than a volume. The law according to which this cube was hollowed can be understood intuitively at a glance. Each square hole is surrounded by eight holes a third its size. And so on, endlessly. The illustrator could not represent the infinity of holes of decreasing size beyond the fourth degree, but it is plain to see that this cube is in the end of infinitely hollow. Its total volume approaches zero, while the total lateral surface of the hollowings infinitely grows. This space has dimension of 2.7268. It therefore lies between a surface (with a dimension of 2) and a volume (with a dimension of 3). ‘Sierpensky’s rug’ is one face of the cube; the hollowings are then squares and the dimension of the ‘surface’ is 1.2618. | mathematics |
http://catalog.fivethousand.net/academics/math | 2024-02-29T03:03:33 | s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474775.80/warc/CC-MAIN-20240229003536-20240229033536-00329.warc.gz | 0.944077 | 894 | CC-MAIN-2024-10 | webtext-fineweb__CC-MAIN-2024-10__0__42750839 | en | Lakeside’s math departments aim to challenge and inspire all students to reach their mathematical potential. We offer a wide range of courses and use a variety of teaching modes to meet the specific needs of Lakeside students. From grades 5 through 12, students are actively engaged in math – working together in groups, at the board sharing solutions, presenting to their peers, debating strategies, and creating a wide range of creative projects. In all courses, emphasis is placed on collaboration, problem-solving, computational thinking, and clearly communicating mathematical ideas and concepts.
We believe that strong math skills play an important role in becoming an engaged global citizen. A solid understanding of a wide variety of mathematical disciplines will enhance students’ abilities to understand their world, explore global issues, and promote social justice through the power of analyzing claims and communicating effectively with real data as well as through computational tools and approaches.
Middle School: A strong foundation
The goal of the Middle School math program is to provide a strong foundation in mathematics through challenging courses that are appropriate to the ages, abilities, and needs of our students. In addition to preparing them for future math endeavors, we want students to be excited by math’s potential for fun and creativity.
We aim to equip students with the mathematical skills of a competent citizen in today’s world.
These skills include the ability to model situations mathematically; to estimate and compare magnitudes; to interpret graphs and statistics; to calculate probabilities; to evaluate numerical and spatial conclusions; to solve problems mentally as well as with paper, calculator, and computer; and to communicate findings effectively. At all levels, students learn to work collaboratively as well as on their own.
Part of what you’re teaching is: What do you do when you encounter an obstacle? In the context of math class, that means helping students set high goals, helping them deal with the fact that sometimes you falter on the way to those goals, and helping them celebrate when they meet those goals. – Tom Rona, Middle School math teacher
The content of our grades 5-8 math courses is normally covered in grades 6 through 9 in other schools. Students progress from arithmetic skills and mathematical thinking through pre-algebra and conceptual frameworks, to algebra and trigonometry. In each course, students deepen their understanding of concepts and skills introduced in previous courses. In addition to our regular math curriculum, many students choose to engage in Math Club (5/6 and 7/8), where they can have fun exploring math and extend their learning through working on challenging problems alone or in groups.
Read more about Middle School math in the Middle School curriculum guide.
Upper School: From the basics to college-level
We offer a wide range of math and computer science courses at the Upper School so that students can be challenged at a level appropriate for them at every grade. Each course emphasizes collaboration, problem-solving, and clearly communicating mathematical ideas and concepts. Since 2015, computer science concepts and principles have been embedded in the math curriculum, reflecting Lakeside’s belief that programming is an important 21st-century skill.
Every Lakeside student gains experience with computer science and programming, even if they never take a computer science class.
For the majority of math courses, we offer regular, accelerated, and honors levels. Students work with their teachers to determine the right level for them each year, and students can move between levels. While only three years of mathematics are required for graduation, the majority of Upper School students take a four-year sequence of algebra 2, geometry, precalculus, and statistics or calculus. All levels of courses at Lakeside provide a firm foundation in mathematics and will prepare students for college math courses. Calculus and statistics courses will prepare students for success on AP tests.
A range of computer science course offerings include everything from an introductory level course for those with no prior experience in programming, to advanced project-based courses such as 3-D prototyping and printing. The program takes advantage of the region’s technology community: Through guest lectures, field trips, and other opportunities, students are exposed to real-world applications of computing technology, including its myriad uses in medicine, sports, robotics, architecture, music games, literature, apparel design, communication, and international development.
Read more about Upper School math and computer science in the Upper School curriculum guide. | mathematics |
https://bignewstime.com/how-many-grams-in-a-pound/ | 2023-02-06T22:19:50 | s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500365.52/warc/CC-MAIN-20230206212647-20230207002647-00769.warc.gz | 0.942003 | 896 | CC-MAIN-2023-06 | webtext-fineweb__CC-MAIN-2023-06__0__208618771 | en | How many grams in a pound? This article provides the answer and the conversion chart for the metric and imperial units. In addition, it offers a calculator to convert grams to pounds. Read on to learn more. And don’t forget to use this conversion chart to convert grams to pounds! This will give you more accurate answers! Listed below are a few examples of how to convert grams to pounds.
Gram is 1/1,000 of a kilogram
A gram is a unit of mass in the International System of Units. It was originally defined as the weight of pure water in a cubic centimeter at the temperature of ice melting. Since the definition of a kilogram is no longer based on a universal prototype, it has been renamed to reflect Planck’s constant, h. It also includes a new definition of the meter and second.
One gram equals 0.001 kilogram. The formula to convert grams to kilograms is to multiply the number of grams by 0.001 and divide it by 1000. For example, if you weigh 1500 grams, divide that number by 1,000. That way, you will get 1.5 kilograms. Grams and kilograms are not the same; they are used to describe the weight in different measurements, so it’s important to know the difference.
The gram is a common unit of mass, used in everyday life. Most grocery stores and non-liquid ingredients are measured in gram. Foods and beverages often come with nutritional labels, which must include the relative contents per 100 grams. This makes the conversion process much simpler and faster. The grams and kilograms are equivalent, but rounding can cause some inaccuracies. However, the kilogram has its advantages.
Converting between metric and imperial units
You may need to convert measurements between the metric and imperial systems to understand what you’re comparing. Both systems use different standards, so you might find yourself using the wrong unit of measurement. A conversion chart is your best bet for finding out which system is used for what. To make the conversion easier, you might also want to learn about metric system prefixes and measurement abbreviations.
Metric systems are widely used in U.S. schools. Many measurement tools are made using both USCS and SI units. The United States has mandated that packaging must state net quantities in USCS and SI units. Metric units use a meter as the base unit. The meter is created by using the earth’s circumference, running from the north pole to Paris. A kilometer is one thousand millimeters.
Despite the popularity of imperial units, metric units are easier to learn. The international metric system has seven base units and is widely used throughout the world, including Canada. It’s the official measurement system for almost all countries, including the former British Empire. Canada switched to the metric system in the 1970s. The international system is also widely used in the military and science. But changing your measuring system can be expensive.
Calculator for converting between gram and pound
If you’ve ever wondered how to convert between gram and pound, you’re not alone. Using the wrong units can result in some disastrous situations. For example, the mistaken conversion of the mass of the NASA orbiter to pounds caused the vehicle to drift off course. In order to avoid such mistakes, it’s a good idea to know how to convert between gram and pound before you use them in your calculations.
First, look for a gram to pound converter. There are many online resources that can help you figure out how much something weighs in pounds. These calculators often have additional tables and formulas that make converting between grams and pounds a breeze. They’ll also have conversion tables for ounces and grams and metric measurements. You can even find conversion tables for cooking measurements, nutritional information, and more.
Another way to convert between gram and pound is to multiply the mass of one gram by 0.002205. For example, one gram is equal to 0.002204622621848776 pounds. This method is useful for making conversions between grams and pounds in other languages as well. However, it’s not as straightforward as you may think. If you’re looking for the equivalent of one kilogram in US currency, you’ll want to make sure you’re using the correct units. | mathematics |
https://jeromechapuis.com/px1nku/far-cry-6-jb-hi-fi-d673e9 | 2021-11-30T03:49:16 | s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358903.73/warc/CC-MAIN-20211130015517-20211130045517-00534.warc.gz | 0.920819 | 2,861 | CC-MAIN-2021-49 | webtext-fineweb__CC-MAIN-2021-49__0__175826958 | en | Linear Algebra (matlab - python) & Matrix Calculus For Machine Learning, Robotics, Computer Graphics, Control, & more ! Linear algebra is a field of mathematics that could be called the mathematics of data. Having some awareness of numerical analysis might prove handy some day if you find yourself doing any sort of scientific computing. Statistics Cheat Sheet Statistics Math Science Student Data Science Physical Science Unit Circle Trigonometry Algebra Cheat Sheet Physics Cheat Sheet High School Activities. MAT185 is loosely a continuation of ESC103. Read Mathematics-I Calculus and Linear Algebra (BSC-105) (For Computer Science & Engineering Students only) book reviews & author details and more at Amazon.in. Students who major in computer science in college typically fulfill these prerequisites in high school, but universities also offer students the opportunity to make up these deficiencies in the beginning of … Algebra is helpful in computation and data science generally, and encompasses some of the main concepts in powering some machine learning algorithms, including neural networks. Recommended if you’ve taken linear algebra before and just need a quick review. A better fit for developers is to start with systematic procedures that get results, and work back to the deeper understanding of theory, using working results as a context. In this course on Linear Algebra we look at what linear algebra is and how it relates to vectors and matrices. Take linear algebra. Offered by Imperial College London. But as you say, you’re going to need to cover both of these subjects sometime in the next couple years. Topics will be chosen from linear equations, systems of linear equations, linear inequalities, functions, set theory, permutations and combinations, binomial theorem, probability theory. MIT Linear Algebra course, highly comprehensive. Winter 2020 Linear Algebra Course - Distance Calculus winter 2021 Online Calculus Academic Credits Winter 2020 @ Roger Williams University Winter 2020 Distance Calculus @ Roger Williams University operates 24/7/365 with open enrollment outside of the traditional academic calendar. Hi PF community, recently i learned about Calculus in one variables and several, so now i'd like to study linear algebra by myself in a undergraduate level, in order to do that i need some textbooks recommendations. Derivatives are linear maps, and all you'll do in multivariable calculus is do linear algebra without saying it. 2. Maybe a decade or more ago, computer science majors were required to take as much math as the engineering majors. Then we look through what vectors and matrices are and how to work with them, including the knotty problem of eigenvalues and eigenvectors, and how to use these to solve problems. 5.1 Linear algebra. This level of mathematical maturity is 120. Learn linear algebra for free—vectors, matrices, transformations, and more. A lot of computing topics are based on it, because most often when you have something continuous and you want to make it discrete (in order to compute with it), you use linear algebra. The word Calculus comes from Latin meaning “small stone”, Because it is like understanding something by looking at small pieces. Saved by Cheatography. Learning linear algebra first, then calculus, probability, statistics, and eventually machine learning theory is a long and slow bottom-up path. For example, knowing how to efficiently solve systems of linear equations doesn't seem very useful unless you're trying to program a new equation solver. \Honors Linear Algebra". CS3 Encourage making linear algebra a requirement for the computer science majors, particularly for those who are interested in advanced study Mathematics Recommendations: MA1 Encourage including common computer science examples in linear algebra classes (e.g., graph analysis, 3D transformations, and speech recognition) If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Some knowledge of vector calculus is a prerequisite for the videos, but no knowledge of geometric calculus is assumed. Why Learn Linear Algebra for Machine Learning? Calculus has two major branches, differential and integral. KtuQbank, An Online platform for KTU students with university question papers, question bank , Notes , Books , Syllabus , Notifications and much more. The entire 6-part series can be watched in under 1 hour. In fact, the first step in solving many engineering problems is to make it a linear algebra problem. The Matrix Cookbook (PDF) – Excellent reference resource for matrix algebra. It’s so important that the unit used to measure computer performance for scientific computation is called a “flop”, standing for “floating point operation” and is defined in terms of a linear algebra calculation. Calculus IV – Ordinary Differential Equations for Engineers. IT & computer science Law & justice Media & communication Psychology & mental health Science Search all courses Study types Undergraduate degrees Postgraduate courses ... Calculus and Linear Algebra 1. It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more rigor-ous mathematics than what is presented in a \cookbook style" calculus … $2,200 $2,200. Khan Academy Calculus series (beginner-friendly). Your upfront cost: $0. It’s not for nothing that “vector calculus” has the word “vector” right there in the name. Stanford CS229 Linear Algebra review. 3. Linear algebra powers various and diverse data science algorithms and applications Here, we present 10 such applications where linear algebra will help you become a better data scientist We have categorized these applications into various fields – Basic Machine Learning, Dimensionality Reduction, Natural Language Processing, and Computer Vision or. Calculus. Free delivery on qualified orders. If you're seeing this message, it means we're having trouble loading external resources on our website. Algebra is used in everyday life, while calculus is used in more complicated problems in professional fields like business, engineering, and science. Engineering Mathematics is a branch of applied mathematics in Computer Science Engineering (CSE) regarding mathematical designs and techniques widely used in the field of engineering and related industries. I've been reading Linear Algebra and its Applications to help understand computer science material (mainly machine learning), but I'm concerned that a lot of the information isn't useful to CS. • From simple circuit solving to large web engine algorithms. 3Blue1Brown Calculus series. Amazon.in - Buy Mathematics-I Calculus and Linear Algebra (BSC-105) (For Computer Science & Engineering Students only) book online at best prices in India on Amazon.in. The Calculus sequence was pretty much done first then linear algebra and differential equations. 13. Offered by Imperial College London. From. Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.. I'll be waiting for your recommendations :). First- and second-order ordinary differential equations; introduction to linear algebra and to systems of ordinary differential equations. Linear Algebra is a basic field of math that is used in all sorts of engineering and science fields. The book assumes no knowledge of vector calculus. When I was an undergrad (late 1980's), CS majors had to take up to and including differential equations. Descriptions come directly from the respective course websites. These algebra courses run the gamut from introductory algebra to linear models and matrix algebra. This course offers a brief introduction to the multivariate calculus required to build many common machine learning techniques. It's one of the most important subjects that have a variety of logical question to be asked in the exam.. Step 2: Calculus for Data Science. It supposed to be a rst linear algebra course for mathematically advanced students. Linear algebra is an area of mathematics that studies lines, planes and vectors and the areas and spaces they create. Most students taking a course in linear algebra will have completed courses in di erential and integral calculus, and maybe also multivariate calculus, and will typically be second-year students in university. Computer Graphics • In computer graphics every element is represented by a MATRIX. It is undeniably a pillar of the field of machine learning, and many recommend it as a prerequisite subject to study prior to getting started in machine learning. 12. Rating: 4.7 out of 5 4.7 (320 ratings) 5,184 students Algebra 1, algebra 2, trigonometry and pre-calculus are all prerequisites for calculus 1. Used in machine learning (&deep learning) to formulate the functions used to train algorithms to reach their objective, known by loss/cost/objective functions. Calculus is a intrinsic field of maths and especially in many machine learning algorithms that you cannot think of skipping this course to learn the essence of Data Science. An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Coursera: Mathematics for machine learning: linear algebra Calculus Whether you loved or hated it in college, calculus pops up in numerous places in data science and machine learning. Calculus is important for several key ML applications. Conclusion: • There are so many application of Linear Algebra in Computer Science. This is misleading advice, as linear algebra makes more sense to a UNE-MTHS120-Calculus and Linear Algebra 1; Please note that your enrolment in this subject is conditional on successful completion of these prerequisite subject(s). Linear algebra is closer to the center of most computer science topics. Algebra. We start at the very beginning with a refresher on the “rise over run” formulation of a slope, before converting this to the formal definition of the gradient of a function. Linear Algebra Cheat Sheet from spoopyy. It’s no surprise that almost all engineering and science programs teach Linear Algebra very early on. Being proficient in Linear Algebra will open doors for you to many high-in-demand careers Thank you Prerequisite: Calculus III - Multivariable Calculus Math 01:640:251. The computations for performing linear algebra operations are among the most important in science. Summary: 1. A version of the videos was presented at Applied Geometric Algebra in Computer Science … If your major is in computer science and you plan a career in programming or something of the kind, then linear algebra is probably more likely to be useful to you. Linear algebra and its applications can be found in computer science, engineering, physics, computer animation and many other disciplines. Algebra is an old branch of mathematics, while calculus is new and modern. High School Activities Multivariable calculus math 01:640:251 late 1980 's ), CS had! Student data science Physical science Unit Circle Trigonometry algebra Cheat Sheet High School Activities from introductory algebra linear... Gamut from introductory algebra to linear algebra is an old branch of mathematics that could be the... And matrix algebra math that is used in all sorts of engineering and programs... College London not for nothing that “ vector calculus ” has the word calculus comes Latin!, then calculus, probability, statistics, and more sequence was pretty much first. Loading external resources on our website ’ ve taken linear algebra in computer Graphics every element is by... Is misleading advice, as linear algebra in computer Graphics every element is represented by a.. 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https://en.pinkmyrideph.com/mexican-youth-win-gold-and-silver-at-the-european-women-s-olympiad-in-mathematics-223575 | 2021-04-22T10:50:20 | s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00083.warc.gz | 0.935131 | 236 | CC-MAIN-2021-17 | webtext-fineweb__CC-MAIN-2021-17__0__61686976 | en | There are two types of girls in the world: those who never learned the multiplication tables and those who know the book by heart Baldor's Algebra, such as Ana Paula Jiménez, Nuria Sydykova Méndez, Karla Rebeca Munguía Romero and Natalia del Carmen Jasso Vera, who participated in the European Women's Olympiad of Mathematics (EGMO).
The four girls of Mexican origin demonstrated their knowledge and passion for numbers, and obtained gold, silver, honorable mentions and the applause of an entire nation.
On April 7, the four young Mexicans named the name of Mexico when they won gold and silver in the Mathematics Olympiad.
The EGMO lasted six days in which, through mathematical problems, equations and calculations, the Aztecs competed against 160 girls of different nationalities and achieved the tenth place among 49 competing teams.
Ana Paula won the gold medal; Nuria and Karla Rebeca, silver; while Natalia del Carmen received an honorable mention for her performance.
When the news arrived in Mexico, various media and friends congratulated them and offered their unconditional support. | mathematics |
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https://yesplay.bet/blog/posts/play-fafi-numbers-online | 2024-04-14T07:14:52 | s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816875.61/warc/CC-MAIN-20240414064633-20240414094633-00368.warc.gz | 0.913407 | 724 | CC-MAIN-2024-18 | webtext-fineweb__CC-MAIN-2024-18__0__15462189 | en | Experience the excitement of Fafi Numbers, a popular numerical game deeply rooted in South African culture. Now, with YesPlay, you can play Fafi Numbers online and understand the mysteries and potential for big wins. Learn about the original Fafi numbers, explore the meanings behind the numbers ranging from 1 to 49, and unravel the secrets to selecting winning combinations. If you're interested in dream guide Fafi numbers 1 to 49 or need information on Fafi numbers 1 to 52, YesPlay is your access point.
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https://barcainnovationhub.com/maximum-demand-scenarios-in-positional-play/ | 2020-04-05T05:47:44 | s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370529375.49/warc/CC-MAIN-20200405053120-20200405083120-00440.warc.gz | 0.93433 | 858 | CC-MAIN-2020-16 | webtext-fineweb__CC-MAIN-2020-16__0__40905128 | en | Players’ conditional response during competition, for example, distance covered at a run, has traditionally been described using the average value covered (in metres per minute) during a half or full game. Later on, shorter game periods were studied (e.g. 15 minutes in Robinson, O’Donoghue, Wooster, 2011; or five minutes in Bradley & Noakes, 2013), which showed more intense periods. However, it has recently been proven (Gabbet et al., 2016) that these values taken from static periods may not represent maximum demand scenarios or MDS. Recently, the application of the rolling technique (Varley et al., 2012) has allowed researchers to confirm the existence of more demanding conditional scenarios than the average values used up to now (Are small-sided games the solution to all our problems?).
This technique examines second by second (or frame by frame, depending on the sampling unit) the chosen period or interval (e.g. 1, 3, 5 or 10 minutes) which is used to determine the highest values of physical variables used as a reference (e.g. distance covered at a speed greater than 14 Km·h-1). Both quantities – the period or established timeframe and the chosen physical performance variable – follow the mathematical relationship indicated in the power law (Katz and Katz, 1999). Thus, when the timeframe is larger, the relative value of the conditional variable decreases. In football, for example, when the timeframe is close to 15 minutes, the conditional variable values are very similar to the average values for a partial or complete game (Lacome et al., 2018).
As well as refining the description of MDS (Martín-García et al., 2018), sports scientists are also beginning to take an interest in understanding whether these scenarios can be replicated in the training process. Specifically, they are asking whether there are play-related tasks that allow them to be replicated (Lacome et al., 2018). This paper explores this idea by applying two original concepts: first, it connects the MDS from multiple variables simultaneously; and second, it compares the MDS from positional play in relative terms to the MDS recorded by each player in competition (e.g. distance covered in % with respect to MDS in competition for the same variable).
The participants were 21 players from FC Barcelona’s reserve team during the 2015-2016 season, and they were grouped by standard positions: centre backs (CD, n=4), full backs (FB, n=6), midfielders (MF, n=3), attacking midfielders (AMF, n=3), and forwards (FW, n=5). The time windows and positional play studied were: 1) 5-minute windows for small-sided games (SSG) [SSG5, players per team = 5, goalkeepers = 2, dimensions= 33*40m, and duration = 6 ±1 min; SSG6, players per team = 6, goalkeepers = 2, wild cards = 1, dimensions= 33*40m, and duration = 6 ±1 min] and 10 minutes for long-sided games (LSG) [SSG9, players per team = 9, goalkeepers = 2, dimensions = 72*65 m, and duration = 12 ±3 min; SSG10, players per team = 10, goalkeepers = 2, dimensions = 105*65 m, and duration = 11 ±3 min] and in competitive matches, which had a timeframe of 45 minutes. The variables analysed represented the different movement systems (locomotor, mechanical, and energetic), such as total distance covered or distance covered at high speed, accelerations/decelerations, or variables related to metabolic power, respectively. The main results are shown in the following figures (1, 2 and 3). The charts give a percentage with respect to periods of maximum demand in the game compared to distance in metres per minute (Figure 1), distance at more than 25 km·h-1 (Figure 2) and number of accelerations, or ACC (Figure 3). The red dashes represent 100% and indicates the limit up to which MDS would be replicated in competition. | mathematics |
https://mmecaroline.com/product/french-kindergarten-math-centres-french-counting-activities-1-10/ | 2023-12-07T03:24:06 | s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100632.0/warc/CC-MAIN-20231207022257-20231207052257-00473.warc.gz | 0.854854 | 239 | CC-MAIN-2023-50 | webtext-fineweb__CC-MAIN-2023-50__0__248221375 | en | Make teaching counting skills fun with this engaging, hands-on counting centre! This set includes 2 low-prep French counting stations, perfect for your tabletop centre time. This clear, straightforward activity is perfect for your French kindergarten students who are learning how to count en français.
Let your students learn comment compter en français using these French kindergarten centres. Your students will love learning to count through play-based learning. They won’t even realize how much they’re learning!
Here’s what you’ll get:
- 10 marker cases with a number written on them (students add the markers)
- 10 marker cases with markers already on them (students add count the markers and add the number)
- 11 markers
- Numbers 0-10, written numerically and in words
These counting centres in French use printable manipulatives provided in the resource, so you won’t have to search your school for some!
Copyright © La Classe de Mme Caroline.
Permission to copy for single classroom use only.
Please purchase additional licenses if you intend to share this product. | mathematics |
https://www.wellesley.school.nz/about/why-wellesley/discovery-day/ | 2019-10-17T07:50:33 | s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986673250.23/warc/CC-MAIN-20191017073050-20191017100550-00028.warc.gz | 0.876101 | 186 | CC-MAIN-2019-43 | webtext-fineweb__CC-MAIN-2019-43__0__97298026 | en | Wellesley Discovery Days for Years 1-8
You and your son are invited to discover the magic of Wellesley and enjoy a fun and interactive day in our unrivalled environment, between the bush and the sea.
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Experience our Specialist Teaching subjects first-hand:
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Discover our Teaching and Learning philosophy:
- Visit our classrooms and see how our boys discover the love of learning in literacy and numeracy. | mathematics |
https://info.crunchydata.com/blog/topic/performance | 2019-07-21T09:25:36 | s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526940.0/warc/CC-MAIN-20190721082354-20190721104354-00025.warc.gz | 0.94967 | 205 | CC-MAIN-2019-30 | webtext-fineweb__CC-MAIN-2019-30__0__143870512 | en | Many applications these days want us to know how close we are to things:
- What are the three closest coffee shops to my current location?
- Which is the nearest airport to the office?
- What are the two closest subway stops to the restaurant?
and countless more examples.
Another way of asking these questions is to say “who are my nearest neighbors to me?” This maps to a classic algorithmic problem: efficiently finding the K-nearest neighbors (or K-NN), where K is a constant. For example, the first question would be a 3-NN problem as we are trying to find the 3 closest coffee shops.
(If you are interested in learning more about K-NN problems in general, I highly recommend looking at how you can solve this using n-dimensional Voronoi diagrams, a wonderful data structure developed in the field of computational geometry.)
How can we use PostgreSQL to help us quickly find our closest neighbors? Let’s explore. | mathematics |
http://chrismenardtraining.com/pivottable-median/ | 2018-07-22T02:40:25 | s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593004.92/warc/CC-MAIN-20180722022235-20180722042235-00227.warc.gz | 0.785739 | 303 | CC-MAIN-2018-30 | webtext-fineweb__CC-MAIN-2018-30__0__207384971 | en | PivotTables do not allow median function. We will create a helper column and use an array function to calculate the median in a PivotTable. Also shown are average, median, averageif, if statement with the median function.
The median function finds the middle number in a range. If you have an odd number of numbers (3, 7, 15 numbers) it will find the middle number. If you have an even number of numbers, (2, 14, 28) if will find the two middle numbers and average them.
Functions used in the video above
- Average – Returns the average (arithmetic mean) of the arguments. For example, if the range A1:A20 contains numbers, the formula =AVERAGE(A1:A20) returns the average of those numbers.
- Median – Returns the statistical median (the middle value) of a list of supplied numbers.
- Array Function
- AverageIf – returns the average (arithmetic mean) of all numbers in a range of cells, based on a given criteria. The AVERAGEIF function is a built-in function in Excel that is categorized as a Statistical Function.
There is no medianif function so we nested the median function with an if statement and made it an array function.
Upcoming Excel Events with Chris Menard in Atlanta
- Administrative Professional Day Conference on April 20, 2018
- Georgia Society of CPAs conference in August 2018 – Cobb Galleria | mathematics |
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