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Mathematics as a discipline is an important and beautiful human endeavor. It is an intellectual discipline worthy of study for its artistic and logical form as well as for its ability to help describe and interpret the world around us. To the extent of their abilities, all students at Portage High School should have the opportunity to learn to view mathematics as a way of thinking and to appreciate the cultural heritage of mathematics. In addition to grasping ideas and understanding their interrelations, it is important for students to communicate these ideas effectively to others. Goals The goals for students relect those stated in the Indiana Mathematics Standards as established by the Indiana State Department of Education. These goals assist students to value mathematics, become confident in one's ability to do mathematics, become a mathematical problem solver, communicate mathematically, reason mathematically, and use technology appropriately.
Try to complete this by our next meeting. You do NOT need to memorize the material. Just take in what you can. 1 - Read and complete pages 24 - 35 of the REA College Algebra. Take notes as you work on the sample problems. If you need help use the EZ-101 study keys book. Remember, this is college material and we have plenty of time. Do not worry if you do not understand it all. We will review the problems at the next class. At our next meeting we will: -review the problems from the first two weeks assignments -will answer your own questions -will view some of the video tapes Email me with any final questions you may have about the material or the exam and we'll find the answers together! Please feel free to make a donation towards our effort of providing you with a well thought out lesson plan for passing the CLEP. Please use the link above to spread the word about this site. Thank you!
new. We distribute directly for the publisher. Just published, an Expanded Edition of a popular [...] Brand new. We distribute directly for the publisher. Just published, an Expanded Edition of a popular book. Ideal for a broad spectrum of audiences, including students in math history courses at the late high school or early college level, pre-service or in-service teachers, and casual readers who just want to know a little more about the origins of mathematics. Can be used a History of Mathematics text, as a Liberal Arts Mathematics Text, or as part of the preparation of future mathematics teachers. Where did math come from? Who thought up all those algebra symbols, and why? What's the story behind? Each sketch contains Questions and Projects to help you learn more about its topic and to see how its main ideas fit into the bigger picture of history. The 25 short stories are preceded by a 56-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today
To start MAPLE 11 CLASSIC WORKSHEET, click the Start button on the bottom left hand corner of your screen, then select MAPLE11 from the popup menu, then select MAPLE11 CLASSIC WORKSHEET with the yellow icon. When you want to save your work, select the disk button on the toolbar. You will be prompted for a file name. To exit Maple, simply select the "exit" option under the "file" submenu in the top left corner of the Maple window. You are about to undertake a tutorial that will guide you through portions of the symbolic manipulation package called Maple. Maple is a powerful program that can be used interactively to do a wide variety of things ranging from tedious algebra to plotting three-dimensional graphics. This tutorial is intended to provide you with an overview of some of Maple's capabilities, as well as warn you about a few of the common pitfalls. In the material that follows you will repeatedly encounter text in the form shown below: > 1 + 1; 2 When text appears like this, the entry in bold following the > sign indicates items that should be entered by you at the Maple cursor. The text that follows is the output produced by Maple in response to your input. In the operation above, for instance, Maple responded to 1 + 1 by performing the addition correctly. Good ! Every Maple command must end with a semicolon as shown in the example above (or a colon if you don't want output displayed). For example, for the sum 1 + 1, enter the following: > 1 + 1; to which Maple responds with: 2 The use of a semicolon is crucial in Classic Maple, but not in the regular Maple. Until you enter a semicolon, Classic Maple assumes that you are still in the process of entering a single command. For example, the command above is equivalent to, > 1 > + 1; 2 Alternately, > 1 > + > 1 > ; 2 In either case, you can recognize that the semicolon behaves as a cue for Maple, indicating that the expression is ready for evaluation. This is a useful feature when dealing with long expressions that require multiple lines of input. You can also combine two commands one one input line, as long as you use the semicolon. Ugly ! What happens if you divide the above number by 999! ? The answer is extremely simple...you can do it in your head. Maple knows about certain special numbers such as E and Pi. For example, if we wish to compute 2*Pi we enter, > Pi * 2; 2 p Case matters. For example, pi is the just the Greek symbol p, whereas Pi is the number 3.14159... that we're used to. Incidentally, for lots of interesting information on Pi, peek into Pi through the ages Note that Maple does not evaluate the expression explicitly. Rather than introduce an approximate numerical value for Pi, it carries the constant along instead. To force Maple to evaluate the expression numerically enter, > evalf(Pi * 2); 6.283185308 evalf Make sure you understand the above instruction by determining E to a 100 decimal places. To compute E, you need to use the exp() function, as exp(1); evalf works in other situations as well. In the following, we will use it to obtain approximate values for the fraction: > 2 + 1/3; 7/3 To evaluate the fraction numerically, we will use evalf but this time with the symbol % which Maple recognizes as shorthand representing the expression on the previous line. > evalf(%); 2.333333333 Maple permits the definition of variables. To define a variable called emu and assign to it a value of 12 we proceed as follows. > emu := 12; emu := 12 Here := signifies assigned to. We can now query Maple for the value of emu, > emu; 12 or, we can multiply emu by 10, > emu * 10; 120 Maple has an excellent Help capability. To access it, you need to click on the Help button on the top right hand side of the Maple window. You can then search the Help database by topic, by text, or complete MAPLE's own tutorial. Almost everything we have done so far we could have done just as fast without ever using Maple. To really begin to take advantage of Maple we move on to some more advanced topics. Lets look at some symbolic calculations using Maple, where we tinker with variables without defining their numerical values, > (x + 2*y)^2; 2 (x + 2 y) Alternately, using shorthand % to refer to the last result, we can expand the expression, > expand(%); 2 2 x + 4xy + 4y Another example: > (x*y - y^2) / (x - y); 2 x y - y -------- x - y Maple does not simplify expressions automatically. In the previous example, for instance, as the numerator equals y*(x - y), the expression reduces to just y. For Maple to perform such a simplification, it must be explicitly requested, > simplify(%); y where the " again refers to the previous result. Having warmed up with some simple algebra, we are in shape to attempt solving algebraic equations. First, consider our old friend the quadratic equation. To make the steps somewhat clearer, we use the assigned to := operation to define a variable that will be our abbreviation for a quadratic equation, > eland := x^2 + 8*x + 12; 2eland := x + 8 x + 12 To solve the equation, eland = 0, enter the following: > solve(eland = 0, x); -2,-6 where x within the solve command specifies the variable to be solved for. Are these in fact solutions to the quadratic equation ? We can use Maple to carry out the check very easily. For example, substituting x = -6 into eland, > subs(x = -6, eland); 0 Therefore, -6 is a solution to eland = 0. Try other choices for x to see if they are solutions. Maple can also solve sets of algebraic equations. In the following we'll use this capability to determine the intersection between two lines. As before, to keep things tidy, we will define variables as abbreviation, > eq1 := y = a*x + c; eq1 := y = ax + c > eq2 := y = b*x + d; eq2 := y = bx + d These commands should strike you as a little odd. So far we have used the assignment operation := to introduce variables as abbreviations for expressions. Here, on the other hand, variables eq1 and eq2 are abbreviations for entire equations. To determine intersections between the two, we need to solve the equations simultaneously. Maple does this really well: > solve({eq1, eq2}, {x, y}); c - d ad - cb {x = - ------- , y = ---------} a - b a - b Easy ! Observe that we have exploited Maple's ability to work with sets to use solve on multiple equations involving multiple unknowns. Within Maple a set of objects is defined by enclosing the objects in a pair of curly brackets {}. With this in mind, the solve command can be seen to instruct Maple to solve the set of equations {eq1, eq2} for the set of unknowns {x, y}. Solutions to simultaneous equations are always returned as a list {unknown 1, unknown 2 ...}. We often want to extract the solution to just one unknown, so we can do further algebraic manipulations. For this purpose, the following trick is helpful >soln := solve({eq1,eq2},{x,y}): >soln[1]; c - d x = - ------- a - b >soln[2]; ad - cb y = --------- a - b This lets you see the solutions one at a time. MAPLE seems to give the solutions in a random order - when you run this tutorial you might find solution[1] is the equation for y, and solution[2] is the equation for x. I guess they do this to make life more interesting. We can substitute these solutions into new equations > eq3 := z = x^2 + y^2: >subs(soln[1],eq3); 2 (b-d) 2 z = ------ + y 2 ( a - b) You can substitute more than one variable into an equation using the syntaxsubs({soln[1],soln[2]},eq3); You can also use subs()to plug numbers into an equation. For example > subs({a=1,b=2,c=3,d=4},soln[1]); x=1 Maple's equation solving is fantastic and we will make a great deal of use of it in EN3. It can be a frustrating function to use, however, because if you make a mistake while typing in one of the equations, Maple will sometimes just sit there and won't tell you what's going on. For example, try the following We get nothing... That's because the system of equations actually has no solution. In eq1 and eq2 the left hand sides are identical, but the right hand sides are different. So Maple is stuck. When you solve a complicated set of equations with lots of variables, a small typo can cause this to happen. Sometimes the equation of interest may not have a closed-form solution. In such cases, Maple can be used to find numerical solutions. For instance, what if we were interested in finding values of x at which cosh(x) = 2*x. To solve this equation numerically: > fsolve(cosh(x)=2*x, x); .5893877635 There are more than one solution to this equation, and fsolve will report the first one it encounters. Depending on the version of MAPLE you are using, you may get a different answer. To check whether this is indeed the solution, find the hyperbolic cosine of this number: > cosh(%); 1.78775527 Dividing this result by 2 should return the original number, > %/2; .5893877635 Clearly, the equation is satisfied. Alternately, we can check the validity of the solution graphically. Consider the curve y = cosh(x) and the line y = 2*x. The two intersect at solutions to the equation cosh(x) = 2*x. To check that the intersection indeed coincides with the solution determined previously, we will use Maple to plot the two over the interval -3 to 3. First, the function cosh(x): > plot(cosh(x), x = -3..3); Here the two dots .. separating the limits of the plot are not accidental. These are required by Maple syntax. If you click on the plot, you will find that you change its size and axes using the plot bottons that appear on the toolbar. Right clicking on it brings up a menu which lets you change various properties of the plot, such as line thickness. Next, we proceed to plot the functions simultaneously to examine their intersection, > plot({cosh(x), 2*x}, x = -3..3); (There are two dots between the -3 and 3 again) Observe that the solution determined numerically does match an intersection. In order to touch up the plot, you might want to add a title and axes labels. To do that, enter instead: Note that you have to use the weird little backwards quotes positioned way up on the top left hand corner of the keyboard. Adding labels to plots in maple is a big pain. This is the second major limitation of MAPLE - you simply can't easily produce publication quality graphs. I usually just have MAPLE produce a bare plot, with no labels, and then export the plot in some format that I can paste into a proper illustrator program. Maple has extensive plotting capabilities. For a glimpse of these the Maple picture gallery at the NCSU Maple Archive is highly recommended. To keep your expectations from running overboard, on the other hand, an example of the sort of graphics Maple is likely to have trouble with. Here we will consider a single example: a three dimensional plot of the function z = sin(x)*sin(y), > plot3d(sin(x) * sin(y), x = -4*Pi ..4*Pi, y = -4*Pi..4*Pi); Observe that the grid used is far too coarse to display the function accurately. Moreover, unlike the two dimensional plots we worked through earlier, the command does not add axes to the plot. We can fix both problems by supplementing plot3d with additional instructions, grid[m, n] to add m and n grid lines along the x and y axes respectively, and axes = FRAME to switch on axes, Maple is highly skilled with calculus as well. For instance, differentiation requires the simple command, > diff(x^2, x); 2 x where x within the diff command specifies differentiation with respect to x. No surprises here. Things get a little more interesting when we use Maple to differentiate the function x*y with respect to x, > diff(x*y,x); y Clearly, Maple can carry out partial derivatives as well. Taking this a step further, let's differentiate x*y first with respect to x and then with respect to y, > diff(x*y, x, y); 1 this can be recognized as the partial derivative of x*y, first with respect to x then with respect to y. Maple can carry out integrals as well. To explore this ability, we'll attempt to integrate 2*x, > int(2*x,x); 2 x which helps us verify both, the integration here, as well as the differentiation performed earlier. We might need to integrate this function between specified limits. Taking the limits to be 0 and 5, for instance, > int(2*x, x = 0..5); Although Maple has an array of predefined functions such as sin(x) and exp(x), occasionally you will find it useful to define your own functions. To define the function sin(t)*exp(-omega*t), for example, proceed as follows: > f(t) := sin(t) * exp(-omega * t); f(t) := sin(t) exp(-w t) With this definition, you have added to Maple's list of functions the new function f(t). In all future operations, it will behave just as any of the predefined functions. For example, to differentiate the function with respect to t you would enter, > diff(f(t), t); You can also find the minimum and/or maximum of a function: > minimize(x^2-3*x+y^2+3*y+3); -3/2 Include the word 'location in the argument list, and it will tell you where the minimum or maximum occurs. >minimize(x^2-3*x+y^2+3*y+3, location); -3/2, {[{y = -3/2, x = 3/2}, -3/2]} You can prescribe a range with which the maximum or minimum can be found. > maximize(exp(-x),x=0..100); 1 Let's try a more complicated function and attempt to find the minimum value of sin^2(theta)+cos(theta) in the range 0<theta<2*Pi. > minimize((sin(theta)^8+cos(theta)),theta=0..2*Pi); minimize(sin(theta)^8+cos(theta),theta = 0 .. 2*Pi) The fact that Maple just returned our original statement means that it cannot handle the complicated function. But complicated maximization and minimization can be done with commnads from the Optimization package. This package is an extra set of functions that Maple provides. To access the package, type The functions Maximize and Minimize (note thea upper case M) find maxima and minima numerically, and can deal with more complicated functions. We can use Minimize, for example, to find the minimum value of sin^2(theta)+cos(theta) in the range 0<theta<2*Pi. > Minimize((sin(theta)^8+cos(theta)),theta=0..2*Pi); [-1., [theta = 3.14159265358979312]] Maple returns the minimum value of the function and the location at which it occurs--even though we did not add the word location, as was required with the minimize (lower case m) command. The Upper case-M commands can handle more than one variable. Here we find the minimum of the function (x-1)^2+(x-y)^2 in the ranges -1<x<-1, and -1<y<-1. > Minimize((x-1)^2 + (x-y)^2,x=-1..1,y=-1..1 ); [0., [x = 1., y = 1.]] And if we want to look for the minimum of this same function but are only interested in values of x and y for which x*(1+y^2) is greater than or equal to 8, we can do this by adding the constraint x*(1+y^2)>=8 to the command as follows: Clearing variables using the restart command Type > emu; 12 Remember that we defined emu to have the value 12? No? Maple, like the proverbial elephant, never forgets (unless you quit MAPLE). When you're solving a problem using MAPLE you often assign values or formulas to many variables. Then, when you want to move on to another problem, you need to clear these assignments. To clear all assignments, just type > restart; Then, just to check > emu; emu It is a good idea to start every worksheet with a restart;command to clear any defined variables from a previous session run in the same window. A remaining issue is the question of printing Maple graphics or worksheets. To print an entire worksheet, just click on the worksheet you'd like to print, and then hit the print button on the Maple toolbar. You can send the output to different printers - the first printer in the list is the one on the left hand side of the computer room; the second is the printer on the right. You can also create a pdf file using Acrobat PDFwriter. Finally, you may want to include a maple graph in a report you are writing - say a Microsoft word document. To do this, you can copy the graph (click on it and use the clipboard icon from the toolbar or right click and select copy from the po-up menu. The, you can paste the graph directly into your Word or other document. If you have a lot of graphs to rpint, you might want to set up Maple so that each graph appears in its window, rather than in the the worksheet. To do this, click the File pull down menu, and select Preferences... Click on the plotting tabe and then select Window int the Plot Display catagory. Now, plot your graph in the usual way: you will find the graph appears in a separate window in the MAPLE interface. To print a graph in its own window, click on this window, and then follow the instructions for printing worksheets (File, Print..., etc) that were outlined in the preceding paragraph. In this tutorial we have considered a range of Maple commands to help you get started with the package. These are, however, only a tiny subset of its capabilities. To proceed from here, depending on your needs, you could either work through some of the more advanced Maple tutorials available on the web (or Maple's own tutorial), or invest in a book on Maple. Once you are comfortable with Maple's basic capabilities, its probably best to aim to be aware of its more advanced aspects rather than attempting to master them all at once, returning to specific aspects only when the need arises.
Algebra Alge­bra is per­haps best defined as the study of "alge­braic struc­tures." Broadly con­strued, alge­braic struc­tures are sets endowed with addi­tional operations—think of the inte­gers (a set) with addi­tion and mul­ti­pli­ca­tion (addi­tional oper­a­tions). Usu­ally, these oper­a­tions allow ele­ments to be com­bined in some way, but some­times they're bet­ter described as allow­ing trans­for­ma­tion of ele­ments into each other—as, for instance, in the case of the cat­e­gory of sets endowed with the usual map­pings between sets. Such struc­tures are ubiq­ui­tous: inte­gers and their var­i­ous exten­sions, the vec­tor spaces you stud­ied in lin­ear alge­bra, groups of trans­for­ma­tions that encode sym­me­tries, abstract cat­e­gories that cap­ture rela­tion­ships between com­plex objects (like groups them­selves) are all exam­ples. Due to this ubiq­uity, alge­bra crops up in all areas of math­e­mat­ics and has a host of applications. The first two struc­tures you are likely to encounter are groups and rings. In gen­eral, groups should be thought of as col­lec­tions of trans­for­ma­tions. That's because objects in a group can be com­posed (usu­ally called "mul­ti­pli­ca­tion") and inverted, just like func­tions, but noth­ing else is required for a set to have the struc­ture of a group. Groups are impor­tant and beau­ti­ful objects. For instance, the set of all invert­ible lin­ear trans­for­ma­tions of a vec­tor space to itself is a group, as is the set of all rota­tions of space (of any num­ber of dimen­sions). These exam­ples also illus­trate the inter­pre­ta­tion of groups as sym­me­tries of some other math­e­mat­i­cal entity—in this case, a vec­tor space. Groups also play this role in the set­ting of per­mu­ta­tions (sym­me­tries of finite sets), geo­met­ric rearrange­ments of shapes (sym­me­tries of poly­gons), and Galois the­ory (sym­me­tries of num­ber systems). This last exam­ple shows how groups can be con­nected to their more sophis­ti­cated cousins, rings. While a ring can be thought of as a group with addi­tional struc­ture, a ring is really a very dif­fer­ent ani­mal. Rather than func­tions and trans­for­ma­tions, rings rep­re­sent num­bers. In this case, you can add them, take their neg­a­tives, and mul­ti­ply them—but that's it. Since many nat­ural num­ber sys­tems lack divi­sion (is one divided by two an inte­ger?), it is excluded from the defin­ing prop­er­ties of rings. When a ring has it any­way, it is called a field—thus, we speak of the "ring of inte­gers," but the "field of ratio­nal (or real, or com­plex) num­bers." Rings serve as a nat­ural gen­er­al­iza­tion of the inte­gers, and they pro­vide a set­ting for the study both of abstract objects that resem­ble them and con­crete num­ber sys­tems extend­ing them, like the ratio­nal num­bers, or the set of all num­bers of the form a + b √5 with a, b integers. Now, all of this is just the begin­ning. We haven't even men­tioned the ques­tion of com­mu­ta­tiv­ity, or the fact that there is a nat­ural way to think of rings as col­lec­tions of func­tions (just ask an alge­braic geome­ter). Nor have we really dis­cussed the rich the­ory that results in study­ing the way alge­braic objects inter­act with other math­e­mat­i­cal enti­ties. Nor the details of Galois the­ory. Nor cat­e­gories. The list goes on and on. But Prince­ton offers many ways for you to get into these and other alge­braic top­ics. This begins with an intro­duc­tory sequence that starts with groups, devel­ops the fun­da­men­tal aspects of the the­ory behind them, then builds up ele­men­tary ring the­ory and the most impor­tant parts of clas­si­cal Galois theory. After you've com­pleted the intro­duc­tory sequence, you will be ade­quately pre­pared to jump into the more advanced courses that inves­ti­gate the top­ics we've men­tioned above. Intro­duc­tory Courses [Show]Intro­duc­tory Courses [Hide] Princeton's intro­duc­tory alge­bra courses cover the three basic alge­braic struc­tures: groups, rings, and fields. A group is a struc­ture with one binary oper­a­tion, such as the set of per­mu­ta­tions of {1, 2, …, n}, with the binary oper­a­tion being com­po­si­tion. A ring is a struc­ture with addi­tion and mul­ti­pli­ca­tion, such as the set of poly­no­mi­als with real coef­fi­cients. A field is a ring where each nonzero ele­ment has a mul­ti­plica­tive inverse, such as the set of real or com­plex num­bers. In the past, Prince­ton intro­duced stu­dents to alge­bra through two courses. One of these (MAT 323), was a basic course cov­er­ing groups, rings, and fields. The other (MAT 322), focused more on rings and fields, and also cov­ered Galois the­ory. How­ever, Prince­ton has restruc­tured its intro­duc­tory alge­bra courses. Now, there will be a two-semester alge­bra sequence. Alge­bra I will mainly focus on groups, and will also cover some rep­re­sen­ta­tion the­ory. Alge­bra Ii will cover ring the­ory, field the­ory, and Galois the­ory. No fur­ther infor­ma­tion is avail­able at this point, but please check the math department's under­grad­u­ate page for announcements. Advanced Courses [Show]Advanced Courses [Hide] What to take before? Intro­duc­tory Sequence. What to take after? Class Field The­ory, Local Fields What to take before? Alge­braic Num­ber The­ory. MAT 447: Com­mu­ta­tive Alge­bra Please check registrar's page or math depart­ment web­site for infor­ma­tion on this course. What to take before? Intro­duc­tory Sequence. What to take after? Intro­duc­tion to Alge­braic Geom­e­try What to take before? Com­mu­ta­tive Alge­bra (not absolutely nec­es­sary)braelling semes­ter. What to take before? Com­mu­ta­tive Alge­bra (a must). What to take after? You'll be ready for any­thing table­sof What to take before? Intro­duc­tory Sequence th What to take before? Intro­duc­tory Sequence What to take after? Alge­braic Num­ber The­ory, Class Field Theory.
History In Mathematics Education - 1 edition Summary: This book investigates how the learning and teaching of mathematics can be improved through integrating the history of mathematics into all aspects of mathematics education: lessons, homework, texts, lectures, projects, assessment, and curricula. Most of the leading specialists in the field have contributed to this ground-breaking book, whose topics include the integration of history in the classroom, its value in the training of teachers, historical support for particular subjects and for stude...show morents with diverse educational requirements, the use of original texts written by great mathematicians of the past, the epistemological backgrounds to choose for history, and non-standard media and other resources, from drama to the internet. Resulting from an international study on behalf of ICMI (the International Commission of Mathematics Instruction), the book draws upon evidence from the experience of teachers as well as national curricula, textbooks, teacher education practices, and research perspectives across the world. Together with its 300-item annotated bibliography of recent work in the field in eight languages, the book provides firm foundations for future developments. Focusing on such issues as the many different ways in which the history of mathematics might be useful, on scientific studies of its effectiveness as a classroom resource, and on the political process of spreading awareness of these benefits through curriculum design, the book will be of particular interest to teachers, mathematics educators, decision-makers, and concerned parents across
Mathematics Department The Mathematics Department has much to offer the students of Hempfield School District. Students are offered a rigorous curriculum of Algebra, Geometry, Precalculus, and Calculus courses, with electives in the fields of Statistics and Computer Science. As attested to by numerous Hempfield graduates, the Hempfield mathematics curriculum prepares our students well for the rigors of college, technical school, and the world of work. Additionally, Hempfield offers Advanced Placement courses in Computer Science, Statistics and Calculus for students who are ready for the challenges these courses afford. Beyond the classroom, Hempfield math students have opportunities to compete in regional, state, and even national mathematics competitions. In grades 6-8, our students have access to the MathCounts competition program. At the high school level, opportunities such as the Pennsylvania Math League contest and the American Mathematics Competition await many of our students. In addition, Hempfield mathletes are invited annually to compete at local colleges and universities to test their mathematical and computer programming skills.
MATH 070Basic Math for the Math Avoiders• 5 Cr. Department Division Builds confidence and skills in arithmetic and pre-algebra. Students discuss symptoms of math anxiety and avoidance, as well as suggestions for overcoming them. Topics include operations with whole numbers, fractions, decimals and percentages, and elements of geometry and pre-algebra. Course is graded pass/fail. Outcomes: After completing this class, students should be able to: Multiply and divide whole numbers. Add, subtract, reduce, multiply and divide positive fractions. Add, subtract, multiply, and divide positive decimal numbers. Solve proportions and set up and solve application problems using ratios and proportions.
books.google.de - As a text for an undergraduate mathematics course for nonmajors, Mathematics and Politics requires no prerequisites in either area while the underlying philosophy involves minimizing algebraic computations and focusing instead on some conceptual aspects of mathematics in the context of important real-world... and Politics
Prerequisites: Math 101/105 or a passing score (12 or higher) on the Calculus Placement Exam (located at Students must have passed the ELM, equivalent test, or appropriate prerequisite class to take this class. Participation: Mathematics is not a spectator sport; doing mathematics involves doing mathematics. Students need to participate in learning activities because these are ways that you, as a student, learn. There are many ways of participation; classroom attendance is the beginning. Asking questions in class, coming to office hours to ask questions, participating in class activites, getting together in a study group, and consulting with other professors or tutors are all ways you can help further your understanding. Ultimately, the best participation is whatever it takes for you to take the ideas and concepts in the class and be able to create your own understanding. Learning environment: Treating others with respect and consideration is critical to the success of each learner. Your personal interactions should reflect this at all times. In addition, your behavior should give each classmate utmost consideration. If you must arrive late or leave early, do so in a way that minimizes the disruption. And of course, please turn off all cell phones, alarms, beepers, etc. while in class. Homework: I will assign homework each week on Monday, and they will be found on the assignments website. Instead of collecting the assignments, there will be weekly homework quizzes on Blackboard. It is important to keep current on the homework because each concept in the class builds on previous concepts, and catching up is much more difficult than keeping current. Your homework is the place where most of your learning will take place in the class. The processes of trying things out, testing, asking questions, running into obstacles, and figuring out how to overcome them are all essential to learning. There will times when you will figure out things relatively quickly, and there will be times when a certain concept takes a lot of time and gets frustrating. This is absolutely normal. It is through persistence and hard work that you will achieve understanding. Here are some words from people who have learned and achieved a lot in life: Genius is one per cent inspiration, ninety-nine per cent perspiration. --Thomas A. Edison The brick walls are not there to keep us out. The brick walls are there to give us a chance to show how badly we want something. Because the brick walls are there to stop the people who donít want it badly enough. --Randy Pausch There are no secrets to success. It is the result of preparation, hard work, and learning from failure. --Colin Powell Homework quizzes: There will be weekly quizzes on the homework. The questions will be based directly on the homework exercises, so you will need your finished homework set when taking the quiz. Each quiz will be available in the assignments section of Blackboard for a short time in the week after the corresponding homework is assigned. Late quizzes will not be accepted, but I will drop the lowest two quiz grades. Midterms: There will be two midterms The midterms are scheduled for the sixth week and the eleventh week. They will be held during the regular class time in the regular classroom. Calculators and notes may not be used on the midterms. Final: The final is scheduled for Tuesday Dec. 9 4:00-6:00pm for the 4:30 class and Thursday Dec. 11 7:00-9:00pm for the 6:00 class. The final will be comprehensive. Calculators and notes may not be used on the final as well. NB: Early finals will be not be given. Please plan accordingly. Makeup Exams: There will be no makeup exams. If you are unable to take one for an excused reason, I will average the rest of your exam grades for the course and use that in place of the exam score. Read the Book! The textbook is a valuable resource which contains a lot of useful information. Additional Resources: The University Math Tutoring Center is available for drop-in tutoring, is located on the second floor of the Broome Library, and is open M-Th 9am-7pm and F 9am-2pm. It is a good place to get math help. Another fantastic resource is the other people in class. Working together is an invaluable help in understanding math, and I highly encourage it. Accommodations for Students with Disabilities: CSUCI, Disability Accommodation Services (DAS), and I are committed to providing reasonable accommodations to students with various documented disabilities (physical, learning, or psychological). If you are a student requesting accommodations for this course, please contact me at the beginning of the semester and make an appointment with DAS (x3331 or TDD x3331) for the verification of accommodation of need. I will work closely together with you and your coordinator to provide necessary accommodations. Academic Honesty: The homework and exams are intended to be representative of the student's own learning or work. If I suspect a violation of academic honesty, then I will discuss the apparent incident with the student to provide them with an opportunity to explain the situation. If I feel that indeed academic dishonesty has occurred, then I will file a report with the Dean of Faculty, the Provost, or the Vice-President for Student Affairs. Depending on the severity of the situation, I may assign a failing grade to the homework/exam/paper, or an 'F' for the course. Students should consult the Honor Code as listed in the 2008-2009 Catalog, section 7. (Paraphrased from the pamphlet, "Top 25 Things New Faculty Should Know About CSUCI") Amendments: Over the course of the semester, it may be necessary to change aspects about the class structure (such as when midterm are given, for example). Whatever changes are made, I will announce them in class. Grades: The problems will be graded on a scale with full points assigned to fully complete and correct work, a medium number of points to partially correct or complete work, and a low number of points to little work or substantially incomplete/incorrect work. Your final grade will be computed as follows: 10% homework quizzes, 25% each midterm, and 40% final. Plus and minus grades will be used where appropriate.
Grades 6-8 Math The goal of the Mathematics Department at the Carmel Campus The goal is that the students, not the teacher or a textbook, be the source of mathematical knowledge. As a result, each student is able to thrive at the pace that best suits them to reach their fullest potential mathematically. Therefore, our students are also then best prepared for entry into Stevenson's Pebble Beach Campus. To accomplish these goals, we schedule math at the same time each day for K-5. We use a highly individualized approach to teaching math in grades 6-8 that has benefits well beyond antiquated tracking approaches to teaching math. We We see the following tenets as essential to our curriculum: that algebra is important as a modeling and problem-solving tool, with sufficient emphasis placed on technical facility to allow conceptual understanding; that geometry in two and three dimensions be integrated across topics at all levels and include coordinate and transformational approaches; that the study of vectors, matrices, counting, data analysis, and other topics from discrete mathematics be woven into core courses; that computer-based and calculator-based activities be part of our courses; that all topics be explored visually, symbolically, and verbally; that developing problem-solving strategies depends on an accumulated body of knowledge. The curriculum is problem-centered rather than topic-centered. The purpose of this format is to have students continually encounter mathematics set in meaningful contexts, enabling them to draw, and then verify, their own conclusions. Our As a result, each student is able to thrive at the pace that best suits them to reach their fullest potential mathematically. The teachers provide individual assessment throughout the year for every student, thus helping to foster skills and content mastery that are unique and relative to every student. Class Web Pages See what's happening this year in grades PK-8 by viewing the individual class web pages. Information Request Request a complete information packet for the Carmel Campus. We will send you an informational viewbook, as well as an application for admission. You many arrange a parent tour and a student school visit as part of the formal application process.
Short details of Horizontal Tank Add-on for MathU Pro: Given the diameter, and length of the horizontal cylindrical tank, calculate the volume of the tank for a given depth of liquid = x.. Creative Creek: Calculators, Software and Consulting for Palm OS, Windows Mobile and MATLAB. Calculators, Software and consulting for Palm OS, iPhone, Windows... Calendar functions for MathU Pro similar to those available on an HP-12C and similar calculators.. Creative Creek: Calculators, Software and Consulting for Palm OS, Windows Mobile and MATLAB. Calculators, Software and consulting for Palm OS, iPhone, Windows Mobile, and MATLAB. Makers of professional calculators for Palm OS, iPhone and Windows Mobile. Our Palm OS, iPhone and Windows Mobile calculators turn your PDA into a advanced scientific,...Program to allow calculation of predictive values and post-test probabilities given input in one of three methods: 1. Data from study (true positive, false positive, true negative, false negative) 2. Sensitivity, Specificity, Pre-test probability 3. Likelihood ratios, Pre-test probability Includes an RTF file that explains Bayesian analysis along with the formulas used, reference to an online calculator as well as instructions for the... Provides conversions/calculations (add, subtract, multiply and divide) with decimals of a foot to feet, inches, sixteenths and visa versa. Also includes a RISE, RUN, SLOPE, PITCH program to calculate the three sides of a triangle (in Ft.In16 format) and the angle of slope (degrees or Ft.In16 on 12" pitch) with input of any two items. Includes comprehensive PDF-based documentation.. Creative Creek: Calculators, Software and Consulting for... Provides conversions/calculations (add, subtract, multiply and divide) with decimals of a foot to feet, inches, sixteenths and visa versa. Also includes an "area" program to calculate the "area of squares/rectangles" in Ft.In format input or in Dc.Ft format input. It will calculate the area of ONE square/rectangle OR run an accumulative total of areas of squares/rectangles (add or subtract feature included here). Includes
Welcome Mathematics is the most central of the STEM disciplines, fields of study in the categories of science, technology, engineering and mathematics considered as vital areas of study in the modern age. As President Obama said at the launch of his 'Educate to Innovate' campaign in November 2009, "Reaffirming and strengthening America's role as the world's engine of scientific discovery and technological innovation is essential to meeting the challenges of this century. That's why I am committed to making the improvement of STEM education over the next decade a national priority." The Department of Mathematics and Statistics plays a vital role in STEM education not only through the advanced training of its own majors and graduate student students but through the support it gives to sister disciplines in the College of Engineering, Forestry and Natural Sciences. This support takes the form of advanced coursework in areas such as numerical analysis and partial differential equations (physics and engineering), classes in statistics (biology and forestry) and through its Statistical Consulting Lab which advises faculty and graduate students across the university in the design of experiments and the analysis of data. The Department of Mathematics and Statistics also prepares students for secondary mathematics teaching, provides further training and professional development opportunities for in-service teachers, and works with schools on a variety of outreach activities. The Department of Mathematics and Statistics also provides coursework to enhance the quantitative reasoning skills of students across the university and in support of the needs of a wide variety of majors, such as elementary education, parks and recreation management and business.
This is a short eBook that describes how to get free high school Algebra 1 help online without having to spend any money, buy anything, join any free trials, or anything like that. Free High School Algebra 1 Help Online | Algebra 1 Help.org. A short ebook explaining a simple way to subtract integers for people who have trouble subtracting integers. This uses a method based on simply changing a subtraction problem to an addition problem based on helping people with algebra. How to Subtract Integers Without Getting Confused | Algebra 1 Help.org.
Biological Sciences Biology: One Equation at a Time[Full] John Berges, Associate Professor Course: BIO SCI 194, SEM 001 Class Number: 26398 Credits: 3 NS Time: TR 3:00 - 4:00 PM Place: TBA Course Description: Biology has been described as "the ideal major for the scientifically-inclined but mathematically-challenged," but paradoxically, many of the most exciting recent discoveries in biology have relied on application of mathematical techniques. This seminar is intended to develop mathematical literacy among biology students, but also to introduce students of more mathematically-oriented sciences to the important applications of mathematics in biological sciences, ranging from medicine to marine biology. Goals of the seminar include: developing an appreciation of the critical importance of mathematics in all areas of biology, improving understanding of the application of specific mathematical approaches in biology, increasing confidence in quantitative problem-solving skills. Work Involved: The seminar explores critical biological questions (chosen by the class) using relatively simple equations. Only basic mathematical skills and biological background are assumed. Our sessions involve in-class experiments, interactive problem-solving (often use computers), group work, and discussion. The course operates in a 'hybrid' format with weekly assignments (generally involving on-line activities) and online discussions. Short field-trips to biology research labs will also be organized. Grading is based on weekly assignments (50%), participation in in-class and on-line discussions (10%), and a final term assignment (40%); there are no formal examinations. Sample Reading: Most of the equations are somewhat more advanced than what we will cover in the course, but it captures the flavor. About the Instructor: John Berges holds degrees in Marine Biology and Oceanography and has studied marine and freshwater ecosystems ranging from the Canadian High Arctic to the Great Barrier Reef in Australia. In Canada, N. Ireland and the U.S., he has tried to convince biology students that mathematics can be fun; his eight-year old son and his cat remain skeptical. John has mixed mathematical abilities: he does his own taxes and has memorized many biologically-important mathematical constants, but struggles to program his MP3 player and has trouble remembering his cell phone number.
Dogue PrealgebraPolynomials in the operations are reviewed, with more challenging examples included. Polynomial division (long and synthetic) is covered in Algebra 2. Occasionally, some Algebra 1 classes do cover the long division, in addition to division by a monomialI have taken the following relevant courses in high school and college: European History, Earth Science, U.S. Government, U.S. History, Sociology, Psychology, Human Geography, English Language, English Literature, Spanish 1,2,3,4, and AP, Political Science, International Relations, Microeconomics, and Macroeconomics
Algebra: Equations and Inequalities - Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines - Solve multi-step inequalities and graph the solution set on a number line - Solve linear multi-step inequalities Algebra: Patterns, Relations and Functions - Understand that numerical information can be represented in multiple ways: - Find a set of ordered pairs to satisfy a given linear numerical pattern then plot and draw a line - Determine if a relation is a function - Interpret multiple representations using equation, table of values and graph Geometry: Constructions - Construct the following using a straight edge and compass: Segment congruent to a segment; angle congruent to an angle; perpendicular bisector; and angle bisector Geometry: Geometric Relationships - Identify pairs of vertical angles as congruent - Identify pairs of supplementary and complementary angles - Calculate the missing angle in a supplementary or complementary pair - Determine angle pair relationship when given two parallel lines cut by a transversal - Calculate the missing angle measurements when given two parallel lines cut by a transversal - Calculate the missing angle measurements when given two intersecting lines and an angle Geometry: Transformational Geometry - Describe, identify, and draw transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations.) - Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation Geometry: Coordinate Geometry - Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change - Determine the y-intercept of a line from a graph - Graph a line using a table of values, and by the slope-intercept method - Determine the equation of a line given the slope and the y-intercept - Solve systems of equations graphically - Graph the solution set of an inequality on a number line - Distinguish between linear and nonlinear equations ax²+bx+c; a=1 (only graphically) - Recognize the characteristics of quadratics in tables, graphs, equations, and situations
Algebra And Trigonometry - With 2 Cds - 4th edition Summary: Bob Blitzers unique background in mathematics and behavioral sciences, along with his commitment to teaching, inspired him to develop a precalculus series that gets students engaged and keeps them engaged. Presenting the full scope of the mathematics is just the first step. Blitzer draws students in with vivid applications that use math to solve real-life problems. These applications help answer the question When will I ever use this? Students stay engaged because the book helps them...show more remain focused as they study. The three-step learning systemSee It, Hear It, Try Itmakes examples easy to follow, while frequent annotations offer the support and guidance of an instructors voice. Every page is interesting and relevant, ensuring that students will actually use their textbook to achieve success! ...show less Hardcover New 0321559851 New Condition ~~~ Right off the Shelf-BUY NOW & INCREASE IN KNOWLEDGE... $99.97 +$3.99 s/h LikeNew Nivea Books Lynnwood, WA Hardcover Fine 0321559851 Like New copy, without any marks or highlights. Might have minor shelf wear on covers. This is Student US Edition. Sealed CD included. Same day shipping with free tracking...show more number. A+ Customer Service! ...show less
Mathematics and Statistics Courses Mathematics and statistics courses are designed (1) to provide mathematics courses in the core curriculum of undergraduate study, (2) to serve the requirements of undergraduate students pursuing a curriculum in business, education, engineering, etc. (3) to provide undergraduate students majoring in mathematics or statistics a thorough preparation for graduate mathematics or employment in industry or education, (4) to provide M.S. or Ph.D. students mathematics or statistics courses needed for their respective majoring field. Courses are numbered as follows: 100 level -- freshmen, 200 level -- sophomores, 300 level -- juniors, 400 level -- seniors, and 500 & 600 levels -- graduate students. Certain 300-, 400- level courses may be taken by graduate students for graduate credit, in such cases, graduate students complete additional research assignments to bring the courses up to graduate level rigor.
You Are Here: Sub-Navigation Computer Lab In Room 242 of the Main Building, there are 25 computers availalbe for students studying mathematics. During the semester, time windows are offered for a "Open Practical Experience", during which students can use the computers in the lab. Information on the equipment and user possibilities can be found under Institute of Geometry and Practical Mathematics (IGPM).
This book is full of clear notes and worked examples for the current AQA GCSE Higher level Modular Maths course. There are loads of tips and quick test questions on every topic to help you get ready for your exams. It's all explained in straightforward language with lots of diagrams, and there's the odd joke thrown in to help break up the revision
at... read more Customers who bought this book also bought: Our Editors also recommend: Essays on the Theory of Numbers by Richard Dedekind Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers. Algebraic Number Theory by Edwin Weiss Ideal either for classroom use or as exercises for mathematically minded individuals, this text introduces elementary valuation theory, extension of valuations, local and ordinary arithmetic fields, and global, quadratic, and cyclotomic fields. The Theory of Algebraic Numbers by Harry Pollard, Harold G. Diamond Excellent intro to basics of algebraic number theory. Gausian primes; polynomials over a field; algebraic number fields; algebraic integers and integral bases; uses of arithmetic in algebraic number fields; more. 1975 edition. Riemann's Zeta Function by H. M. Edwards Superb study of the landmark 1859 publication entitled "On the Number of Primes Less Than a Given Magnitude" traces the developments in mathematical theory that it inspired. Topics include Riemann's main formula, the Riemann-Siegel formula, more. Number Theory and Its History by Oystein Ore A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Fascinating, accessible coverage of prime numbers, Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, and more. Fundamentals of Number Theory by William J. LeVeque Basic treatment, incorporating language of abstract algebra and a history of the discipline. Unique factorization and the GCD, quadratic residues, sums of squares, much more. Numerous problems. Bibliography. 1977 edition. Continued Fractions by A. Ya. Khinchin Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Properties of the apparatus, representation of numbers by continued fractions, and more. 1964 edition. Game Theory: A Nontechnical Introduction by Morton D. Davis This fascinating, newly revised edition offers an overview of game theory, plus lucid coverage of two-person zero-sum game with equilibrium points; general, two-person zero-sum game; utility theory; and other topicsSieve Methods by Heine Halberstam, Hans Egon Richert This text by a noted pair of experts is regarded as the definitive work on sieve methods. It formulates the general sieve problem, explores the theoretical background, and illustrates significant applications. 1974 edition. Three Pearls of Number Theory by A. Y. Khinchin These 3 puzzles require proof of a basic law governing the world of numbers. Features van der Waerden's theorem, the Landau-Schnirelmann hypothesis and Mann's theorem, and a solution to Waring's problem. Solutions included. Elementary Number Theory: Second Edition by Underwood Dudley Written in a lively, engaging style by the author of popular mathematics books, this volume features nearly 1,000 imaginative exercises and problems. Some solutions included. 1978 edition. Uniform Distribution of Sequences by L. Kuipers, H. Niederreiter The theory of uniform distribution began with Weyl's celebrated paper of 1916 and this book summarizes its development through the mid-1970s, with comprehensive coverage of methods and principles. 1974 edition. The Method of Trigonometrical Sums in the Theory of Numbers by I. M. Vinogradov This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition. Product Description: ativity-divisibility, quadratic congruences, additivity, and more. Bonus Editorial Feature: George E. Andrews, Evan Pugh Professor of Mathematics at Pennsylvania State University, author of the well-established text Number Theory (first published by Saunders in 1971 and reprinted by Dover in 1994), has led an active career discovering fascinating phenomena in his chosen field — number theory. Perhaps his greatest discovery, however, was not solely one in the intellectual realm but in the physical world as well. In 1975, on a visit to Trinity College in Cambridge to study the papers of the late mathematician George N. Watson, Andrews found what turned out to be one of the actual Holy Grails of number theory, the document that became known as the "Lost Notebook" of the great Indian mathematician Srinivasa Ramanujan. It happened that the previously unknown notebook thus discovered included an immense amount of Ramanujan's original work bearing on one of Andrews' main mathematical preoccupations — mock theta functions. Collaborating with colleague Bruce C. Berndt of the University of Illinois at Urbana-Champaign, Andrews has since published the first two of a planned three-volume sequence based on Ramanujan's Lost Notebook, and will see the project completed with the appearance of the third volume in the next few years. In the Author's Own Words: "It seems to me that there's this grand mathematical world out there, and I am wandering through it and discovering fascinating phenomena that often totally surprise me. I do not think of mathematics as invented but rather discovered." — George E. Andrews
Algebra 1 - Student TextbookThe Algebra I Student Text includes scriptural principles woven throughout but also an "Algebra and Scripture" spread in each chapter. Concepts are presented with examples and explanations. Other features include "Algebra Around Us" and sections on "Probability and Statistics." Homework sections are on three levels. Cumulative Review questions are located at the end of every section. Procedures and definitions are color-coded for reference. A TI-83 Plus graphing calculator is recommended for use with this course. Customer Reviews We really enjoyed BJUP's Algebra I, 2nd Edition. We used it for all three of our children as first year algebra and enough problems on the new concepts course is strongly scoped...it compares to 1 1/3 years of high school algebra as compared with Portland Community College's sequencing. Our daughter challenged out of PCC's Math 65 on the basis of this book alone with the single addition of simple functions (from BJUP Algebra II). Of the BJUP math books, this book, and their level 7th and 8th math, are their best math books.
In this course, students will learn to analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. At the conclusion of this course, students will be able to indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy and be able to apply them in other circumstances. Classroom activities and worksheets will involve students in learning about the problem—solving process.
With over a million users around the world, the Mathematica software system created by Stephen Wolfram has defined the direction of technical computing for the past decade. The enhanced text and hypertext processing and state-of-the-art numerical computation features ensure that Mathematica 4 takes scientific computing into the next century. New to this version: visual tour of key features, practical tutorial introduction, full descriptions of 1100 built-in functions, a thousand illustrative examples, easy-to-follow descriptive tables, essays highlighting key concepts, examples of data import and export, award-winning gallery of Mathematica graphics, gallery of mathematical typesetting, dictionary of 700 special characters, a complete guide to the MathLink API, notes on internal implementation, and an index with over 10,000 entries copublished with Wolfram Media. [via] This book covers the use of Mathematica as programming language. Various programming paradigms are explained in a uniform manner, with fully worked out examples that are useful tools in their own right. The floppy disk contains numerous Mathematica notebooks and packages, valuable tools for applying each of the methods discussed. [via] Physics and computer science genius Stephen Wolfram, whose Mathematica computer language launched a multimillion-dollar company, now sets his sights on a more daunting goal: understanding the universe. A New Kind of Science is a gorgeous, 1,280-page tome more than a decade in the making. With patience, insight, and self-confidence to spare, Wolfram outlines a fundamental new way of modelling complex systems. On the frontier of complexity science since he was a boy, Wolfram is a champion of cellular automata--256 "programs" governed by simple non-mathematical rules. He points out that even the most complex equations fail to accurately model biological systems, but the simplest cellular automata can produce results straight out of nature--tree branches, stream eddies, and leopard spots, for instance. The graphics in A New Kind of Science show striking resemblance to the patterns we see in nature every day. Wolfram wrote the book in a distinct style meant to make it easy to read, even for non-techies; a basic familiarity with logic is helpful but not essential. Readers will find themselves swept away by the elegant simplicity of Wolfram's ideas and the accidental artistry of the cellular automaton models. Whether or not Wolfram's revolution ultimately gives us the keys to the universe, his new science is absolutely awe-inspiring. --Therese Littleton[via]
The following feature story appeared in the campus publication MOSAIC in November, 1997.Although some of the courses, students, and faculty members referenced in the story may have changed in the meantime, it still provides a full and accurate picture of the Mathematics Department. For the most current course information and faculty listing, we encourage you to visit the program's homepage. Mathematics The numbers don't tell the whole story It is tempting to characterize Trinity's mathematics department by the impressive numbers it can present. The department provides about 10 majors in each graduating class with a rigorous degree program and a low student-to-faculty ratio. At the same time, the department provides about half of Trinity's undergraduates — hundreds of students each year — with the mathematics and statistics courses that underpin aspects of sociology, economics, biology, and several other disciplines. And here's a number for the College's mathematicians to take pride in: four of Trinity's last seven valedictorians have been mathematics majors. But, as mathematics students at Trinity know, numbers don't tell the whole story. According to Seabury Professor of Mathematics and Natural Philosophy David A. Robbins, who chairs the mathematics department, mathematics students are expected not only to perform mathematical operations correctly but also to think, analyze, and communicate. He offers the example of a lab assignment in his first-year calculus course in which students are given fictionalized tax-table information and a number of related problems to solve. They must learn a number of vocabulary definitions, apply various mathematical functions, provide approximations, and explain their assumptions as part of a 10-page lab report that is treated much like a writing assignment in any other course. "We want to know: 'What kind of problem-solving tools and arguments can you build?' and 'How can you use available information to make reasonable estimates in a given problem?'" says Robbins. "We're not just looking for answers. What we're looking for is solutions." Hard work, strong support Finding solutions, according to many mathematics students at Trinity, is rigorous work. It involves spending hours and hours on one homework assignment and is the main reason why collaborative studying — initiated by students themselves and encouraged by faculty members — is fundamental to the experience and culture of mathematics majors. Says Jedidiah Belcher Northridge '98, "Math majors are a small group. Because we're small and because the homework is hard, we have to work together. We really bond because of it." Mathematics faculty members characterize their departmental philosophy as somewhat conservative. In order to obtain a mathematics education that is sufficiently deep and appropriately broad, students must pursue a structured sequence of courses. It's a lot of mathematics, and majors often feel like they live in the mathematics department. "All the math majors claim that the second floor of the Mathematics, Computing, and Engineering Center is their second home," says Michelle L. Lombard '98, President's Fellow in mathematics and a double major in computer science. The supportive faculty with its open-door policy is one reason mathematics majors "tough out" the hard parts, according to Sarah E. Wilbour '99, who double majors in mathematics and religion. "All the teachers in the department are wonderful," she says. "They make you feel very comfortable. If you are having a problem, they will help you." Mathematics for the non-major Mathematics faculty members readily admit to loving mathematics for its own sake, but students can also experience the discipline through courses with broader, interdisciplinary appeal. Associate Professor of Mathematics Paula A. Russo is the director of the Interdisciplinary Science Program, a special two-year honors program for selected first-year students, which allows students to explore linkages between science and mathematics that are not covered in traditional courses. Other mathematics courses offer more of a slant toward real-world applications. Professor of Mathematics John P. Georges's personal interest in public policy was the impetus for the establishment several years ago of a course called "Judgment and Decision-Making," which Georges jokingly calls "Common Sense 101." A requirement for public policy majors, the course, says Georges, explores "how one might size up a particular situation from a quantitative point of view." Taking examples from medicine, law, foreign policy, and other areas, students apply such concepts as utility and risk to make a systematic analysis of situations and to understand the process of formal decision-making. In "Introduction to Mathematical Modeling," a course taught by Lecturer in Mathematics Philip S. Brown, Jr., students apply mathematical models to situations in the life, social, and physical sciences, and in engineering. Brown says that economics majors find it particularly useful but that many others have also creatively applied mathematical modeling to whatever happens to spark their interest. One student recently developed a mathematical model of a beating heart. Another examined random number generation as it applies to the NBA draft lottery. Others have explored catastrophes in wildlife populations. According to Brown, students who love mathematics but who major in another discipline find that his course provides ideas about how they can use mathematics in their chosen field. Outside of the classroom, the mathematics department is striving to become more of a presence on campus. "We're reviving our undergraduate colloquium series this year," says Assistant Professor of Mathematics David Cruz-Uribe. He and Assistant Professor of Mathematics Melanie Stein have used the departmentally sponsored lecture series (cosponsored by the Undergraduate Mathematics Club) to bring a number of speakers to campus. Also helping to make Trinity a math-friendly place is the Aetna Mathematics Center, which shares faculty members with the mathematics department and, in a complementary and supporting role to the department, offers a number of 100-level courses, administers mathematics testing, and employs student tutors to assist their peers. Many career paths Robbins notes that like other liberal arts students, mathematics students have many and varied career options after graduation. While some recent graduates have taken actuarial positions with prominent employers, and others do research and teaching at prestigious graduate programs, many mathematics majors also succeed in medical school, law school, and a number of other areas. Although he is uncertain about his plans after graduation, Jed Northridge '98 is confident that his foundation in mathematics will serve him well. "So much of being a math major comes down to how one perceives things and to having an analytical mind," he says. When he is in the throes of a complex equation he sometimes wonders, "When will I ever need to know this? But at the same time," he adds, "I know I am training my mind to look for algorithms to solve problems, and these are analytical skills I'll use every day."
Cerritos Prealgebra introduces matrices and their properties. Biology course is designed to enable you to develop advanced inquiry and reasoning skills, such as designing a plan for collecting data, analyzing data, applying mathematical routines, and connecting concepts in and across domains. The result wiHowever, I am not an expert in advanced chess theory. I
BEGIN:VCALENDAR PRODID:-//Microsoft Corporation//Outlook MIMEDIR//EN VERSION:1.0 BEGIN:VEVENT DTSTART:20101115T163000Z DTEND:20101115T180000Z LOCATION:290 DESCRIPTION;ENCODING=QUOTED-PRINTABLE:ABSTRACT: This workshop will continue the hands-on introduction to the SAGE Mathematics =0AComputing Environment. This session will focus on using SAGE as a tool for=0Aexploring advanced topics related to recent mathematical research. This will =0Ainclude an overview of the advanced programs such as GMP and PARI that are=0Aincluded in the SAGE package. The session will also include a presentation on=0Ainteger relation algorithms and some recent results. SUMMARY:Math: Computational and Experimental Math, Part 3 PRIORITY:3 END:VEVENT END:VCALENDAR
Intended Outcomes for the course 1. Use quadratic, rational and radical models in academic and nnon-academic environments. 2. Recognize connections between graphical and algebraic representations in academic and non-academic settings. 3. Interpret graphs in academic and non-academic contexts. 4. Be prepared in future coursework that requires the use of algebraic concepts and an understanding of functions. Outcome Assessment Strategies Assessment shall include: The following topics must be assessed in a closed-book, no-note, no-calculator setting: a.finding the equation of the linear function given two ordered pairs stated using function notation b.solving rational equations c.solving radical equations d.determining the domain of rational and radical functions e.evaluating algebraic expressions that include function notation At least two proctored closed-book, no-note examinations, one of which is the comprehensive final. These exams must consist primarily of free response questions although a limited number of multiple choice and/or fill in the blank questions may be used where appropriate. Assessment must include evaluation of the student's ability to arrive at correct and appropriate conclusions using proper mathematical procedures and proper mathematical notation. Additionally, each student must be assessed on their ability to use appropriate organizational strategies and their ability to write conclusions appropriate to the problem. 2.1.3.Represent the domain in both interval and set notation, where appropriate 2.1.4.Apply unions and intersections ("and" and "or") when finding and stating the domain of functions 2.1.5.Understand how the context of a function used as a model can limit the domain 2.2. Range 2.2.1.Understand the definition of range (set of all possible outputs) 2.2.2.Determine the range of functions represented graphically, numerically and verbally 2.2.3.Represent the range in interval and set notation, where appropriate 2.3. Function notation 2.3.1.Evaluate functions with given inputs using function notation where functions are represented graphically, algebraically, numerically and verbally (e.g. evaluate ) 2.3.2.Interpret in the appropriate context e.g. interpret where models a real-world function 2.3.3.Solve function equations where functions are represented graphically, algebraically, numerically and verbally (i.e. solve for and solve for where and gshould include but not be limited to linear functions, rational functions, radical functions and quadratic functions) 2.3.4.Solve function inequalities algebraically (i.e. , , and where and are linear functions and and where is an absolute value function) 2.3.5.Solve function inequalities graphically (i.e. , , and where and should include but not be limited to linear functions, and for quadratic and absolute value functions) 2.4. Graphs of functions 2.4.1.Use the language of graphs and understand how to present answers to questions based on the graph (i.e. read the value of an intersection to solve an equation and understand that is a number not a point) 2.4.2.Determine function values, solve equations and inequalities, and find domain and range given a graph 3.Rational Functions (continued from MTH 91) 3.1. Solve rational equations 3.1.1.Check solutions algebraically 3.2. Solve literal rational equations for a specified variable 3.2.1.Introduce variables with subscripts 3.3. Applications 3.3.1.Solve distance, rate and time problems involving rational terms using well defined variables and stating conclusions in complete sentences including appropriate units 3.3.2.Solve problems involving work rates using well defined variables and stating conclusions in complete sentences including appropriate units 4.Quadratics 4.1.Recognize a quadratic equation given in standard form, vertex form and factored form 4.2. Solve quadratic equations by completing the square 4.3.Find complex solutions to quadratic equations by the quadratic formula or by completing the square 4.3.1.Understand the graphical implications (i.e. when there is a complex number as a solution to a quadratic equation) 4.3.2.Interpret the meaning in the context of an application 4.4. Quadratic functions in vertex form 4.4.1.Graph a parabola after obtaining the vertex form of the equation by completing the square 4.4.2.Given a quadratic function in vertex form or as a graph, observe the vertical shift and horizontal shift of the graph 5.8.2.Understand that extraneous solutions found algebraically do not appear as solutions on the graph 5.8.3.Solve literal radical equations for a specified variable 5.10.Calculator 5.10.1. Approximate radicals as powers with rational exponents 5.10.2. Find the domain and range of radical functions 5.10.3. Solve radical equations graphically 5.10.4. Use graphical solutions to check the validity of algebraic solutions Addendum ·Functions should be studied symbolically, graphically, numerically and verbally. ·As much as possible, instructors should present functions that model real-world problems and relationships to address the content outlined on this CCOG. ·Function notation is emphasized and should be used whenever it is appropriate in the course. ·Students should be required to use proper mathematical language and notation. This includes using equal signs appropriately, labeling and scaling the axes of graphs appropriately, using correct units throughout the problem solving process, conveying answers in complete sentences when appropriate, and in general, using the required symbols correctly. ·Students should understand the fundamental differences between expressions and equations including their definitions and proper notations. ·All mathematical work should be organized so that it is clear and obvious what techniques the student employed to find his answer. Showing scratch work in the middle of a problem is not acceptable. ·Since technology is used throughout the course, there is a required calculator packet for students that gives directions for several graphing calculators. The students should understand the limitations of calculator—i.e. when the calculator gives misleading information. Examples of the calculator's limitations include the following: when finding horizontal intercepts, the calculator sometimes gives something like y = 3E-13; the calculator rounds to 12 or fewer decimal places; some calculators appear to show vertical asymptotes on the graphs of rational functions; it appears that the graph of touches the x axis; the calculator does not show holes on rational function graphs; the calculator cannot handle very large numbers, e.g. etc. ·Exploration of difficult rational exponents, as in 4.5, should be limited. Basic understanding is essential and a deep understanding takes more than one course to develop. Examples should be limited to one or two variables, keeping things as simple as possible while covering all possibilities. E.g. , , , . ·As much as possible, instructors should present functions that model real-world problems and relationships to address the content outlined on this CCOG. ·In 3.3.1, when solving applications of quadratic equations, a complex solution should be interpreted as the graph never reaching a particular real world y-value.
WEEK OF MAY 20th Created on Saturday, 18 May 2013 10:33 Written by Joe Chamberlin ONLY THREE MORE WEEKS TO GO! This week we cover the highlights of Chapters 9 and 10. MONDAY: Shapes and Formulas of conics, including circles, ellipses, and hyperbolas. We will also start our next project... cutting shapes with stained glass. TUESDAY: We go 3-D again, with cones and spheres, along with distances and midpoints in x-y-z space. Watch out for a quiz sometime! WEDNESDAY: Polar coordinates (another way to locate a point) and polar equations, along with some honors level engineering math. And we will try to finish up our projects. THURSDAY: Multi-chapter review, and TEST. The following WEEK OF MAY 27: We will just do Chapter 11, more thoroughly, because it contains the two basic ideas of calculus. And we will have gone thru the major ideas of the book. So the final week will be preparing for the class final! WEEK OF MAY 13 Created on Friday, 10 May 2013 12:48 Written by Joe Chamberlin Six chapters down, six more to go! Again, we are just skimming the highlights of functions, reviewing your algebra and introducing some new formulas and notations. MONDAY: In the AM, a little Ch.6 review on vectors, and then a Ch. 4-6 REVIEW TEST. For the PM, Chapter 7.1 and 7.2 on solving systems, and a brief look at how matrices do it. And maybe we will try to float our boats again. TUESDAY: Jump into Chapter 8, which is more "beginning calculus" oriented... 8.1 thru 8.3 are on series, and introduce summation notation. Expect a pop quiz in there somewhere. WEDNESDAY: Sections 8.5 thru 8.7 are on counting and probability, which will be a fun way to challenge your lovely brains. And THURSDAY: will be, as usual, Chapter review and TEST. SPECIAL NOTE FOR HAYDEN, LEVI AND STEPHEN: Make sure you get a worksheet for Chapter 9 before you leave for Israel. Have fun! Maseltov! 3RD WEEK OF PRECAL: MORE TRIG Created on Wednesday, 08 May 2013 11:51 Written by Joe Chamberlin Monday we will do Chapter 4, part of 5, Review and TEST. Tuesday we have solemn assembly, but we will still do Law of Sines and Cosines at start of Chapter 6. We will also look at waves (heart, brain, and tidal), and start building our boats. Wednesday we will review Law of Sines and Cosines, and throw in Herons rule for figuring out area, before we have more boats and a special afternoon chapel. Thursday we finish up Chapter 6 with Vectors, another Trig TEST, and hopefully, float our boats!
Advanced School and Workshop on Matrix Geometries and Applications Description Linear algebra is a fundamental topic in mathematics. It is used in almost all branches of mathematics and is among the most important mathematical disciplines for applications to science and technology.
Trigonometric Rules of Integrals In this lesson, Professor John Zhu gives an introduction to the trigonometric rules of integrals. He briefly overviews the trigonometric rules, the integral of SIN, as well as COS, SEC, & CSC. He works through several example problems similar to those on AP tests. This content requires Javascript to be available and enabled in your browser. Trigonometric Rules of Integrals Memorize! Careful not to confuse with trig derivative rules Useful especially during multiple choice portion of AP exam Trigonometric Rules of Integrals Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
This course introduces the concepts of finite mathematical structures. Topics include set theory, logic, proof techniques, functions and relations, graphs, trees, and combinatorics. Expected Educational Results As a result of completing this course, the student will be able to do the following: 1. Use critical thinking skills to solve problems by modeling the problem as an instance of the finite mathematical structures studied in the course; 2. Demonstrate understanding of the concept of a finite mathematical structure based on experience with various examples of mathematical structures, especially those with application to computer science; 3. Construct and understand proofs based on direct or indirect reasoning, mathematical induction, or the pigeonhole principle; 4. Apply the basic operations for sets, namely, union, intersection, complement, and subset formation; 5. Construct, interpret, and evaluate logical statements involving and, or, negation, and implication; 6. Describe similarities and differences in the mathematical structures of sets and logical statements in terms of properties for the basic operations in each; 7. Classify a relation as one-to-one, onto, or functional; 8. Determine if a relation is an equivalence relation, a partial order, a permutation, or a tree; 9. Given a finite relation, construct its incidence matrix, graph/digraph, and inverse; 10. Compose two sets given as ordered pairs, incidence matrices, or graphs; 11. Determine if a partial order is a Boolean algebra; 12. Represent a Boolean function as a circuit; 13. Traverse a tree in preorder, inorder, or postorder; 14. Describe the language of a phrase structure grammar; 15. Classify a grammar as Type 0, 1, 2 (context-free), or 3 (regular); 16. Represent a context-free or regular grammar with syntax diagrams or in BNF notation. General Education Outcomes I. This course addresses the general education outcome relating to communication by providing additional support as follows: A. Students develop their listening skills through lecture and through group problem solving. B. Students develop their reading comprehension skills by reading the text and by reading the instructions for text exercises, problems on tests, or on projects. Reading mathematics text requires recognizing symbolic notation as well as analyzing problems written in prose. C. Students develop their writing skills through the use of problems that require written explanations of concepts. II. This course addresses the general education outcome of demonstrating effective individual and group problem-solving and critical-thinking skills as follows: A. Students must apply mathematical concepts previously mastered to new problems and situations. B. In applications, students must analyze problems and describe problems through pictures, diagrams, or graphs, then determine the appropriate strategy for solving the problem. III. This course addresses the general education outcome of using mathematical concepts to interpret, understand, and communicate quantitative data as follows: A. Students must demonstrate proficiency in problem-solving skills including applications of finite mathematical structures, functions and relations, graphs, combinatorics and logic. B. Students must write functions to describe real-world situations and interpret information from both the function (relation) rule and the graph of the function (relation). C. Students must solve problems in combinatorics, graph theory and logic that often arise in modeling numerical relationships. ENTRY LEVEL COMPETENCIES Upon entering this course the student should be able to do the following: 1. Analyze problems using critical thinking skills. 2. Use algebraic symbols to make a meaningful statements. 3. Identify a function. 4. Compose two functions. 5. State the domain and range of a function. 6. Sketch and identify a one-to-one function and its inverse. 7. Find the inverse of a linear function. Assessment of Outcome Objectives I. COURSE GRADE Exams, assignments, and a final exam prepared by individual instructors will be used to determine the course grade. II. DEPARTMENTAL ASSESSMENT This course will be assessed every five years. The assessment instrument will consist of a set of free response questions that will be included as a portion of the final exam for all students taking the course. A committee appointed by the Executive Committee of the Mathematics Academic Group will grade the assessment instrument. III. USE OF ASSESSMENT FINDINGS The Math 2420 Committee, or a special assessment committee appointed by the Executive Committee of the Mathematics Academic Group, will analyze the results of the assessment and determine implications for curriculum changes. The committee will prepare a report for the Academic Group summarizing its finding.
Course Descriptions MTH099 BASIC MATH (3). Helps students develop proficiency in fundamental mathematical skills as a prerequisite for MTH100. Includes: arithmetic operations on whole numbers, fractions and decimals, percentages, ratios and proportions, and an introduction to geometry and basic algebra. This course does not count in the 124 hours required for graduation. Each Fall/Each Spring. MTH100 ALGEBRA I (3). Review of high school algebra and an introduction to more advanced topics. Includes solving first degree equations, simplifying polynomials, factoring, solving literal equations, the rectangular coordinate system and graphing lines, solving simultaneous equations, solving and graphing linear inequalities, and solving quadratic equations. Students scoring 16 or below on the ACT test must take MTH099 before taking MTH100, unless placement testing indicates placement in MTH100. Each Fall/Each Spring. MTH112 MATHEMATICS FOR TEACHERS I (4). An elementary study of the basic properties and underlying concepts of number systems. This content course emphasizes problem solving techniques and a structural study of the whole number, the integers, rational numbers, decimals, and real numbers. Each Fall. MTH150 ALGEBRA III (3). A study of rational and polynomial functions and their graphs and techniques for solving rational and polynomial equations. Includes logarithms, inequalities, complex numbers, sequences, and matrices and determinants, as time permits. Provides essential background in precalculus mathematics to prepare students for Calculus I. Emphasis on exploring and analyzing the behavior of functions and the connections among those functions and real-world problems. Prerequisite: MTH120 or math placement. Each Fall/Each Spring. MTH152 TRIGONOMETRY (3). A study of the circular and angular trigonometric and inverse trigonometric functions and their graphs, and trigonometric forms of complex numbers. Emphasizes solving real-world problems using trigonometric functions. Includes the unit circle, right triangle applications, verification of identities, and exponential and logarithmic functions. Provides essential background in precalculus mathematics to prepare students for Calculus I. Prerequisite: MTH120 or math placement. Each Fall. MTH162 STATISTICS FOR SCIENCE STUDENTS (4). Students learn the fundamental tools used to analyze sets of data and the standard methods for displaying data. Prerequisite: MTH120. Spring 2007. MTH171 CALCULUS I (4). An introduction to the basic concepts of limits and derivatives of functions of a single real variable. Includes plane analytic geometry, differentiation, curve sketching, maxima and minima problems, applications of the derivative, and an introduction to anti-derivatives and integration. Emphasis is on the behavior of functions and their derivatives and the use of these to model real-world systems. Graphing technology is used as an important tool for both the learning and exploring of concepts as well as for applications based problem solving. Prerequisites: MTH 150 or math placement. Each Fall. MTH172 CALCULUS Il (4). A continuation of Calculus 1. Differentiation and integration of trigonometric, exponential, logarithmic, and hyperbolic functions, and an in-depth look at methods of integration, and applications of the integral. Emphasis is placed on the behavior of functions, their derivatives and their integrals and the use of these to model real-world systems. As in Calculus I, graphing technology is used as an important tool. Prerequisite: MTH171. Each Spring. MTH241 DISCRETE MATHEMATICS (3). An introduction to discrete mathematical elements and processes. Includes sets, functions, concepts of logic and proof, Boolean algebra, combinatorics, algorithmic concepts, and graph theory and its application. Students in this course often encounter their first experiences with formal mathematical proof techniques. Emphasis is placed upon applications of the many elements of discrete mathematics in a variety of real-world settings. The use of technology is incorporated for the benefit of both the learning of concepts as well as the solving of real-world applications problems. Prerequisite: MTH150. Each Spring. MTH305 LINEAR ALGEBRA (3). Matrices, vectors, and linear transformations. Matrices and determinants and their properties are developed and used in applications of vector space concepts. The use of technology is integral to the conceptual, the computational and the problem solving aspects of the course. Prerequisite: MTH172 or permission of the department. Each Fall. MTH312 CALCULUS III (4). The third course in the Calculus sequence. Students continue to investigate the application of the Calculus to the solution of problems of both physical and historical importance including the resolution of Zeno's paradox, convergence and divergence of infinite sums, motion in the plane and in space, the shortest time curve between two points (the brachistochrone problem) and centers of mass. Topics include parameterization of curves, vectors, sequences, infinite sums, power series, approximation of functions using the Taylor polynomial, solid analytic geometry, partial derivatives and gradients, multiple integrals and their application to areas in the plane and volumes beneath surfaces. This course demonstrates how the Calculus unified seemingly diverse concepts from geometry, algebra, the study of motion and other physical problems. Prerequisite: MTH172. Each Fall. MTH320 DIFFERENTIAL EQUATIONS (3). Methods for solving first and second order differential equations and linear differential equations of higher order. Includes standard techniques such as change of variables, integrating factors, variation of parameters, and power series. An introduction to numerical methods is also included. An introduction to the application of calculus connecting mathematics to real-world situations in other disciplines is given. Physical systems in physics, chemistry and engineering are modeled using differential equations. Prerequisite: MTH 312. Spring of even numbered years. MTH335 ABSTRACT ALGEBRA (3). This course presents an axiomatic approach to the study of algebraic systems. It begins by investigating the most fundamental concepts behind integer arithmetic. It then shows how all other arithmetic operations involving integers are justified from these basic concepts which are called postulates. Other topics involving integers such as proof by induction, divisibilty, congruence and modular arithmetic are also discussed. A general discussion of algebraic systems such as groups, rings, integral domains and fields includes the tools used to analyze algebraic systems such as sets, mappings between sets, relations defined on sets, permutations, homomorphisms and isomorphisms. These tools are used to compare algebraic systems defined on sets of integers, rational, real and complex numbers. Examples involving matrices, coding theory and applications to computer science are used to illustrate the concepts. Prerequisite: MTH172. Each Spring semester. MTH345 HISTORY OF MATHEMATICS (3). This course is a careful study of the major contributions to mathematics from throughout the world and how these contributions are blended into the mathematical structure in which we now function. General topics covered include: the birth of demonstrative mathematics, the dawn of Modern Mathematics, Descartes' and Fermat's Analytic Geometry, the exploitation of the Calculus, the liberation of Geometry and Algebra. Prerequisite: MTH172. Fall of odd numbered years. MTH350 PROBABILITY (3). A theoretical basis for Statistics. Students discuss combinatorics and the classical definition of probability and then proceed to a more axiomatic approach to the subject. Discussions include the topics of sample spaces, events, conditional probability, random variables, probability distribution and density functions, mathematical expectations, moments and moment generating functions. The normal distribution and the central limit theorem are discussed in detail. Probability histograms, graphs and area beneath graphs are emphasized to provide an intuitive, geometrical understanding of the concepts. Prerequisite: MTH312. Fall of odd numbered years. MTH360 MATHEMATICAL STATISTICS (3). An introduction to the basic concepts involved in analyzing sets of data derived from scientific experiments. A rigorous treatment of sampling, estimation of population parameters, using appropriate distribution functions, hypothesis testing, correlation and regression and analysis of variance using the concepts presented in the course on Probability. Students process a data set from a real-world application using computer technology and the concepts presented. Prerequisite: MTH350. Spring of even numbered years. MTH370 MODERN GEOMETRIES (3). The knowledge of Euclidean geometry acquired in high school is used as a basis for generalization. Familiar Euclidean concepts and theorems are modified and extended to produce other geometries with unusual and interesting properties. Structure and formal proof are stressed. The non-Euclidean geometries' component of the course provides an opportunity to see that a modern theoretical model of the universe which depends on a complex non-Euclidean geometry supports Einstein's general theory of relativity. Topics include: Axiomatics and Finite Geometries, Geometric Transformations, Constructions, Convexity, Topological Transformations, Projective Geometry and Non-Euclidean Geometries. Prerequisite: MTH171. Fall of even numbered years. MTH380 NUMERICAL METHODS (3). An introduction to the methods of numerical approximation and error analysis. Topics include numerical techniques of integration and interpolation, iterative solutions of equations and systems of equations. Real-world problems from other disciplines such as engineering and physics are modeled and solved using computer technology. Prerequisites: MTH305 and familiarity with a programming language. Spring of odd numbered years.
BookGateway.com » Education Your Gateway to Great Books!Thu, 16 May 2013 01:01:55 +0000enhourly1Hot X:Algebra Exposed by Danica McKellar 06 Dec 2010 22:04:38 +0000admin McKeller is a genius! One of the subjects most in need of some excitement is math and she found a way to do that. McKeller takes the subject of algebra and curls its hair, does its makeup and buys … Read the rest]]>Danica McKeller is a genius! One of the subjects most in need of some excitement is math and she found a way to do that. McKeller takes the subject of algebra and curls its hair, does its makeup and buys it a new gown. We are left with an amazingly easy (and fun) to read book that takes the mystery out of the feared subject. Each section has info on the topic at hand, then peppers in Quick Notes (tips), Step-by-Step examples (showing work), Takeaway Tips (reminders) and a bunch of examples on how to do the topic. I was so enamoured with the book that I gave it to my daughter who is 11 years old to see what she thought (and how this played out with the target audience. After all, every parent is looking for the next best way to help their children learn but we all wonder if it actually works.) Here is what she said about the book: Arieltopia:This book was about how easy algebra is when you understand how to do it. I think it is a great book and I recommend it for all young ladies in junior high through high school. Girls only because it talks a little about guys, but not anything parents would need to worry about. I really enjoyed this book and I hope you do too. The author has also written two other math-related novels. This book is written by the New York bestselling author of Math Doesn't Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail. Her other book is titled Kiss My Math: Showing Pre-Algebra Who's Boss. The three are related and at the bottom of every page, page numbers in the other books are listed in case you are either lost or just do not understand. This book really does help. My math grade increased alot and I can only use some of the facinating algebra tips in this book. Just think what it would do for girls in high school! I really learned alot of cool math tricks and I hope you pick up a copy of this book right away! I agree. This is a great resource for parents and teens alikeArieltopia is a founding book blogger for BookGateway.com and has generously provided this review. She is an 11 year old avid reader – usually going through a book a day – who gives readers a unique perspective on Young Adult and Teen Fiction; an actual teenager's perspective. Her blog is
Description: Presentation by Maria H. Andersen. The process of learning algebra should ideally teach students good logic skills, the ability to compare and contrast circumstances, and to recognize patterns and make predictions. In a world with free CAS at our fingertips, the focus on these underlying skills is even more important than it used to be. Learn how to focus on thinking skills and incorporate more active learning in algebra classes, without losing ground on topic coverage
stu... read moreElementary Concepts of Topology by Paul Alexandroff Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures. An Introduction to Algebraic Topology by Andrew H. Wallace This self-contained treatment begins with three chapters on the basics of point-set topology, after which it proceeds to homology groups and continuous mapping, barycentric subdivision, and simplicial complexes. 1961Counterexamples in Topology by Lynn Arthur Steen, J. Arthur Seebach, Jr. Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography. Differential Topology: First Steps by Andrew H. Wallace Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. 1968 edition. General Topology by Stephen Willard Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.Real Variables with Basic Metric Space Topology by Robert B. Ash Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993Product Description: students to acquire a feeling for the types of results and the methods of proof in mathematics, including mathematical induction. Subsequent problems deal with networks and maps, provide practice in recognizing topological equivalence of figures, examine a proof of the Jordan curve theorem for the special case of a polygon, and introduce set theory. The concluding chapters examine transformations, connectedness, compactness, and completeness. The text is well illustrated with figures
Grade 9-12 Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college. TG.1.0 Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians. TG.2.0 Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions. TG.3.0 Students know the identity cos 2 (x) + sin 2 (x) = 1: TG.3.1 Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity). TG.3.2 Students prove other trigonometric identities and simplify others by using the identity cos 2 (x) + sin 2 (x) = 1. For example, students use this identity to prove that sec 2 (x) = tan 2 (x) + 1. TG.4.0 TG.5.0 Students know the definitions of the tangent and cotangent functions and can graph them. TG.6.0 Students know the definitions of the secant and cosecant functions and can graph them. TG.7.0 Students know that the tangent of the angle that a line makes with the x- axis is equal to the slope of the line. TG.8.0 Students know the definitions of the inverse trigonometric functions and can graph the functions. TG.9.0 Students compute, by hand, the values of the trigonometric functions and the inverse trigonometric functions at various standard points. TG.10.0 Students demonstrate an understanding of the addition formulas for sines and cosines and their proofs and can use those formulas to prove and/ or simplify other trigonometric identities. TG.11.0 Students demonstrate an understanding of half-angle and double-angle formulas for sines and cosines and can use those formulas to prove and/ or simplify other trigonometric identities. TG.12.0 Students use trigonometry to determine unknown sides or angles in right triangles. TG.13.0 Students know the law of sines and the law of cosines and apply those laws to solve problems. TG.14.0 Students determine the area of a triangle, given one angle and the two adjacent sides. TG.15.0 Students are familiar with polar coordinates. In particular, they can determine polar coordinates of a point given in rectangular coordinates and vice versa. TG.16.0 Students represent equations given in rectangular coordinates in terms of polar coordinates. TG.17.0 Students are familiar with complex numbers. They can represent a complex number in polar form and know how to multiply complex numbers in their polar form. TG.18.0 Students know DeMoivre's theorem and can give n th roots of a complex number given in polar form. TG.19.0 Students are adept at using trigonometry in a variety of applications and word problems.
Course Requires a Media Kit to be Purchased by Course Sponsor (see additional details below): No Description: No matter what you plan on majoring in once you go off to college, you will have to take at least one math course before you graduate. Statistics is required by just about every major. Business, science, and technology degrees need basic calculus. Even many education and liberal arts programs require a course in graphical analysis and/or trigonometry. That is why Math You Can Use In College was developed. We will spend time on concepts you could possibly use again and not on the concepts you will probably never see after high school. This course is application-based and focuses on important real-life topics including: A common thread throughout the course is the use of spreadsheets to help evaluate these mathematical explorations. Students should have, at a minimum, a fundamental understanding of how spreadsheets work. All students are required to have access to Microsoft Excel, or an alternative spreadsheet based program. An online graphing calculator will also be used during the coursegovhs.org. 14 Intro to Calculus -Basic differentiation -Applications of the derivative 15 Final Assessment -Summative Assessment -Course evaluation survey Course Objectives: -Learn to navigate and work cooperatively in this environment -Become familiar with the graphing calculator and its applications -Introduce and use basic trigonometry -Explore concepts of graphical analysis -Discuss basic skills and concepts used in statistics -Use concepts learned to solve practical applications -Learn what math classes you can expect to take in college.
Course Main Navigation Bachelor of Education (Secondary) Minor In Mathematics Education This minor includes statistics, such as organising numerical data estimation and hypothesis testing; problem solving and analysis; mathematical modelling using differential and integral calculus and analytic geometry; and linear algebra, including matrices and matrix arithmetic. Students will be able to plan a variety of mathematics lessons, assessments and activities, with a pedagogical focus on developing an appreciation of mathematics as a useful and creatively interesting area of study. Minor structure This unitset structure contains information about the units which comprise the course as well as the credit points required to successfully complete it. Content covered in this minor includes statistics, such as organising numerical data estimation and hypothesis testing; problem solving and analysis; mathematical modelling using differential and integral calculus and analytic geometry; and linear algebra, including matrices and matrix arithmetic. Students will be able to plan a variety of mathematics lessons, assessments and activities, with a pedagogical focus on developing an appreciation of mathematics as a useful and creatively interesting area of study. Note: Students must have passed either WACE General Mathematics 2C/2D or 3A/3B to do this minor. A satisfactory result in WACE 3C/3D is also desirable.
Features MATHEMATICS A GOOD BEGINNING 7th EDITION Here is a more complete list of the 7th edition's features that illustrate why it is such a valuable teaching tool: MGB has fully integrated the new Common Core State Standards for Mathematics (CCSSM) into the text and supporting activities. MGB includes a learning trajectoryfor every content chapter. Learning trajectories constitute a specific mathematics goal, the developmental path (progression) students follow to achieve that goal, and the instructional tasks necessary to facilitate students' learning along that path (i.e., Clements & Sarama, 2009; Fuson, Caroll & Drueck, 2000). Learning trajectories are foundational to the CCSSM, and no other mathematics methods text integrates them into all content topics. MGB places heavy emphasis on pedagogical content knowledge (PCK) within every content chapter. Research has shown that teachers in the U.S. suffer from weak mathematical PCK (Ma, 2000), a deficiency this text will help to overcome. MGB includes a chapter on number theory, a topic critical to the development of algebraic concepts yet missing from all other elementary mathematics methods texts. MGB'scomputational algorithms have been reformulated to support student's number sense, place value understanding, estimation skills, and mental mathematics. MGB is written using informal language that is non-threatening to pre-service teachers with math anxiety. At the same time, the authors carefully build the reader's conceptual understanding of precise mathematical vocabulary. MGB includes a booklet of full-size reproducible Resource Sheets (RS) that support sensory input for activities that develop key mathematical concepts.The resources in this booklet can sensitize teachers to the kinds of materials that are appropriate mathematics teaching and learning aids. MGB incorporates the authors' years of research on diagnosis of student misconceptions into an assessment section in every content chapter. For every major concept covered in each chapter, an explanation of students' typical conceptual difficulties is provided. MGB's authors have a wealth of experience in preparing teachers to teach mathematics, experience that has informed the content, presentation of concepts, and book length (200 pages shorter than the typical methods text). MGB provides a Study Guide for each chapter to help pre-service teachers gain maximum benefit from the content and to provide teacher educators with a wealth of meaningful activities they can assign for coursework. MGB's authors believe that classroom teachers must recognize that they are teachers of children, as much as they are teachers of mathematics. They must know the mathematics they teach and must be competent to communicate content in a way that children can understand. For every content chapter, MGB presents a list of essential learning expectationsthat illustrates how children's learning will progress. Within every content chapter, MGB Spotlights authors and articles that will help pre-service and in-service teachers enhance their knowledge. MGB's companion website will keep readers informed of current topics in mathematics education. See it for yourself! Simply register and log in to view samples from our text and resources on the Evaluate the Book page! This page is only available to logged-in registered users.
Precalculus (Math 1322 and Math 1323) is a two-semester sequence that is designed to prepare students to be successful in a calculus course. The topics of the course include (but are not limited to) Solving equations and inequalities Graphing Polynomial and rational functions Exponential and logarithmic functions Trigonometric functions and their inverses Right angle and unit circle trigonometry Selected topics from analytic geometry In short, Precalculus is an amalgamation of studies in algebra, trigonometry, and coordinate geometry chosen to meet the needs of those who will need to complete one or more semesters of calculus. Midterm 1
Essentials of College Algebra, Alternate the Ninth Edition of College Algebra by Lial, Hornsby, and Schneider has been specifically designed to provide a more compact and less expensive alternative to traditional textbooks; Essentials of College Algebra better meets the needs of colleges whose College Algebra courses do not include the more advanced topics covered in the longer text. Simply put, Essentials of College Algebra gives students a solid foundation in the basic functions of college algebra and their graphs, starting with a strong review of intermediate ... MOREalgebra concepts up front and ending with an introduction to systems and matrices. Focused on helping students develop both the conceptual understanding and the analytical skills necessary to experience success in mathematics, the authors present each mathematical topic in this text using a carefully developed learning system to actively engage students in the learning process. The book addresses the diverse needs of today's students through an open design, current figures and graphs, helpful features, careful explanations of topics, and a comprehensive package of supplements and study aids. Essentials of College Algebra , Updated Edition, 1/e,has been specifically designed to provide a more compact and less expensive alternative to better meet the needs of colleges whose algebra courses do not include the more advanced topics. The authors have focused the content of this book on helping students master the basic functions in college algebra and their graphs, while including a strong review of intermediate algebra at the beginning of the text and an introduction to systems of linear equations in Chapter Five.
Math 8 starts out the year developing the basic math skills needed for all of the units to be studied through June. Equation Solving Word Problems Geometry Graphing Lines & Angles Students will be expected to participate appropriately in class by taking guided notes which will directly correlate to their homework for the night. Homework will be assigned at the end of each class - students will receive a copy of the guided notes attached to their homework. The expectation is that the notes they take in class will stay in their binders, while the notes copy attached to their homework will be used at home to complete the assignment. IF HOMEWORK IS NOT COMPLETED, IT WILL BE EXTREMELY DIFFICULT TO PASS MATH 8. Students will be preparing in each unit for the NYS Math 8 Exam, which will be given in mid April. »Online Textbook This link will take you to the online textbook we are using this year. Occasionally, we may have assignments which could be done through the website. Each student has a specific login username (their student ID) and were given a password at the beginning of the year (math08). Passwords should be changed once a student has logged in for the first time. This link can be used for review as it offers online tutorials for a quick refresher.
25-050. MATHEMATICAL CONCEPTS. 3:3:0 This course provides students with mathematical tools and problem- solving skills needed to move comfortably and confidently into Mathematics 075, 101 and 105. The concepts explored include Number Systems, Ratio, Proportion, Percent, Measurement, Algebra, Graphing and Geometry. This course does not carry credits toward graduation. 25-075.INTRODUCTION TO ALGEBRA. 3:3:0 The course provides students with a solid foundation in algebra and problem-solving skills needed to move comfortably and confidently into College Algebra, Survey of Mathematics, or Mathematics for Primary and Middle Grade Teachers. Topics include the applications of linear and quadratic equations and inequalities to real world problems, graphing, rational and radical expressions, and systems of linear equations. This course does not carry credits toward graduation. 25-101. SURVEY OF MATHEMATICS I. 3:3:0 A course designed to acquaint students with problem-solving strategies, sets and applications, logic, arithmetic in different bases, real number system, and algebra. Prerequisite: Two units of high school mathematics. Credit: three hours. 25-102. SURVEY OF MATHEMATICS II. 3:3:0 A course designed to acquaint students with consumer mathematics, geometry, mathematical systems, introduction to probability and statistics, and an introduction to computers. Prerequisite: Mathematics 101. Credit: three hours. 25-105. MATHEMATICS FOR TEACHERS I. 3:3:0 This course is designed to acquaint prospective PK-8, vocational and special education teachers with the structure of the real numbers system, its subsystems, properties, operations, and algorithms. Topics include problem solving, logic, number theory, and mathematical operations over the natural, integer and rational numbers. The course emphasizes heuristic instruction of students with different learning styles. Prerequisite: Two years of high school Mathematics, including Algebra and Trigonometry. Credit: three hours. 25-106. MATHEMATICS FOR TEACHERS II. 3:3:0 A course designed to introduce problem-solving skills and heuristic instruction to prospective PK-8, vocational and special education teachers. Topics include real numbers, percents and interest, radicals, rational exponents, probability, statistics, geometry and measurement. Prerequisite: Mathematics 105. Credit: three hours. 25-121. COLLEGE ALGEBRA. 3:4:0 A course designed to expose students to polynomials, factoring, rational expressions, complex numbers, rational exponents, radicals, solutions of equations, linear and quadratic inequalities, functions and graphs, and synthetic division. A graphing calculator is used for learning and discovery in this course. Prerequisite: a minimum of three (3) units of college preparatory mathematics. Credit: three hours; four contact hours. 25-122. TRIGONOMETRY. 3:3:0 A course designed to prepare students for calculus. Topics include exponential and logarithmic functions, trigonometric functions and graphs, trigonometric identities, trigonometric equations, inverse trigonometric functions, laws of sines and cosines and applications, matrices and determinants, and systems of equations. Prerequisite: Mathematics 121. Credit: three hours. 25-125. FINITE MATHEMATICS. 3:3:0 The course is designed to prepare students for business calculus and quantitative business data analysis. Topics include counting techniques and series, systems of linear equations and inequalities, matrix algebra, linear programming, and exponential and logarithmic functions. Prerequisite: Mathematics 121. Credit: three hours. 25-203. COLLEGE GEOMETRY. 3:3:0 A course designed to prepare teachers in geometry. Topics include: axiomatic systems, methods of proof, formal synthetic Euclidean geometry, measurement, transformations, introduction to non-Euclidean geometries, and geometry within art and nature. Course emphasis will additionally be placed upon geometry education, problem-solving heuristic, and pedagogy. Prerequisite: Mathematics 122 or its equivalent. Credit: three hours. 25-204. NON-EUCLIDEAN GEOMETRY. 3:3:0 A treatment of Euclid's parallel postulate, nature of proof, characteristics of a mathematical system, Lobachevskian Geometry, and Riemannian Geometry. Prerequisite: Mathematics 203. Credit: three hours. 25-205. MATHEMATICS FOR TEACHERS III. 3:3:0 This course is designed to prepare prospective PK-8, vocational and special education teachers for solving mathematical problems originating from different disciplines. Topics include techniques and modes of operation in geometry, measurement, algebra, trigonometry and calculus. Prerequisite: Mathematics 106. Credit: three hours. 25-213. DISCRETE MATHEMATICS I. 3:3:0 An introduction to discrete mathematical structures for computer science with emphasis on logic, counting techniques, set theory, mathematical induction, relations, functions, and matrix algebra. Prerequisite: Mathematics 122. Credit: three hours. 25-214. DISCRETE MATHEMATICS II. 3:3:0 Principles and applications of discrete mathematical structures in computer science. Topics include Boolean algebra and switching functions, finite state machines, graph theory, trees and mathematical techniques for algorithmic analysis. Prerequisites: Mathematics 213 and 251. Credit: three hours. 25-225. CALCULUS FOR BUSINESS AND SOCIAL SCIENCES I. 3:3:0 An introduction to functions, limits and continuity, the derivative, marginal functions, maxima/minima, integrals and fundamental theorems of calculus, applications of differentiation and integration in Business and Economics. Prerequisite: Mathematics 125. Credit: three hours. 25-226. CALCULUS FOR BUSINESS AND SOCIAL SCIENCES II. 3:3:0 A continuation of Mathematics 225 covering a more general treatment and business applications of integration, partial derivatives, optimization problems and LaGrange multipliers, and multiple integration. Credit: three hours. 25-241. ELEMENTARY STATISTICS. 3:3:0 A course designed to introduce students to descriptive statistics, measures of central tendency and dispersion, probability, statistical inference, correlation, and regression analysis. Prerequisite: Mathematics 121. Credits: three hours. 25-251. CALCULUS I. 4:4:0 An introduction to limits, continuous functions, rate of change, derivatives, implicit differentiation, maximum and minimum points, and their applications, and development and application of the definite integral. Prerequisite: Mathematics 122. Credits: four hours. 25-252. CALCULUS II. 4:4:0 A continuation of Mathematics 251 covering logarithmic, exponential, trigonometric and hyperbolic functions, techniques of integration, indeterminate forms, improper integrals, Taylor's formula and infinite series. Prerequisite: Mathematics 251. Credit: four hours. 25-253. CALCULUS III. 4:4:0 A continuation of Mathematics 252 to include polar coordinates, vectors and parametric equations, solid analytic geometry and the calculus of several variables. Prerequisite: Mathematics 252. Credit: four hours. 25-313. LINEAR ALGEBRA. 3:3:0 A treatment of linear equations, matrices and determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. Prerequisite: Mathematics 252. Credit: three hours. 25-341. PROBABILITY. 3:3:0 This course is a treatment of probability theory with stochastic processes. Topics include sample spaces, probability measures, discrete and continuous random variables, sums of independent random variables, law of large numbers, and the Central Limit Theorem. Markov chain models and their applications in the social and natural sciences are included. Prerequisite: Mathematics 251, and 313. Credit: three hours. 25-351. ORDINARY DIFFERENTIAL EQUATIONS. 3:3:0 A treatment of the solutions and applications of first order linear, homogenous and non-homogenous linear nth order differential equations. A presentation of the power series solutions, Laplace transform, linear systems of ordinary differential equations, and methods of numerical solutions. Prerequisites: Mathematics 252, and 313. Credit: three hours. 25-403. METHODS OF TEACHING MATHEMATICS IN THE SECONDARY SCHOOLS. 3:3:0 A study of the methods and materials used in teaching high school mathematics. This course introduces current educational theory, reform organizations and research methodologies. Topics include NCTM standards, effective teaching models, lesson plans, classroom management, professionalism, technology in the classroom, and current issues and trend. Prerequisite: Mathematics 252. Credit: three hours. 25-411. ALGEBRAIC STRUCTURES I. 3:3:0 A study of set theory, functions, integers, groups, matrices, permutation and symmetric groups, LaGrange theorem, normal and factor groups, and homomorphisms. Prerequisite: Mathematics 252 and 214 or its equivalent. Credit: three hours. 25-412. ALGEBRAIC STRUCTURES II. 3:3:0 A continuation of Mathematics 411 covering rings, integral domains, ideals, polynomial rings, principal ideal domains, and unique factorization domains. Prerequisite: Mathematics 411. Credit: three hours. 25-431. NUMERICAL ANALYSIS. 3:3:0 An introduction to the solutions of equations in one variable, direct methods and matrix techniques for solving systems of equations, interpolation and polynomial approximation, numerical differentiation and integration, and the initial value problems for ordinary differential equations. Prerequisite: Mathematics 252 and Computer Science 240 or 262 or other programming language. Credit: three hours. 25-451. ADVANCED CALCULUS I. 3:3:0 A treatment of vector spaces, differentiation of vector valued functions, and functions of several variables, partial derivatives, maximum and minimum of functions of several variables, Taylor's formula and applications, line and double integrals, Prerequisite: Mathematics 253. Credit: three hours. 25-452. ADVANCED CALCULUS II. 3:3:0 A continuation of Mathematics 451 covering curve and double integrals, Green's Theorem, triple and surface integrals, Divergence Theorem in 3-D space, Stoke's Theorem, Differentiability and the Change of Variable Theorem for functions from Rn into Rm, the Jacobian Matrix, the inverse mapping and implicit function theorem. Prerequisite: Mathematics 451. Credit: three hours. 25-461.INTRODUCTION TO REAL ANALYSIS. 3:3:0 An introduction to ordered and Archimedean fields, the theory of limits and continuity of functions, topological concepts, properties of continuous functions, the theory of differentiation and integration, and selected topics from power series and functions of several variables. Prerequisite: Mathematics 451. Credit: three hours. 25-471. COMPLEX ANALYSIS. 3:3:0 An introduction of complex numbers, Cauchy-Riemann equations, analytic and harmonic functions, elementary functions and their properties, branches of logarithmic functions, inverse trigonometric functions, the Cauchy-Goursat theorem, the Cauchy integral formula, Monera's theorem, Maximum Modula of functions, Taylor and Laurent series, residues and poles, linear fractional transformations. Prerequisite: Mathematics 452. Credit: three hours. 25-491. HISTORY OF MATHEMATICS. 3:3:0 A study of the evolution of mathematics. Topics include the scope and history of the Egyptian geometry, Greek and Arabic mathematics, the mechanical world, probability theory, number theory, non-Euclidean geometry, and set theory. Prerequisite: Mathematics 203 and 253. Credit: three hours. 25-498. TOPICS IN MATHEMATICS. 3:3:0 A treatment of selected topics in mathematics. (This is a senior capstone course.) Prerequisite: Approval of the Department of Mathematics. Credit: three hours. 25-499. SEMINAR IN MATHEMATICS. 3:3:0 A treatment of selected topics in mathematics augmented by invited guest speakers and student presentations. Prerequisite: Approval of the Department of Mathematics. Credit: three hours. Department Homepage Delaware State University Applied Mathematics Research Center (AMRC) was initially funded by the Department of Defense (DoD) in 2003. AMRC is designed to create a research environment where multidisciplinary groups work together to solve applied mathematics problems in military and other areas. The research center consists of faculty of Mathematics, Computer Science, Electrical Engineering, and Biotechnology, research associates, visiting professors and an administrative assistant. The major goals are: to establish a permanent research base at Delaware State University which produces new knowledge and quality, publishable, peer-reviewed research relevant to DoD research goals to enhance participation and substantial involvement of minority graduate (M.S. and Ph.D.) and undergraduate students and faculty in Science and Mathematics research to provide additional training in mathematics and sciences to minority female high school students by involving them a summer program (GEMS), and therefore to prepare more minority students (especially women) in sciences and mathematics to foster long-term research collaboration among scientists with Army Research Laboratories, and other national government and academic institutions; and 5) to ensure long term sufficient research funding MAIN RESEARCH AREAS Ground Penetrating Radar Imaging Buried object detection using GPR has attracted tremendous attention in the past decades because of its important military, such as mine detection, and commercial applications. Our current work aims to use vector multiresolution representation for the antenna array receiving data in multifrequency ground penetrating radar (GPR), and solves the inverse scattering problem, and then uses the hidden Markov model (HMM) in the wavelet transform domain for the target detection. We plan to expand our GPR imaging research in three aspects: continuing to investigate our current research targets; developing algorithms for 3-D GPR imaging; and processing real land mine GPR data with new algorithms. The NURBS methods of Computer geometric design in automatic representing 3D objects NURBS is the most popular and widely used method and tool in the field of computer geometric design in representing and manipulating 3D objects. The objectives of the project are to study the following problems in reconstruction of smooth surfaces, which are: producing polygonal model from scattered and unstructured 3D data, and/or even from 2D data; mesh quadrilaterization of the polygonal model; and the representation of the parametric surfaces on each quadrilateral patch, and the construction of NURBS surface model. Image Registration The research task is to develop software in C or MATLAB that will create a unified image from a sequence of smaller images. The dyadic combination of images is the basic operation; the recursive implementation of this combination will constitute the desired algorithm. A data set of the Blossom Point test range will be used as the data source. We will identify relevant features that allow images to be merged. It is expected that these features will also be applicable to similar images. This software will be developed with the expectation that it will be enhanced to include problems associated with scaling, and then 3D image reconstruction. Signal Processing in Data Mining The ultimate goal of the proposed research is to provide advances in technology towards successful development, testing, refinement and application of intelligent, self-adaptive software systems. The approaches integrate computer vision systems, soft computing and evolutionary computational paradigms, complex adaptive software structures and robust machine learning algorithms. In addition, we aim towards practical design, development, prototyping and evaluation of a knowledge-based software system that will integrate theoretical aspects of the proposed techniques into user-friendly application equipped by advanced user interface and enhanced data base management capabilities. Biotechnology The research focuses on nucleotide sequence and chromatin structure requirements for integration. We will also deal with the scientific, social, and ethical issues related to the field of Biotechnology, present the elements of biostatics and numerical methods needed for quantitative data analysis and interpretation, and provide practical experience with the use of software and databases in the investigation of problems critical to biotechnology and molecular biology to our undergraduate students. Other Research Areas Inverse Ill-Posed Problems, Numerical Analysis, Partial Differential Equations, Integral Equations, Wavelets and Image Analysis, Scientific Computation, and Mathematical Physics. Outreach Delaware State University (DSU) will conduct the pre-college program Girls Explorations in Mathematics and Science (GEMS). GEMS is a three-week summer residential program involving hands-on explorations in mathematics, biology, and information technology with research activities. This project will offer 20 motivated high-potential female high school students entering tenth and eleventh grades an opportunity to integrate and apply concepts from these disciplines to problem solving. GEMS program is designed to stimulate and extend students' interest in these fields and encourage them to investigate careers in mathematics, biology, and information technology. This addresses the problem of under-representation of women, in particular minorities, in these fields. Three college professors and three high school teachers, who are assisted by six undergraduate/ graduate female students, conduct the project. The curriculum has been carefully designed to expose students to research methodology, to enable them to see the connections between mathematics, biology, and information technology. The participants work in small groups and use computers extensively to explore and discover mathematical and biological concepts. Department Homepage Rightbar: Faculty ETV Building Room 107 Ph: 302-857-7051 Fax: 302-857-7054 Body: Overview The objectives of the Mathematical Sciences Department are to provide opportunities for students to develop functional competence in mathematics; an appreciation for the contributions of mathematics to science, engineering, business, economics, and the social sciences; and the power of critical thinking. The Department strives to prepare students to pursue graduate study and for careers in teaching, government, and industry. The Department aims to provide the student with a course of study directed toward an understanding of mathematical theory and its relation to other fields of study. This study includes an emphasis on precision of definition, reasoning to precise conclusions, and an analysis and solution of problems using mathematical principles. Students who select a major in the Department must complete the general education program which is required of all students. Request more information Curriculum Options for Majors MATHEMATICS: The requirements for a major in Mathematics are: Mathematics 191,192, 213, 214, 251, 252, 253, 313, 341, 351, 411, 451, and 498; One of 412, 452; Physics 201 and 202; and a minimum of six (6) hours selected from Mathematics courses numbered 300 or higher, excluding 403. With departmental approval, three hours may be submitted from Physics 311-312 and 404. MATHEMATICS WITH COMPUTER SCIENCE: The requirements for a major in Mathematics with Computer Science are: Mathematics 191,192, 213, 214, 251, 252, 253, 313, 341, 351, 431 and 498; Physics 201, 202; Computer Science 240, 261, 262, 360, 461 and 495; and a minimum of twelve (12) hours selected from Mathematics courses numbered 300 or higher, excluding 403. MATHEMATICS EDUCATION: The requirements for a teaching major in Mathematics are: Mathematics 191,192, 203, 213, 241, 251, 252, 253, 313, 341, 403, 411 and 491; Education 204, 313, 318, 322, 357, and 412; Physics 201 and 202; Psychology 201; and Computer Science 261. Students must take and pass PRAXIS I and apply for admission to the TPE prior to the start of their junior year. Students must pass PRAXIS II prior to student teaching. OPTION FOR MINORS To provide an opportunity for students to obtain a minor concentration in mathematics, the Department of Mathematical Sciences offers the following option: Minor in Mathematics: Twenty-one (21) hours distributed as follows: Mathematics 251, 252, 253; and nine (9) additional hours selected from Mathematics courses at the 300 level or higher, excluding 403. Leftbar: Free Student Tutoring Resources The Department of Mathematical Sciences offersfree mathematics tutoringin the Mathematics Laboratory (ETV 128). Tutoring sessions are available for any student who needs assistance in their mathematics courses. Mathematics Laboratory tutors are responsible students with a 3.3 GPA or higher. Tutoring session times are flexible to accommodate any student's schedule. Typical hours of operation are Mondays through Fridays with times varying from 9 a.m. to 8 p.m.. Actual hours of operation with specific tutor information are posted on the door of the Mathematics Laboratory each semester. If you have any questions, please contact the Department of Mathematical Sciences at ext. 7051.
Algebra Age 15+ Time 2h. Students find transforming functions one of the most demanding topics in mathematicsat this level. In particular, the effect a has on the function, f(x) for y=af(x) and y=f(ax) and understanding just what a stretch is. This activity documents the most succesful approach I've had with this topic. It approaches the idea from the angle of transforming shapes, looking at the effect on the coordinates, then applying the same transformations to graphs. [Show][Hide] This is a very complete activity that makes use of Geogebra and includes ready made applets and help videos for teachers who may have little experience or confidence in using technology in the classroom. Watch the following video (no sound) to get an overview of the activity: Age: 14+ Time: 2h. This is a perfect activity to discover the properties of quadratic graphs. An investigation to 1) describe the axis of symmetry, 2) find the vertex form and 3) describe the zeros of a quadratic function. It includes fun quizzes and is concluded with a firefighter game where Sam must aim the water jet correctly to put out the fire. Great fun! Click show to see short video overview of activity [Show][Hide] Age: 14+ Time: 1h Questions start off easy (one or two vert/horiz inequalities) to ensure all students can be engaged - will they save the eggs from the Pterodactyls? The aim of the activity is to focus student attention on how coordinates relate to the inequality and hence facilitate a better understanding of which side of an inequality students should shade. Playable on ipad etc. also. Age: 14+ Time: 1h Students have to modify the inequalities to trap each ghost in turn within their "laser fields" (no software required). Care is required because if their inequalities aren't precise they could easily burn the baby! Levels increase in difficulty, from one to three ghosts, but only using linear inequalities. Playable on ipad also. Age: 15+ Time: 1hr + This activity introduces students to the concept of even and odd functions, i.e. functions with properties f(x) = f(-x) and f(x) = -f(-x). There follows an investigation into the properties of adding, multiplying and finding composites of these functions e.g. even function + even function =? Age 11+ Time: 1h Students take the orders at Luigi's or Taj's Waiter of the Year competition using a single letter to abbreviate each starter, main etc. Simplify the algebra and substitute in the prices to finalise the bill. This leads into letters as variables: Spin the fruit machine to select a number target before rolling a die to substitute in. Self-checking exercise to finish or for use as a homework. Lots of human interaction! Age 13+ Time: 2h This is a very complete activity to get students factorising quadratic expressions for the first time. It includes 2 arcade games to practise expanding brackets, a product and sum puzzle and a self-checking spreadsheet for factorising. Watch the following video for an overview[Show][Hide] Age: 14+ Time: 1h+ This activity will challenge high achieving students to learn about the properties of exponential functions and their transformations. Interactive applets and quizzes get the students to discover the properties for themselves then there are a couple of games to challenge them to 'copy the function'. Watch the short video below for a quick overview.[Show][Hide] Age: 14+ Time: 1-2h+. Students use Geogebra to plot, then try and find a function to fit Olympic winning data for the men and women's 100m, High Jump, Show jumping and men's weightlifting from 1896 to the present. What are the limits of human physical abilities? This is a great activity to develop students' mathematical modelling: who will predict most accurately the winning times for the forthcoming Olympics? Age: 12+ Time: 1h What changed during the Renaissance? This activity looks at the revolution in using algebra to describe geometries, graphs, 3D perspective and the introduction of decimal notation. It can be used as part of a Renaissance School Day where students make links between subjects and then present their findings in a whole school assembly. Overview of this day, lead by History department, available here. Age: 15+ Time 1.5 hr + This activity gets students to produce families of trigonometric functions (like the one on the right) using dynamic geometry software. By exploring the effect of changing parameters they really get a deep understanding of the properties of the main transformations: translations and stretches. Get ready for "Oos and Ahhs"! Age: 12+ Time 1 hr + A computer with internet access is required for this set of five interlinked activities where students are introduced to the equation of a straight line. A structured investigation is followed by a bowling game where students are required to enter the correct equation in order to be able to bowl over the pins and get a strike. A really entertaining way to learn about gradient and y intercept. Age: 13+ Time: 1-2h. Estimation is a key skill in all areas of maths, but perhaps particularly so in Trial and Improvement. Using mini-whiteboards, paper, in pairs or teams students use what they know to estimate square and cube roots of numbers they don't know. They then use Excel to try and hone their answers to 1, 2 or 3 d.p. accuracy. Students can also create their own Excel questions and solutions. Age: 15+ Time 1 hr. This Age: 15+ Time: 30mins-1h. Students use geometry software to model wave pictures from real-life objects and situations. In doing so, students will investigate the effects of the coefficients for sine and cosine waves e.g. y = a cos[b(x-c)]+d asking themselves: "What Changes?", "What Stays the Same?". No software is required Age: 15+ Time 1-2 hrs Using Autograph or the free Geogebra or Microsoft Maths 4.0, students investigate the functions of the sine and cosine graph. Students record the key, defining points in a pre-prepared table: coordinates of the maximum and minimum and x-intercepts, as they change different parameters using the constant controller or sliders. Without technology, students then have to predict [Show][Hide] Age: 15+ Time 1h This activity introduces sine and cosine graphs using the video of the construction of a Ferris wheel that demonstrates the link with triangles. Students then sketch the graph of their movement on the Big Wheel. The aim is to link the sine and cosine ratios to a circle. Students use calculators to plot the graphs exactly (spotting symmetries to save them calculation time!). VM also available. Age: 11+ Time: 1hr+ This activity gets students to explore the ideas of factorising simple linear expressions. However, it does it in a way that never mentions factorising! Students will need to think critically to solve some puzzles about multiplying out number grids. By turning the questions around, students will then discover the rules for factorising. Students should be able to [Show][Hide] multiply simple algebraic expressions before they attempt this activity. Age: 11+ Time: up to 1hr. Practise programming spreadsheets with simple formulae. Use the spreadsheet to examine the relationships and patterns between the numbers in magic squares. Do all of this while you get lost in this fantastic challenge! Create a 7 x 7 magic square with a 5 x 5 magic square inside it and a 3 x 3 one inside that! Age: 12+ Time: 1h. In this activity, students are given a target and have to choose expessions that correspond to the target e.g. even number: 2n-2. They then make up their own targets and/or cards to match. In the second activity students match a series of formulae to their symbolic meaning, word meaning and physical world context. All activities focus on the concept of letter as "variable". The last activity [Show][Hide] develops students effective internet and textbook etc. research skills. Age: 12+ Time: 2 hours. In this investigation, students explore the sums of consecutive numbers and their divisors with the hope of discovering and proving that the sum of n consecutive numbers is divisible by n when n is odd. This is a gentle introduction for young students to the idea of proof! Using algebraic terms to represent unknown numbers and very simple algebraic manipulation, [Show][Hide] students see the power of algebra. It therefore provides them with a reason and motivation to learn more about this often elusive topic. Before attempting this activity, I would expect students to have had a little exposure to adding simple algebraic expressions together. Use card games to get students practising and revising solving equations. Playing in pairs, threes or fours students roll a die, in combination with the cards, to win their partner's cards. There are many possible games using these cards, as well as a range of levels from Apprentice to Mathmagician. Age: 12+ Time: 30mins to 1h Age 14+ Time 30-40 minutes. Match the waves with their functions! The discussions and reasoning that take place during this type of activity can be incredibly valuable and effective. It is a simple idea, but so often the simple ideas can be the most effective. It is also a nice alternative to a traditional exercise. When well practised, this is not a desperately difficult concept and it can be very satisfying [Show][Hide] to be able to quickly make the link and either deduce a function from the graph or the other way round. This simple activity lends itself to group work and presents the kind of challenge that usually engages students This group activity gets students to match a physical world scenario e.g. pressure exerted by an elephant of 400kg mass, with its associated data (a number relation), the equation that defines this relationship, a graph and the nth term rule. This provokes student discussion to air and refine students' conceptions of the relationship between these topics. Age: 14+ Time 1 hr. Age: 15+ Time 1 hr. Challenge students to really understand the concept of a function. Match a set of input values with a function and a corresponding set of output values. There are eight sets of three to make and only one correct solution. This activity is 'old meets new'. Students work with cut out bits of paper but can use calculators/computers to help them solve the puzzle! Age: 12+ Time: 1-2 hours. This activity is another great example of a puzzle whose solutions can be modeled by an algebraic sequence (linear). The puzzle provides an engaging introduction and an incentive to generalise, which helps students with this traditionally difficult idea. The puzzle can be modeled by a linear sequence and broken down into a series of different linear sequences that combine to form the overall model. [Show][Hide] As such this activity has lots of scope for relating sequences to physical situations, breaking them down in to parts and seeing how algebraic manipulation links the different solutions together. This is a good deep problem that only involves linear sequences. Age: 12+ Time: 1-2 hours Bring life to this classic sequences problem by getting students out of their chairs and jumping around to solve the problem. This is a terrific problem for generating and investigating a quadratic sequence. It can be looked at from a number of angles and demonstrating the way they link together gives a very satisfying result. This problem has been around for a while and this activity is really about [Show][Hide] A card game to introduce students to quadratic equations. Playing in pairs, threes or fours students roll a die, in combination with the cards, to win their partner's cards. There are many games possible using these cards. Age: 12+ Time: 10-30 minutes This immediately absorbing and engaging activity requires students to use graphing software. The aim is to explore the basic transformations of a function, e.g. y=f(x-a), y=f(ax) for the quadratic function. However, the questions are disguised in videos of moving graphs that students are asked to reproduce. This challenge provides a great incentive to explore, experiment and share ideas. Age: 15+ Time: 1h This activity is about linking the graphing of quadratics with the equations themselves by looking at their key features. Students match pieces of information with different graphs using logical deduction. This practical group activity leads to being able to sketch graphs from their equations. Age: 15+ Time: 1h In one hour students should have worked out how to "factorise quadratics" for themselves using patterns in the factorisations given by CAS software, such as TiNspire, Geogebra, WolframAlpha or Derive. "How to" videos are included for those inexperienced in using these programmes. A second activity relates factorising to the "Grid Method" of multiplication including the use of an online virtual manipulative. Age: 13+ Time: 1-2h This is a great introductory lesson to linear graphs. Students will act as coordinates on a huge grid. Holding A3 sheets of white paper up when a rule requires it, they will plot coordinate pictures and straight line graphs following instructions such as, "Hold up your sheet is your x and y coordinates add together to make 9!" A webcam and a projector can add an extra dimension to this practical activity. Age: 9+ Time: 30m to 1hr A real game that is fun to play and, when investigated, generates a great example of an exponential sequence. Ideal activity for exploring sequences in general and for introducing these functions. It is a practical activity that can be enhanced with access to computers. Age: 13+ Time: 1 hour In this activity students will use a graphing package to explore the link between geometrical patterns, sequences and their graphical representations. There are 3 levels of difficulty starting with linear sequences moving on to quadratic, then other more challenging sequences. Age: 12+ Time: 1-2 hours Use Excel or any other spreadsheet to explore the patterns in linear or arithmetic sequences. Students are quickly drawn to striking patterns and the teacher's role is careful questioning aimed at asking students to articulate the whats? and whys? Age: 11+ Time: 1h Use dynamic geometry software to find the quadratic equations that model some photographs of real-life objects. This activity will get students to understand the effect of changing the parameters in the general equation y = a(x - b)² + c. Three Geogebra files are provided and are ready to use. No software is needed. Age: 14+ Time: 1h By the end of the hour students should have worked out how to "factorise" for themselves by looking for patterns in the factorisations given by CAS software such as TiNspire and Derive. "How to" videos are included, for those inexperienced with the technology, to help ensure teacher and student time is focused on the mathematics. Age: 12+ Time: 1h Re-arrange simple formulae with this matching pair activity. 32 cards are cut out and matched up to give 16 pairs of equivalent formulae with different subjects. This activity promotes much discussion and helps iron out fallacies. Age : 14+ Time : 1 hr Students get practice in finding the nth term of arithmetic and geometric sequences. Sequences are presented in a graphical form and students are required to find their nth terms. Ti Nspire calculators are recommended to get the most out of this activity and allow students to play with and test their own conjectures. Age: 15+Time: 1hr How many ways to win a 3D game of three in a row? A real physical game situation that leads to algebraic sequences. There are many ways to investigate this problem and this makes a great project for Algebraic Investigation. Age: 14+Time: 1hr to a whole week. Who's the fastest in your class? How do you know they are "fast"? What does "fast" mean exactly? Student's discuss the above, then race 100m and use the distance, speed, time formulae to work out: If they maintained this speed, could they set a new marathon record?! Age : 12+ Time: 2hrs Formulae often seem so abstract to students, expressed as they are using algebra, yet they are one of the most applied area of mathematics! Students are asked to search Google images and find one or two images to go with each formula. Students then share their pictures with the rest of the class and discuss what each letter represents and how it describes a relationship. Age: 12+ Time: 1-2hrs Students all too often do not realise that functions are all around them: on the dance floor, in the swaying of the branches of a tree . . . . and in people holding their hands in the air in joy! This activity gets them to use their body to feel the transformation! Age: 15+ Time: 5mins to 1h (use sections as starters/plenaries or full resource in a single lesson). Bend a wire to "feel" the shape of the different functions such as sinx, cosx, x3 etc. and their transformations e.g. sin(x-90), Cos3x, etc. Given an equation/function, can you draw the graph on a mini-whiteboard? Age: 15+ Time: 20mins to 1h (starter/plenary or full lesson) Many marks can be lost in exams because of a lack of precision in the exact coordinates of a transformation. Students are taken outside the classroom to give them a physical experience of how functions define coordinates. The discussion between students is useful for drawing out student misconceptions. Careful questioning can challenge these misconceptions. Age:15+ Time: 20mins to 1h (starter or full lesson) Many students find the symbols and meanings used in equations difficult to understand. This activity uses the excellent "balancing scales" manipulative to give students an intuitive understanding of how to solve equations - through experiment and discovery. Age: 11+ Time: 1h
Synopsis This book is packed with practice questions for students taking the AQA GCSE Foundation level Modular Maths course. It thoroughly covers all the topics for the current exams with a range of exercises to test your maths skills. The answers come in a separate book (9781841465807). Matching study notes and explanations are also available in the CGP Revision Guide (9781841465432
The author presents his approach to how undergraduate students in mathematics, business, computer science, and engineering should be introduced to the science of decision making. The material is designed to prepare the student for more advanced topics. The level of mathematics required is deterministic mathematics at an elementary level, including linear equations and graphs. Introductory probabilistic notions are assumed, but they are not used extensively and can be introduced by the instructor. The target audience is juniors, seniors, and advanced lower-division students. The text is for a one-semester course. You may copy this unique Krieger Book Number into the Quote and Information Form, for quick processing, if you're interested in this book
Elementary Linear Algebra - 6th edition ISBN13:978-0618783762 ISBN10: 0618783768 This edition has also been released as: ISBN13: 978-0547004815 ISBN10: 0547004818 Summary: The cornerstone of Elementary Linear Algebra is the authors' clear, careful, and concise presentation of material--written so that students can fully understand how mathematics works. This program balances theory with examples, applications, and geometric intuition for a complete, step-by-step learning system.The Sixth Edition incorporates up-to-date coverage of Computer Algebra Systems (Maple/MATLAB/Mathematica); additional support is provided in a corresponding tec...show morehnology guide. Data and applications also reflect current statistics and examples to engage students and demonstrate the link between theory and practice. ...show less 2008 Hardcover Fair CONTAINS SLIGHT WATER DAMAGE / STAIN, STILL VERY READABLE, SAVE! This item may not include any CDs, Infotracs, Access cards or other supplementary material. $34.00 +$3.99 s/h Good The Best Textbooks Ypsilanti, MI342nd day shipping offered. SHIPS NEXT DAY! lost new book shine from shelving and shipping, still brand NEW $39.40 +$3.99 s/h New Solr Books Skokie, IL No comments from the seller $41.36 +$3.99 s/h New TheBookCzars Downingtown, PA 2008-07-03 Hardcover New 2nd day shipping offered. SHIPS NEXT DAY! lost new book shine from shelving and shipping, still brand NEW. $41.45 +$3.99 s/h Good ocbookstx Richardson, TX 0618783768
Bob Miller's Basic Math and Pre-Algebra for the Clueless by Miller, Bob Bob Miller's fail-safe methodology helps students grasp basic math and pre-algebra. Utilizing the author's acclaimed and patented fail-safe methodology for making mathematics easy to understand, Bob Miller's Basic Math and Pre-Algebra for the Clueless enhances students' in understanding the basics. Cool sites. Homework help for kids on the Net by Trumbauer, Lisa Provides descriptions and Web addresses for numerous Internet sites that provide information for homework, including reference sources, museums, and sites for mathematics, history, trivia, and more. Homework helpers. Geometry by Wheater, Carolyn C. Concepts are explained in everyday language before the examples are worked. Good habits, such as checking your answers after every problem, are reinforced. There are practice problems throughout the books, and the answers to all of the practice problems are included. The problems are solved clearly and systematically, with step-by-step instructions provided.
... More About This Book a time — at your own speed. A user-friendly, accessible style incorporating frequent reviews, assessments, and the actual application of ideas helps you to understand and retain all the important concepts. THIS ONE-OF-A-KIND SELF-TEACHING TEXT OFFERS: Questions at the end of each chapter and section to reinforce learning and pinpoint weaknesses A 100-question final exam for self-assessment Detailed examples and solutions Numerous "Math Notes" and "You Try It" items to gauge progress and make learning more enjoyable An easy-to-absorb style — perfect for those without a mathematics background If you've been looking for a painless way to learn calculus, refresh your skills, or improve your classroom performance, your search ends here. Related Subjects Meet the Author Steven G. Krantz is the Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 30 books on mathematics including a best- 24, 2006 Calculus Extra-Mystified Calculus Demystified is not like the other math books in the Demystified series. It's much more opaque, and isn't particularly suited for filling in the gaps. The book skims over a huge chunk of derivatives in a single chapter. There are no answers to the 'you try this' exercises, which are mystifyingly complex, so (unlike Algebra Demystified, for example) you don't know if you've got it right or not. The exercises in chapter 2 assume you've read chapter 5 (!) and learned 'non-trivial' (the author's words) facts about limits. Even Finney/Thomas doesn't expect you to have mastered material from later in the book to do the exercises. Calculus Demystified would not be all that suitable for people taking calculus the first time (home school, AP, college, etc), but might be OK for people who already know it who need to review (although you'd have to remember calculus fairly well to hold your own). Wasn't this book 'beta tested' by first-time calculus students? 4 out of 4 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. nezbit Posted February 22, 2011 Not so demystified Would have been better to use money to get sparknotes. Purchased book to help with Calculus studies. Got through the basics easily, but the REAL calculus wasn't so easy. This book lacked detailed examples for beginners or intermediates. The audience of this book was more for teachers and advanced mathmaticians. This book also lacks practice problems to help you use the material. 2 out of 2 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. Anonymous Posted October 18, 2009 informative I'd recommend this book to anybody who needs to catch up on their calculus skills. Not the best choice for beginners. Great for references. 1 out of 1 people found this review helpful. Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged.
Post navigation Reading Math My Algebra II kids don't like to read the textbook. Heck, neither do my calculus students. This isn't surprising. It's extra work and it's hard. My class also makes it hard for them, because I do not use the textbook as a skeletal structure for the course. I teach mainly out of my own materials, and use the book more as a supplement. But that doesn't mean that I don't want them reading math. Kids are never taught to "read" a math textbook. If they ever do approach a math textbook, they approach it like a history book. The read it linearly. They also read it passively. Their eyes glaze over. They read words, but they don't try to connect the words to the equations or pictures. They don't read with a pencil in their hands. They hope for some Divine Knowledge to descend upon them simply by having the book open and their eyes on it. That doesn't work. We all know this. Reading math is an active thing. And so recently I've started talking with my class about it. To start this process/discussion, one that I hope continues, I gave my students a worksheet to fill out (see above). I love the honesty with which they responded. For question A, some representative responses: "I read what was assigned to me but did not read anything extra." "I find that textbook reading is pretty boring, so I don't do it unless I have to." "I did not because I had assumed I wouldn't learn things I needed. All I would do was look at examples." "No, I find it difficult to understand math when reading it in paragraphs; it makes more sense to me with a teacher." "I did not generally read my math textbooks. I did, however, always look over the example problems." Some responses for Question B: 1. The writing can be confusing, wordy, and not thorough 2. The book is BORING 3. Small print 4. Too many words for math 5. Outdated examples Some responses for Question C 1. Everything is all in one place 2. Have a glossary 3. Can read at own pace; refer pack to the text when I get stuck 4. Sidenotes! Diagrams! Pictures 5. Real life examples 6. Definitions clear 7. Key terms are highlighted 8. Wide range of example problems with step by step instructions 9. Colors! I hope to do more as we go along. I might have them learn on their own, using the textbook (and the online video help) a whole section or two. There's no reason they can't learn to use the book to be independent learners. I will give them class time and photocopies of the section they need to learn, and they will have to figure things out by the end of the class for a 3 question quiz. I also hope that by the end of the year, we can use their critique of math textbooks for them to write their own textbook. Okay, okay, not quite. That's way too ambitious for me. Two years ago I had my Algebra II kids write really comprehensive Study Guides for the final exam. This year I might ask my kids to pick some of the hardest material and create their own "textbook" for it. They'll get to write it in pairs, and then they can share their finished product with the rest of the class. That will probably happen in the 3rd for 4th quarter. Anyway, I thought I'd share. Since I like to emphasize the importance of mathematical communication to my kids (though I don't do it nearly enough), I thought I'd talk about this one additional component in addition to getting students to talk and write math… READING MATH! Post navigation 3 thoughts on "Reading Math" I found that reading "How to read a book" by Mortimer J Adler really helped me learn how to read a book I intended (or needed to) learn from. Most people (according to the book, and I agree) never learn to read beyond an elementary level, and this book teaches you how to read at a higher level. Works really well when you start using the techniques and such while reading the book. I'd encourage you to check it out. My son has learned most of his math from reading books—he finds classroom instruction excruciatingly slow and has a hard time staying alert. He does sometimes need an explanation different from the one in the book, which (so far) I've been able to provide for him. Unlike your students, he finds the colors, sidebars, and gratuitous pictures distracting rather than helpful. So far, the best books for him have been from the Art of Problem Solving series, which have very clear but concise explanations. I think that reading speed makes a big difference: kids who read slower than talking speed have a harder time gathering information from books than from oral presentation. I still remember that linear algebra class I took at the local college. The prof taught the value of sloooooow reading. (it ruined his ability to read a novel at a fast pace) I turned this into a lesson.
Need Algebra I Help? No Fear, Yourteacher.com is Here! Whether you are trying to figure out if you have enough gallons of gas in your car to make it to the next gas station while driving on the interstate or trying to figure out how many chocolate bars you can purchase at 65 cents a piece with the $3.25 in change you found in your jacket pocket, you need algebra to arrive at the correct answer. Both of these examples can be expressed as algebraic equations. For example, the chocolate situation can be visualized by the equation 0.65x = 3.25. In case you were dying to know, the answer is 5. Learning algebra can be tricky. Just when you finally feel like you have mastered the art of numbers, they decide to throw all these letters into the mix just to confuse you. Don't worry, we have just the tools to help you understand what these X's and Y's are all about. If you are student struggling with your Algebra I homework, or your reviewing for a math placement exam/standardized test for college, or even if you are a parent who can't quite remember how to find common factors to help your child with his/her homework, then you have come to the right place. We have all the tools you need to learn Algebra I for the first time or review your Algebra I skills. One of our newest authors, Yourteacher.com, has a comprehensive collection of easy-to-follow Algebra I tutorials available for purchase. The founders of Yourteacher.com have been teaching algebra through online tutorials since 1998 so we know we are putting you in good hands. Their instructional content has helped tens of thousands of students worldwide. On MindBites, there are a wide range of Algebra I topics to choose from include multiplying integers, graphing lines and equations, finding common factors, simplifying radicals, multiplying polynomials, and much more. All the lessons include Algebra I problems so you can practice along. Yourteacher.com has 40 Algebra I lessons available which can be purchased individually or as a series. The MindBites family would wish you luck, but we don't think you need any! We are positive that once you are done with these series, you will be an Algebra I Whiz. Need help with more advanced algebra material? We have that too. Check out the Algebra subcategory on the MindBites site to find all your algebra tutorial needs.
... read more Customers who bought this book also bought: Our Editors also recommend:Fundamental Concepts of Geometry by Bruce E. Meserve Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations. A Course in the Geometry of n Dimensions by M. G. Kendall This text provides a foundation for resolving proofs dependent on n-dimensional systems. The author takes a concise approach, setting out that part of the subject with statistical applications and briefly sketching them. 1961 editionFoundations of Geometry by C. R. Wylie, Jr. Geared toward students preparing to teach high school mathematics, this text explores the principles of Euclidean and non-Euclidean geometry and covers both generalities and specifics of the axiomatic method. 1964 edition. The Geometry of René Descartes by René Descartes The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart MillA Modern View of Geometry by Leonard M. Blumenthal Elegant exposition of the postulation geometry of planes, including coordination of affine and projective planes. Historical background, set theory, propositional calculus, affine planes with Desargues and Pappus properties, much more. Includes 56 figures. Problems and Solutions in Euclidean Geometry by M. N. Aref, William Wernick Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. More than 200 problems include hints and solutions. 1968 edition. Proof in Geometry: With "Mistakes in Geometric Proofs" by A. I. Fetisov, Ya. S. Dubnov This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editionsProduct Description: curves, theories of perspective, architectural form, and concepts of space
Graph Theory and Complex Networks: An Introduction GTCN aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science. I take the starting-point that mathematics for most students is unnecessarily intimidating. Explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. Taking this approach has allowed me to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks. In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they: Have learned how to read and understand the basic mathematics related to graph theory Understand how basic graph theory can be applied to optimization problems such as routing in communication networks Know a bit more about this sometimes mystical field of small worlds and random networks. The full text of Graph Theory and Complex Networks (GTCN) is available as a "personalized" download ("personalized for" at the top of each page and "your email address" at the bottom of each page) or from Amazon for $25.00. Additional course materials are also available at this site. You will be amused to read about the difficulty of graph/network notation: It is also not that difficult, as most notations come directly from set theory.
Mammoth, AZ ACT Math we must now deal with division. Division causes more difficulties because we cannot divide by zero. Algebra 2 mainly involves ratios of some sort: with rational functions there could be a zero in the denominator; radical functions could have a negative exponent and hence a zero in the denominator is important to understand the basic concepts of algebra before continuing to Algebra II. Students will learn to solve equations and inequalities. They will become proficient in factoring and simplifying algebraic fractions
This program offers all the algebra content students need to master in an accessible, informal format. Features Student Edition now contains more prerequisite skills practice, a new English/Spanish Glossary, sections on Standardized Test Practice and Mixed Problem-Solving, and references to the TI-84 Plus graphing calculator Resources are now conveniently arranged by chapter, saving you time and effort in preparing lessons Technology New! ExamView® Pro Testmaker CD-ROM allows you to create customized tests and study guides in minutes. Add or edit existing questions, integrate graphics, and more! Built-in state and national correlations. New! Online Learning Center gives you access to many valuable resources connected to your Glencoe textbook. The Online Learning Center is organized into two parts—the Student Center and the Teacher Center—with links to a wide variety of appropriate online resources. New! What's Math Got to Do With It? Real-Life Video video series engages students with relevant problem-based examples that show how math is used in real life.
MATH Essential Math Essential Math focuses on mastering the skills needed to be successful in life and to get ready for Algebra. Topics for Essential Math include problem solving, estimation, decimals, percents, fractions, proportions, money skills and basic geometry-students will learn to handle the basics with a deeper understanding and a greater degree of accuracy. The class is co-taught by a special education teacher and a mathematics teacher. The length of the course is one or more semesters, depending on the needs of the individual student. In Essential Math, students use the Holt McDougal Mathematics series within the learning management setting to view videos of topics and complete practice assignments. The student will be scheduled to meet in a webinar with one of the teachers at least weekly, either individually or in a small group. Class activities include the following for each mathematics topic: Weekly meetings where students and instructor can discuss math topics, course progress, any questions, and just to get to know one another better Topic Preview to review skills and include re-learning activities as needed Short videos that present the topic and show how to solve example problems Topic practice with feedback Vocabulary practice Problem solving and estimation practice Throughout the course, students will actively participate in their own learning and will also benefit from personal feedback to help them continue to improve their mathematic skills. Course materials: Holt McDougal Mathematics series Standards met: This course does not meet high school standards. It may be counted as an elective unless listed as a math course in a student's IEP In Math Skills and Topics, which is a one-quarter class, students review and learn about various math topics and how to overcome math or test anxiety. Throughout the course, students will practice to help prepare for standardized math tests, such as the MCA Math test or the Math GRAD test. Class activities include the following: attend weekly class meetings to work on solving practice math test questions together Course materials: : the Holt Mathematics series will be used as resources. Other readings and websites will be assigned and provided in the course. Software: Students need to have Microsoft Word and Excel or Open Office Standards met: This course is designed to help students overcome math anxiety, to help prepare for a standardized math test or retest, or for students who want to explore and review math topics, including topics from algebra 1, geometry, statistics, and probability. It does not meet high school math standards, but can be counted as an elective. Credit: 0.25 for one quarter, counts as a general elective Honors Opportunity: No Beginning Algebra focuses on the concepts of algebra-writing and simplifying expressions, solving equations, graphing on the coordinate system and looking at the rules of algebra and the properties of numbers. It is a one-semester class designed to get a student ready to succeed in Algebra 1A In Beginning Algebra, students use the Holt McDougal Mathematics Course 3 online text. Students are able to view videos of topics, see step by step solutions to problems, and access supplemental materials through this text. Class activities include the following: Periodic meetings where students and instructor can discuss math topics, course progress, any questions, and just to get to know one another better Chapter preview (Are You Ready?) to review skills and include re-learning activities as needed Presentations that explain the lesson and show how to solve example problems Exercises for each section Vocabulary practice Chapter projects, quizzes and tests Zany Brainy extra credit problems each week Throughout the course, students will actively participate in their own learning and will also benefit from personal feedback to help them improve their mathematic skills. Standards met: This course is designed to get the student ready for Algebra 1 and does not meet high school standards. It may be counted as an elective unless listed as a math course in the student's IEP. Mastering the concepts of algebra is very important to continued success in other mathematics courses. In Algebra 1 A, students will learn the why and the how of proportional reasoning and variation, linear equations including recursive sequences, graphing linear equations, solving equations and inequalities, and data analysis including graphs and statistics. Algebra 1 B looks at solving systems of equations and inequalities, using exponents, functions, and classifying numbers. Both courses use an online text that focuses on developing an understanding of the topic, investigating the exciting worlds of algebra, and gaining skills that can evolve and be adapted to new situations. Neat, online interactive tools are available to help algebra really come alive. Class activities will be varied to include the following: Investigations that explore the concepts of algebra Reading guide worksheets to help students focus on key concepts from the text Daily practice with reflection Discussion topics designed to let students learn from and about their classmates Engaging projects in which students gather their own data from the world around them to examine different aspects of algebra and to learn how algebra is used in various careers Quizzes and tests to evaluate students' progress and understanding Phone check in assignments where students and instructor can discuss course progress, any questions, and just to get to know one another better Throughout the courses, students will actively participate in their own learning and will also benefit from personal feedback to help them continue to improve their mathematic skills. In this one-semester course, students develop their problem solving skills in order to work with graphs, statistics, and introductory probability concepts. The focus is on mathematical literacy and practical problem solving; examples are drawn from music, sports, economics, public health, and other areas of life. Class activities include discussions, experiments, projects, and using software to make sense of statistics. Course materials: Excel or Open Office; Fathom software; online readings from a variety of sources Standards met: This course meets all standards and benchmarks in the Data Analysis & Probability strand of the Minnesota 2007 Math Standards for Grades 9-11. Credit: 0.5 Honors Opportunity: Yes Prerequisites: None—this course is appropriate for students at all levels who need to meet the Data Analysis & Probability standards or for those who need a one-semester math elective. Students use The Geometer's Sketchpad software to explore geometric concepts and make discoveries. Topics covered include angles and angle relationships; parallel and perpendicular lines; transformations, symmetry and tessellations; coordinate geometry; triangle relationships; quadrilaterals; polygons and polyhedra; Pythagorean Theorem and special right triangles; circles; perimeter, area, and volume; congruent triangles and proofs; and similarity and trigonometry. Course materials: The Geometer's Sketchpad software; online readings from a variety of sources; teacher created notes, videos and tutorials. Standards met: This course meets all standards and benchmarks in the Geometry & Measurement strand of the Minnesota 2007 Math Standards for Grades 9-11. Credit: 0.5 Honors Opportunity: No Prerequisites: None—this course is particularly appropriate for students who do not have the time in their schedule for a full-year sequence. It is important, however, for students to consult with their counselor regarding number of math credits as the year-long Sketchpad Geometry A and B course may be a better option. In this course, students will regularly use The Geometer's Sketchpad software to explore geometric concepts and make discoveries. Additional practice with geometric properties and theorems will be provided through our online textbook, worksheets, and online games. You will apply the geometry skills you learn to a variety of situations and problem types. Topics covered in Geometry A include reasoning and proof, parallel and perpendicular lines, triangle relationships, and quadrilaterals. In Geometry B, topics include area, volume, circles, and right triangle trigonometry. Course materials include video clip examples, interactive applets for inquiry-based learning, and real world application problems. Students also explore geometric relationships using The Geometer's Sketchpad, a powerful mathematical modeling tool. Course activities include discussions, labs, and problem sets—offering each student a mathematics learning environment where they can understand and excel. The Algebra 2 course will prepare students for a college Algebra class. Topics covered in Algebra 2 A include a review of algebraic properties, linear functions and graphs, linear systems, matrices, quadratic equations and functions, polynomials and polynomial functions. Topics covered in Algebra 2 B include radical functions and rational exponents, exponential and logarithmic functions, rational functions, quadratic relations, sequences, series, and probability and statistics. Course materials include video clip examplesThe Precalculus courses will prepare students for college Calculus. Topics covered in Precalculus A include algebraic and periodic functions, trigonometric properties, applications of trigonometric functions, and circular and parametric functions. In Precalculus B, topics include fitting functions to data, probability, polar equations, complex numbers, sequence, series, limits and derivatives. Course materials include examples from diverse online sourcesCalculus will tie together the mathematics you have learned in previous courses. The courses are designed to for the college-bound student, and when taken together will cover much of the same content as a first semester college calculus class. Calculus A topics covered include: Properties of limits, intermediate value theorem, derivatives, chain rule, derivatives of products and quotients, related rates, integrals, Riemann sums, the fundamental theorem of calculus. Calculus B Topics covered include: calculus of exponential and logarithmic functions, l'Hospital's Rule, critical points and points of inflection, integration by parts. Passing the Advanced Placement Exam in May will allow students to earn college credit. Students who choose to not take the AP Exam will be able to work on the Calculus B material through the last day of the academic year in June. In addition to an online text, students will access both teacher created and Web based resources. Learning will take place through a variety of methods, including the following: auto-graded assignments designed to give you immediate feedback, Sketchpad activities to help you discover and explore topics, and semester projects. Chapter tests and quizzes will also be given. In Discrete Math students will explore unique real world problems that cannot be directly solved through writing an equation or applying a common formula. The course does not require learning a large number of definitions, formulas, and theorems; instead a creative mind, problem solving skills, and visualization will be helpful! Discrete Math will cover a variety of topics to help us answer some real world questions: Euler circuits (What is the best route for the mailman to take?) Voting methods (Will we get a different winner if we hold a different type of election?) Map coloring (How many colors are needed so that no countries that are touching are the same color?) Matrices and tournaments (How can we determine a winner if all individuals have not played each other?) Fair division (How many seats should Minnesota have in Congress?) Course materials: The Geometer's Sketchpad software; online readings from a variety of sources SCIENCE Physical Science: Matter and Energy In this one-semester 9th grade course, students use journals, discussions, at-home and online labs, and structured web quests to explore introductory physical science concepts which will prepare them for high school chemistry and/or physics. Course materials: Online edition of Physical Science: Concepts in Action (Prentice Hall, 2006 Physical Science. This one-semester course focuses on how the Earth has changed over time and how it continues to change. Topics include: interactions of Earth systems; human impact on Earth systems; geology and plate tectonics; climate and climate change; and a descriptive history of the universe and solar system. Course activities include weekly journal and discussion assignments; webquests; online and at-home labs—all with an emphasis on critical thinking and reasoning from evidence. Students are asked to apply the concepts they are learning to their home community—through assignments such as a geology tour of your area and a state-of-your-watershed report. Course materials: Online edition of Earth Science (Prentice Hall, 2006); other selected web sites. Students are asked to identify native geological features and building stone in their communities, so some flexible transportation should be considered. Other labs are conducted online and supplies are not required Earth and Space Science. Biology deals with living systems. In each course, students consider basic concepts of biology, and how different biologists use their studies of living systems to try and answer questions. Students also look at how scientists describe the biological world; practice some of the thinking, observing, and communication skills that scientists use; and apply biological ideas to the world around them. Each course gives students the opportunity to participate in online discussions, conduct some biological investigations (labs and fieldwork) away from the computer, and complete unique assignments to help them develop the building blocks for further biology studies. Throughout both courses, assignments are designed to give students some freedom and creativity in the assignments that they complete, while engaging with important content. For example, in Biology A, students to write a newsletter on an ecosystem for possible publication; in Biology B, students to write a letter to Charles Darwin. Units covered in Biology A include: Scientific Process and Basic Chemistry, Ecology, Cells, Genetics, and Biotechnology and Bioethics. Topics covered in Biology B include the following: Darwin's Theory of Evolution, Evolution of Populations, The History of Life, Classification, Bacteria and Viruses, Protists, Fungi, Plants, Sponges and Cnidarians, Worms and Mollusks, Arthropods and Echinoderms, Nonvertebrate Chordates, Fishes and Amphibians, Reptiles and Birds, Mammals, and Human Systems. Course materials: Online edition of Prentice Hall Biology (the Miller/Levine "dragonfly book", 2006); other selected web sites. Each semester, students will need to provide some common household supplies including colored paper, yarn, markers, and several grocery supplies that are easily found—the list is available on the MNOHS web site and will be updated one week before the start of each semester. Click here for details. Before a student can enroll in a MNOHS science course, MNOHS must receive a permission form signed by a parent or guardian (if the student is under 18). Standards met: These courses meet all standards and benchmarks in the following strands of the 2009nMinnesota Science Standards for Grades 9-12: The Nature of Science and Engineering; Life Science. This one-semester course offers an overview of essential biology content including: cells, diversity of organisms, interdependence of life, heredity, biological populations change over time, flow of matter and energy, and the human organism. This course will blend online demonstrations, scientific research, home laboratory activities, and course discussions to help reinforce concepts. Course materials: Online edition of Prentice Hall Biology (the Miller/Levine "dragonfly book", 2006); other selected web sites. Students will need to provide some common household supplies including colored paper, yarn, markers, and several grocery supplies that are easily found one-semester course meets all standards and benchmarks in the following strands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering; Life Science. This quarter-length course meets all benchmarks of the Evolution strand of the Minnesota Academic Standards in Life Science while focusing on companion animals in a social context. Topics include: the genetics, breeding, and evolution of companion animals; the small animal industry; small animal safety; responsible pet ownership; animal rights: and animal welfare. Assignments vary from individual research, to creative writing about companion animals. For example, students write a letter from the perspective of an animal to inform his or her owner that they are sick. Students also have the opportunity to engage in discussions about current events that deal directly with companion animals, genetics, and evolution. Course materials: Online readings from a variety of sources; other selected web sites. Students will need to provide some common household supplies including colored paper, markers, and several grocery supplies that are easily found. Students will also be asked to visit several local businesses as a part of this course, so some flexible transportation should be considered Anatomy and Physiology to help students meet the biology graduation requirement. It meets some of the standards and benchmarks in the following strands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering; Life Science. Chemistry helps us to make sense of the world we live in—from why soap cleans greasy plates to whether or not biofuels are a beneficial energy path. First semester topics include lab techniques and safety; scientific methods; measurement; chemical and physical change; kinetic theory and states of matter; atomic structure; periodic table and trends; electron configuration; chemical bonding; and an intro to nanotechnologies. Second semester topics include laboratory safety; problem solving and dimensional analysis; chemical quantities; the gas laws; chemical reactions; balancing equations; solution chemistry; reaction rates and equilibrium; conservation of mass and energy; acids, bases, salts; carbon-based chemistry; and nuclear chemistry. Students use online graphing techniques, at-home labs and virtual labs to investigate chemistry concepts. Authentic scenarios are presented each week for analysis and discussion; these allow students to construct their own meaning of the concepts presented. Course materials: Online edition of Chemistry (Prentice Hall, 2005); selected web sites. Students are asked to purchase an inexpensive set of science equipment and common household materials Chemistry A and B will have surpassed the following strands and substrands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering (all); Physical Science (Substrands 1, 4, and part of 3); Chemistry (all). Credit: 1.0 (Semester A = 0.5 credit, Semester B = 0.5 credit.) Honors Opportunity: Yes Prerequisites: None for Chemistry A. Algebra 1 and Chemistry A, or the equivalent, for Chemistry B. Physics A addresses the concepts of one and two dimensional motion, Newton's Laws of motion, vectors, forces, and momentum. Physics B addresses the concepts of work, gravity, planetary motion, waves, light, sound, and Einstein's Theory of Relativity. Course materials: Conceptual Physics (Prentice Hall, 2009 Physics A and B will have surpassed the following strands and substrands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering (all); Physical Science (Substrands 2 and 3); Physics (all). Credit: 1.0 (Semester A = 0.5 credit, Semester B = 0.5 credit.) Honors Opportunity: Yes Prerequisites: Physics A and B may be taken independently of one another. Algebra 1 is required for both courses. This quarter-length course meets all benchmarks of the Human Interactions with Living Systems substrand of the Minnesota Academic Standards in Life Science, as well as some benchmarks of the Structure and Function substrand, while focusing on human anatomy and physiology. Topics include: the nervous system, nutrition and digestion, circulation and the respiratory system, how the body responds to disease and infection, internal regulation of the body and reproduction and development. Assignments will vary from simulations to connect body systems to labs requiring at home participation Biology of Companion Animals, to help students meet the biology graduation requirement. It meets some of the standards and benchmarks in the following strands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering; Life Science. This quarter-length course meets all benchmarks of the Interdependence Among Living Systems substrand of the Minnesota Academic Standards in Life Science while focusing on Minnesota forests. Topics include: tree anatomy and physiology, tree identification, forest ecology, silviculture, forest protection and management. During this course, students will completing a variety of assignments ranging from completing research on forests in Minnesota to exploring trees and forest ecosystems in their local communities. Students also have the opportunity to engage in discussions about current events that deal directly with forestry and ecology Food Science, to help students meet the biology graduation requirement. It meets some of the standards and benchmarks in the following strands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering; Life Science. This quarter-length course meets all benchmarks of the Structure and Function substrand of the Minnesota Academic Standards in Life Science while focusing on food science. Topics include: microbiology, cell structure and function, food safety, food preservation, nutrition, food development and packaging. Students will complete both laboratory and computer based assignments. Students also have the opportunity to engage in discussions about current events that deal directly with food science topics Forestry, to help students meet the biology graduation requirement. It meets some of the standards and benchmarks in the following strands of the 2009 Minnesota Science Standards for Grades 9-12: The Nature of Science and Engineering; Life Science. LANGUAGE ARTS Myths and Legends A & B For centuries, people have sought to explain the world around them, and this quest has led to a rich variety of legends and myths. In Myths and Legends, students will explore myths, legends and folklore from diverse world cultures. Reading and comprehension strategies are emphasized each week, and students will review writing skills and formal essay formats as well. The vocabulary units in both semesters center around Greek and Latin prefixes, bases, and suffixes, which will give students skills to decode and define new words they encounter. Semester A will focus on myths from various cultures that work to explain creation; nature and the elements; and life cycles. Students will write and present a research essay on an ancient culture to review research skills and the MLA format. Semester B will focus on the heroic cycle, and students will read a version of The Odyssey and John Steinbeck's novella The Pearl. Students will also read and discuss local folk heroes from Minnesota. As a final project, students will choose a modern novel or film to analyze based on the heroic cycle. Course materials: All required works are available online or provided within the course. Standards met: All strands of the Minnesota Language Arts standards are addressed. The American Literature Survey courses explore a variety of writings that reflect the rich history, diverse cultures, and of the United States. The first semester focuses on short stories and poetry from a variety of authors and time periods and the novel To Kill a Mockingbird by Harper Lee. Students will review plot structure and literary techniques. The second semester focuses on American folklore, famous essays and speeches. We will also be reading the play Inherit the Wind by Jerome Lawrence and Robert Lee. Students will continue to refine writing skills and focus on critical thinking skills. Course materials: Most required works are available online or provided within the course. The required novel for American Literature A (Harper Lee's To Kill a Mockingbird) and play for American Literature B (Inherit the Wind by Jerome Lawrence and Robert Lee) may be borrowed from a library, purchased, or provided by the school. Standards met: All strands of the Minnesota Language Arts standards are addressed. The English Survey courses focus on reading and writing skills through the use of high-interest literature and current event articles. Grammar and vocabulary refreshers are also featured in each week's assignments. The first semester focuses on the theme of technology and how its rapid changes are affecting our society. Students read short stories by Ray Bradbury, a novella by Ayn Rand (Anthem), and others. They review and practice several different essay forms. The second (B) semester's theme is the changing perceptions of society throughout each decade. Students read samples of literature and non-fiction articles from several historic periods, and continue to practice and refine writing skills. The novel for this semester is Stanley Gordon West's Until They Bring the Streetcars Back. Course materials: Most required works are available online or provided within the course. The two required novels, Ayn Rand's Anthem, and Stanley Gordon West's Until They Bring the Streetcars Back, may be borrowed from a library, purchased, or provided by the school. Standards met: All strands of the Minnesota Language Arts standards are addressed. In these courses, students explore short stories, articles, drama, poetry, and non-fiction. Through guided reading experiences, online discussion, writing assignments and responding to reflection questions, students examine the components and structure of each genre. In addition, students conduct web quests, perform research, and develop creative writing projects. Students will improve their expository writing, reading comprehension, and comprehension and synthesis skills. Students practice all stages of the writing process including pre-writing, rough draft and final draft. Our topics will be serious, satirical, imaginative, dramatic and thoughtful: something for everyone! This year-long sequence surveys the central themes of American literature. Semester A begins with Native American stories and the colonial period, and concludes with a close look at impact of slavery on American intellectual thought. Semester B covers the Civil War years to the present. Students read a wide variety of stories, plays, essays, poems, journals and historical accounts from a variety of authors with diverse perspectives. To explore these writings, students engage in all-class discussions, conduct guided as well as research-oriented web quests, and answer questions about the readings. During first semester, students read one novel chosen from a recommended reading list, and develop a critical essay. Several times during each semester, students pull back and write a reflective essay on the themes covered. Creative writing opportunities ask students to write free verse poetry and to imagine a fictional character's journal. This semester-long course explores literary voices through time and many cultures in an attempt to discover the ideas and ideals that make people similar, or that open doors to new ways of seeing and being. We begin by reading creation stories and mythologies from diverse cultures. Other works include Modernist poetry and fiction ("The Metamorphosis" by Kafka); ancient Greek tragedy (Oedipus the King by Sophocles); wisdom literature of ancient China and Japan; and modern African fiction (Things Fall Apart by Chinua Achebe). Short stories, essays, travelogues, biographies and memoirs from around the world round out the reading experiences. Students make connections to their own lives and times in reflective reader response journals, participate in threaded class discussions, use the writing process to produce fiction, poetry, creative non-fiction, and analytical writing, make extensive use of internet resources to conduct author studies, and actively work on vocabulary development. Students step back in time to explore our literary roots with a semester-long survey of British Literature. The course covers The Anglo-Saxon Period through the Elizabethan, Romantic, and Victorian periods. As they study such classic works as Beowulf, Macbeth, and "The Rime of the Ancient Mariner," students hone their skills as close readers, listeners, viewers, and critical thinkers. They practice both analytical and creative writing. Other activities include virtual tours of England, creating a "Shakespearian" style sonnet, engaging with Jonathan Swift in satirical social commentary, exploring the tenets of nature, spontaneity, and self-expression that inspired Romantic poets like Wordsworth and Keats, and appreciating the emerging voices of Romantic and Victorian women novelists. Vocabulary study, working with literary terms, class discussions, guided practice with study and reading strategies, writing mini-lessons, and reader response journals are an integral part of each week's course work. Research Learning brings the "information age" to life by helping students to design an independent learning project proposal and write a 5-8 page research-based persuasive paper formatted in MLA style. The course starts at the beginning – with inquiry. What does the student want to learn more about? Inquiry questions drive the research learning process. Students then learn to use library databases, the internet, and local experts to find and evaluate a variety of information resources, conduct original research, compile notes and data, cite their sources, prepare an annotated Bibliography, take a point of view, create a thesis, write to and for a specific audience, and document their learning growth—all skills that promote high school success and college readiness. The media has become one of the most powerful institutions in the world as access to newspapers, blogs, data, videos, Facebook and Twitter has exploded across the Internet. This semester-long introduction to journalism focuses on the role of journalism in a democracy as well as writing a variety of articles. This class is for students who want to learn to be savvy consumers of the news and try their hand at writing the news. In the first 8 weeks, students will evaluate, explore and identify various news sources and aspects of the news. The second 8 weeks will focus on writing articles, from editorials to feature articles. Throughout the course, students will be reading, interacting and sharing news experiences, from the web, to the TV and around the world. In this one-semester composition course, students develop written communication skills. To achieve that goal, students practice description, word choice, sentence variety, imagery and many other techniques as they are used in sketches, essays, stories, speeches and poems. Writing assignments vary from paragraph descriptions to a full research paper on a student-selected topic. Many types of writing are practiced, including film reviews, poetry, character sketches and incident essays. By building their writing skills, students are better able to express their ideas for school assignments, in the workplace, and in personal messages. Who knows, some students may even write the first chapters of a novel! Course materials: No required text Standards met: All benchmarks in the Writing Strand of the Minnesota Language Arts standards are addressed. SOCIAL STUDIES Civics This course will examine all elements of our nation's government including how our society formed, the reasons we chose to have a democratic government, and the problems our nation faces. We will look at these elements by using our textbook, researching the Internet, reading case studies, and through group discussions. As a member of this course you will become more informed about our nation and learn new methods of understanding and researching. Course materials: Civics (Prentice HallIn this course we will examine the land, culture, environment, and the impact of humans around the world. We will explore many regions including the United States, Canada, Europe, Russia, China, Southeast Asia, the Middle East, and Africa. We will learn how-to read maps, what different cultures eat, and how life differs from region-to-region. Course materials: World Geography (McDougal Littell, 2003). We will also use many research articles and Internet sites; links and attachments will be provided in class. Standards met: This course meets all standards and benchmarks in the Geography strand of the Minnesota Academic Standards in History and Social Studies for Grades 9-12. This year-long course surveys the geographical, intellectual, political, economic and cultural development of the American people and places. Semester A focuses on colonization to the beginning of the 20th Century. Semester B covers the history of the United States during the 20th century. Student will read and listen to a wide variety of historical events and personal stories. The course will allow each student to pursue individual historical interests alongside the standard curriculum. Through weekly assignments, course discussions, and research projects, students will learn the critical aspects of American history and the details that textbooks cannot cover. Course materials: The Americans (McDougal Littell, 2003) Standards met: All strands of the Minnesota United States History standards are addressed. This year-long sequence surveys the evolution of world societies. Semester A focuses on ancient times through 1500. Semester B examines 1500 through the present times. In addition to the text, students read and listen to a wide variety of historical events and personal stories. These courses will help students to become familiar with the world's societies and cultures, as well as with developments in politics, religious thought, philosophy, economics and literature. The courses include historical, multicultural, geographical, economic, technological, social, political and current event strands which are taught both independently and integrated with one another throughout. Both courses allow students to pursue individual historical interests alongside the standard curriculum. Through weekly assignments, course discussions, research projects, and exams, students will learn the critical aspects of World History and the details that textbooks cannot cover. Standards met: These courses meet all standards and benchmarks in the World History and Historical Skills strands of the Minnesota Academic Standards in History and Social Studies for Grades 9-12. Credit: 1.0 (Semester A = 0.5 credit, Semester B = 0.5 credit.) This course examines the basic principles and structure used in economic decision making; topics include the analysis of economic institutions; social issues; and the basic objectives of efficiency, equity, stability, and growth of economic activity. In class we will take a hands-on approach and deal with real life decisions, personal finance, and economic choices and outcomes in the long and short-run. Course materials: Economics (Prentice Hall, 2005). We will also use many research articles and Internet sites; links and attachments will be provided in class. Standards met: This course meets all standards and benchmarks in the Economics strand of the Minnesota Academic Standards in History and Social Studies for Grades 9-12. This course will take an in-depth look at the U.S. Government by examining each of the three branches (Legislative, Executive, and Judicial) including: their roles and responsibilities, outside influences, and the current leaders in each branch. We will also research government programs, the foundation of democracy, election policies, past leaders—and we will write legislation. Course materials: Magruder's American Government (Prentice Hall, 2003This semester-long course will introduce students to the scientific study of human behavior. Course topics will include research methods, historic and modern approaches to the study of psychology, sensation, consciousness, learning, memory, intelligence, heredity and environment, development of the individual, motivation, emotion, perception, personality, abnormal behavior and therapy. Course Materials: Psychology: Principles in Practice (Holt) Standards met: This course addresses all strands of the American Psychology Association National Standards. Electives Visual Arts Explore visual arts! Using a variety of media (such as pencil, paint, collage and sculpture), students create projects that range from the political to the personal and whimsical—for example, a collage that makes a powerful visual statement about an important issue or a Picasso-like sculpture splashed with color and pattern. A key focus is the language of art, known as the Elements and Principles of Design. Some key art movements are studied as well as the larger question: "What is Art?" The course utilizes a wealth of internet art resources. For example, a favorite project is the Independent Artist Study, where students "circle the virtual globe" as they examine the life and work of a favorite artist and create a piece of art in the same style. Feedback and reflection are other important parts of the learning process, facilitated by online class discussion boards and the students' interactive personal Art Journal. This class will open students' eyes to new ideas about art and creativity. Course Materials: Students are asked to purchase an inexpensive set of art materials—the list is available on the MNOHS web site and will be updated one week before the start of each semester. Standards met: Students come to understand the Elements and Principles of Design and can apply them in art creation and analysis. Study the world through the arts. Explore all types of visual art. Learn to think about art as it relates to you and the world around. See the connection between art and history. What does it all really mean? This class will open new doors to you and encourage you to see the arts in new ways. Students will have the opportunity to create several art projects of their own—such as an art gallery brochure and a collage (cut and paste, or digital). Students are also encouraged to share art they discover or create themselves. Course Materials: Internet Resources Standards: Students come to understand the Elements and Principles of Design and can apply them in art creation and analysis. This course is designed for students with an interest in gaining introductory experience in a variety of media art forms. The goal is to produce media arts projects that will teach students the steps, in all aspects of photo editing, video production, and animation. Students will learn key concepts related to successful photographic composition and manipulation, creation of multiple genres of video production, as well as gain experience creating stop-motion animation. These projects are designed to give students the opportunity to develop skills that may proceed to independent work beyond this course. Course Materials: Adobe Photoshop Elements and Premiere software will be provided by MNOHS. Students need access to a digital camera. Standards met: Most strands of the Minnesota Media Arts standards are addressed. In this semester length course, students will explore fundamental musical concepts while engaging with questions such as "What is Music?" and "Can Music Tell a Story?". The course teaches the elements of music including staves, clefs, notes, meter and rhythm, keys, scales, basic harmonization, and form. Students work with music theory software and music notation software to learn basic fundamentals; this allows them to create their own compositions. Through guided listening assignments, students will explore particular aspects of music—for example, rhythm and meter, musical style, or featured instruments. One of the more important features of this class is developing and sharing each student's tastes in music by introducing favorite bands, singers, and composers to one another. Honors Opportunity: Yes Prerequisite: The course is designed for students at various levels of musical experience who want to do different things in music. Students should have an interest in working with traditional music notation. This first-year Spanish sequence will introduce students to the basics of Spanish and give them confidence to begin to express themselves in a new language. While "traveling" around the Spanish-speaking world, students communicate about their family and friends, likes and dislikes, school, food and healthy lifestyle choices. Lessons 1 (Holt) Standards met: These courses meet national standards, developed with input from the World Languages Quality Teaching Network. This second-year Spanish sequence will build on the basics covered in Spanish 1 in order to increase students' confidence to express themselves in a second language. While "traveling" around the Spanish-speaking world, students will be communicating about their family and friends, their neighborhoods and cities, discussing daily life, vacations, childhood experiences 2 (Holt) Standards met: These courses meet national standards, developed with input from the World Languages Quality Teaching Network. Credit: 1.0 (Semester A = 0.5 credit, Semester B = 0.5 credit.) Honors Opportunity: No Prerequisites: Spanish 1 A and B, or the equivalent, for Spanish 2A. Spanish 2A, or the equivalent, for Spanish 2B. This third-year Spanish course will build on the material covered in Spanish 2 in order to increase students' confidence to express themselves more completely in a second language. While "traveling" around the Spanish-speaking world, students will be communicating about shopping, vacations, pastimes and sports, As in previous levels, there Levels 2 and 3 (Holt)br> Standards met: These courses meet national standards, developed with input from the World Languages Quality Teaching Network. In the first semester of this fourth-year Spanish course, students will build on the material covered in previous levels to gain confidence in all four skills areas—reading, writing, listening and speaking. While "traveling" around the Spanish-speaking world, students will be communicating about family, the fine arts, and the media. Lessons will focus on specific strategies to help students improve their skills. During the second semester, students will be reading a variety of short stories, poetry and other writings from Hispanic authors from around the world. Students will continue to review grammar in context of the writings and have ample opportunity to listen to and speak the language by listening to the audio samples and recording spoken exercises using Voice Thread. Students will communicate frequently with the instructor through writings and oral activities and discussions. The demands of our changing world make career planning an essential part of any high school curriculum. Career trends are dynamic, change as fast as our technology and evolve with global economic realities. This course invites students through a purposeful exploration to help identify strengths of their personalities, interests, intelligence, learning styles, and values. Then they investigate various career and education options that are well suited to their strengths. Students learn and practice essential workforce skills (SCANS) including how to write dynamite resumes and cover letters and how to ace a job interview. In addition, students are introduced to relevant tools and processes that they will use to examine post-secondary education options. As they have identified career possibilities in the first part of this course, they also learn about the education and training requirements of each career field they may enter. Students will learn about various funding options available to pay for school, they will explore types of school/training choices and gain important understanding of the criteria they must meet to enter this post-secondary phase of their career. Students who complete this course will have the skills and knowledge needed to continue with effective career processes today and in the future. Course Materials: Students link to some of the most important and up to date career and education resources available on the internet. In addition to ISEEK and other well-known career sites, we provide access to an array of sites that comprise a cutting edge career seeking process.) In a new 'global economy' it is becoming clear that competition for jobs will be fierce. Career trends are dynamic, change as fast as our technology and evolve with global economic realities. Workers need to acquire new job-content skills for a modern economy and to develop those soft-skills or transferable skills that employers have always valued. Soft skills are universally demanded by employers and include knowing how to communicate effectively, make decisions, handle conflict, show initiative on the job and become dependable and responsible employees and business owners. This course will also introduce concepts related to consumer economics, and other life-long learning applications. In the course students will identify and further develop essential work skills, and will apply them to the work setting. The job site will be a laboratory. Students will be asked to recognize and practice skill sets on the job and to report/discuss these concepts with other students in the course. The real life experiences will help to bring the course concepts to life for the student workers. Students are required to be employed before enrolling in the course. Course Materials: Students link to some of the most important and up to date career and education resources available on the internet. In addition to iSEEK and other well-known career sites, we provide access to an array of sites that comprise a cutting edge skill development process. Students will also be required to seek cooperation from supervisors in the student's work place. Teens in the 21st century face many choices when it comes to their health, and health information seems to change daily. There are always new theories, discoveries, and treatments. This course enables students to gain the skills necessary to make healthy and informed decisions; critical thinking skills are emphasized. Students consider what they will need to know to live a healthy lifestyle and how they will keep these concepts close throughout their life. Students will explore a broad range of topics that are determined by the Minnesota Academic Health Areas. A limited number of behaviors contribute markedly to today's major killers—heart disease, cancer, and injuries. These behaviors, often established during youth, place young people at significantly increased risk for serious health problems, both now and in the future. They include: Tobacco use Unhealthy dietary behaviors Inadequate physical activity Alcohol and other drug use Sexual behaviors that can result in HIV infection, other sexually transmitted infections, and unintended pregnancies Behaviors that may result in intentional injuries (violence and suicide) and unintentional injuries (motor vehicle crashes) By using interactive Internet sites and the most current sources and information available, students will focus on health promotion and risk reduction. Course materials: Online readings from a variety of sources. Standards met: This course meets local standards, developed with input from the Minnesota Health and Physical Education Quality Teaching Network. The best way to live a healthy life is to prevent health problems before they occur. This course creates opportunities for students to apply new skills and knowledge to experiencing the benefits of a physically active lifestyle. Students will be required to complete a mixture of physical activities, online assignments, tests, and a research paper—and to record in their workout log cardiovascular, flexibility, strength and endurance activities. They will learn about proper weight, good diet, and managing stress. By the end of the course, they will have gained the knowledge needed to begin developing healthy habits that will last a lifetime. Course materials: Online readings from a variety of sources. Standards: This course meets local standards, developed with input from the Minnesota Health and Physical Education Quality Teaching Network. Credit: 0.5 Honors Opportunity: No Prerequisite: Before a student can enroll in the PE course, MNOHS must receive a permission form signed by a parent or guardian (if the student is under 18). ELL Essential Skills focuses on English reading, writing, speaking and listening while developing skills you need to succeed in other courses. The learning activities are designed for you as an individual English Language Learner (ELL). This course is taught by an ESL teacher. It is one or more semesters long – depending on the needs of the individual student. Course Materials: No textbook used; Materials, including various online websites and resources, provided by the teacher on a weekly basis For general information
In this article, we take a rapid journey through the history of algebra, noting the important developments and reflecting on the importance of this history in the teaching of algebra in secondary school or university. Frequently, algebra is considered to have three stages in its historical development: the rhetorical stage, the syncopated stage, and the symbolic stage. But besides [...]
Mathematics Departmental Page The Broughton Mathematics department strives to provide high-quality instruction to enable high school students to solve problems creatively and resourcefully, to compute fluently, and to prepare them to fulfill personal ambitions and career goals in an ever-changing world. It is based on a philosophy of teaching and learning mathematics that is consistent with the current research, exemplary practices, and national standards. The North Carolina Standard Course of Study describes the mathematical concepts, skills, operations, and relationships that are the significant mathematics that all North Carolina students should learn and understand. All students are now required to complete four years of high school mathematics, including Algebra I and Geometry or Algebra II, and pass the Algebra I EOC. Broughton offers a wide variety of math courses, including Advanced Placement and International Baccalaureate courses. All courses emphasize the use of technology and the development of mathematical literacy
Mathematics is one of the oldest and most universal means of creating, communicating, connecting and applying structural and quantitative ideas. The discipline of Mathematics allows the formulation and solution of real-world problems as well as the creation of new mathematical ideas, both as an intellectual end in itself, but also as a means to increase the success and generality of mathematical applications. This success can be measured by the quantum leap that occurs in the progress made in other traditional disciplines, once mathematics is introduced to describe and analyses the problems studied. It is therefore essential that as many persons as possible be taught not only to be able to use mathematics, but also to understand it. Students doing this syllabus will have been already exposed to Mathematics in some form mainly through courses that emphasise skills in using mathematics as a tool, rather than giving insight into the underlying concepts. To enable students to gain access to mathematics training at the tertiary level, to equip them with the ability to expand their mathematical knowledge and to make proper use of it, it is, therefore, necessary that a mathematics course at this level should not only provide them with more advanced mathematical ideas, skills and techniques, but encourage them to understand the concepts involved, why and how they "work" and how they are interconnected. It is also to be hoped that, in this way, students will lose the fear associated with having to learn a multiplicity of seemingly unconnected facts, procedures and formulae. In addition, the course should show that that mathematical concepts lend themselves to generalisations, and that there is enormous scope for applications to the solving of real problems. Mathematics covers extremely wide areas. However, students can gain more from a study of carefully selected, representative areas of Mathematics, for a "mathematical" understanding of these areas, rather than to provide them with only a superficial overview of a much wider field. While proper exposure to a mathematical topic does not immediately make students into experts in it, that proper exposure will certainly give the students the kind of attitude which will allow them to become experts in other mathematical areas to which they have not been previously exposed. The course is, therefore, intended to provide quality in selected areas, rather than a large area of topics. To optimise the competing claims of spread of syllabus and the depth of treatment intended, all items in the proposed syllabus are required to achieve the aims of the course. None of the Modules of the two Units making up the whole course will, therefore, be optimal. However, Unit 1, representing the basics of the syllabus, is assessed separately, can stand on its own, can be combined with other Units, such as Statistical Analysis, and can be separately certified. Unit 2, which will also be separately assessed and certified, will also be accessible on its own by students who have already adequately covered the material contained in Unit 1. While there will be a great deal of attention to the application of mathematics to solving problems arising in other areas, including mechanics and statistics, it is not the intention to develop a general account of these subjects; there is, therefore, no section on statistics or mechanics; these are expected to be specifically addressed in other courses. Through a development of understanding of these areas, it is expected that the course will enable students to: Develop mathematical thinking, understanding and creativity; Develop skills in using mathematics as a tool for other disciplines; Develop the ability to communicate through the use of mathematics; Develop the ability to use mathematics to model and solve real world problems;
Applied Mathematics is the application of Mathematics to the modeling and solving of practical, real world problems. It is at the core of many disciplines, ranging from Business, Finance, and Economics, through Geography and Geology to all branches of Engineering and the Sciences. The First Year course in Arts assumes no previous knowledge of Applied Mathematics and there is extensive tutorial support available throughout the year
More About This Textbook Overview Perfect for students approaching the subject for the first time, this book offers a superb overview of number theory. Now in its second edition, it has been thoroughly updated to feature up-to-the-minute treatments of key research, such as the most recent work on Fermat's coast theorem. Topics include divisibility and multiplicative functions, congruences and quadratic resolves, the basics of algebraic numbers and sums of squares, continued fractions, diophantine approximations and transcendence, quadratic forms, partitions, the prime numbers, diophantine equations, and elliptic curves. More advanced subjects such as the Gelfond-Schneider, prime number, and Mordell-Weil theorems are included as well. Each chapter contains numerous problems
098 Developmental Arithmetic (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is less than 15 or COMPASS Math score of 30 or less. Fundamental topics in arithmetic, geometry, and pre-algebra. 099 Developmental Algebra (3-0-3). Credit not applicable toward degrees. Required of students whose ACT Mathematics Main score is at least 15 but less than 19 or COMPASS Math score of 31 to 58. Fundamental topics in algebra for students with insufficient knowledge of high school level mathematics. PR: ACT Mathematics Main score of 15 or grade of "S" in MATH 098. 109 Algebra (3-0-3). Real numbers, exponents, roots and radicals; polynomials, first and second degree equations and inequalities; functions and graphs. PR: ACT Mathematics main score of 19 or grade of "S" in MATH 099. 211 Informal Geometry (3-0-3). Theorems are motivated by using experiences with physical objects or pictures and most of them are stated without proof. Point approach is used with space as the set of all points; review elementary geometry, measurement, observation, intuition and inductive reasoning, distance, coordinate systems, convexitivity, separation, angles, and polygons. No field credit for math majors/minors. PR: MATH 101 or higher. 220 Calculus I (4-0-4). A study of elements of plane analytical geometry, including polar coordinates, the derivative of a function with applications, integrals and applications, differentiation of transcendental functions, and methods of integration. PR: MATH 109 and MATH 110, or GNET 116, or ACT Mathematics main score of 26 or COMPASS Trigonometry score of 46 or above. 250 Discrete Mathematics (3-0-3). Treats a variety of themes in discrete mathematics: logic and proof, to develop students' ability to think abstractly; induction and recursion, the use of smaller cases to solve larger cases of problems; combinatorics, mathematics of counting and arranging objects; algorithms and their analysis, the sequence of instructions; discrete structures, e.g., graphs, trees, sets; and mathematical models, applying one theory to many different problems. PR: MATH 109 and MATH 110 or GNET 116. 290 Topics in Mathematics (1-4 hours credit). Formal course in diverse areas of mathematics. Course may be repeated for different topics. Specific topics will be announced and indicated by subtitle on the student transcript. PR: Consent of instructor. 400 Introduction to Topology (3-0-3). A study of set theory; topological spaces, cartesian products, connectedness; separation axioms; convergences; compactness. Special attention will be given to the interpretation of the above ideas in terms of the real line and other metric spaces. PR: MATH 240. 490 Topics in Mathematics (1-4 hours credit per semester). Advanced formal courses in diverse areas of mathematics. Courses may be repeated for different topics. Specific topics will be announced and indicated by subtitle on transcript. PR: Consent of instructor.
10 Units 1000 Level Course Available in 2013 Mathematics Advanced prepares students for undergraduate courses requiring a background in mathematics. This first semester course is a prerequisite for EPMATH125 Advanced Mathematics in the second semester. The depth and treatment of this course is similar to 2 Unit Higher School Certificate mathematics. Topics include algebra, surds, solution of equations, trigonometry, functions, co-ordinate geometry and differential calculus. Objectives In the course students will: 1.obtain a background in topics mentioned in the brief course description. 2.develop students' mathematical skills equivalent to 2 unit HSC level. 3.demonstrate a broad understanding of the course.
The study of mathematics is not only exciting, but important. Mathematicians contribute to society by helping to solve problems in such diverse fields as medicine, business, industry, government, computer science, physics, psychology, engineering, and social science. Mathematics is often done in conjunction with another field: biology, physics, economics, or a host of others. Mathematical modeling is used to solve real problems in a variety of fields. Statistics is a growing field, particularly in those fields dealing with human behavior. Many topics in "pure math" have important applications in computer science. There is a national shortage of teachers in all the mathematical science (pure math, applied math, statistics, and computer science) at all levels, so any of these fields goes well with teaching and/or research.
How to Best Prepare for Mathematics Because of the highly quantitative nature of Carnegie Mellon's curriculum, your four years of secondary school mathematics should include at least algebra, geometry, trigonometry, analytic geometry, and elementary functions. This level of preparation is strongly recommended for all five majors on the Qatar campus. The following list of abilities reflects the basic skills important for success in Carnegie Mellon's mathematics sequence. In addition, we look for students who can read carefully and interpret what has been read in the context of solving a problem. You should be able to demonstrate these skills without a calculator: Be able to graph quadratic functions, ellipses, circles, and hyperbolas. Be able to manipulate algebraic expressions including using rules of exponents. Be able to complete the square of a quadratic expression and recognize when completion of the square is appropriate. Be able to determine the domain of a function. Understand the function concept including the composition of functions and be able to recognize the functions from which a given function is composed. Be able to determine the intersection of two lines or a line and a quadratic function. Be able to determine the equation of a line and understand when lines are parallel or perpendicular in terms of their slopes. Be able to solve linear inequalities and quadratic equations including equations that arise in novel circumstances. Be able to use properties of logarithmic functions to simplify expressions and solve equations. Be familiar with the graphs of logarithmic and exponential functions. Know the definitions of the trigonometric functions, be familiar with their graphs and periodicity, be able to evaluate trigonometric functions using standard triangles, and know basic trigonometric identities including the Law of Cosines. Know the Pythagorean Theorem and be able to apply it. Be able to recognize and use proportional relationships including those derived from similar triangles. Be able to use knowledge of basic plane and solid geometric figures to express relationships among them, e.g. when one is inscribed in another.
Points, lines and distances in twocing algebraRecognizing mathematics, continuedComputer Science Students are going to understand the structure of computer we use in our everyday life and study the relation between logic circuit, C Language and software. Author(s): 001 License information Related content Rights not set No related items provided in this feed Introduction to Algorithm and Data Structures Author(s): 001
Welcome to the Algebra II/Trigonometry portion of the site! On this and the following pages, we'll try to clear up some common problems people have with intermediate algebra (Algebra II) and trigonometry (which ought to have a class of its own just to learn how to pronounce it). Everything from solving basic equations to the trigonometric ratios are covered. After each section, there is an optional (though highly recommended) quiz that you can take to see if you've fully mastered the concepts. And don't forget to visit the message board and the formula database.
Fractions, Decimals & Percentage certificate course Learning Fractions, Decimals and Percentage is a distance learning course that will enable you to learn these topics quickly without disrupting your present lifestyle! Learn from the comfort of your own home and study when it's convenient for you - there are no time limits. Take your exams online and finish with an academic Certificate of Completion from CIE Bookstore. If you ever need help you can call or e-mail our staff of instructors for immediate attention. Special Introductory Offer: Save $60 off normal tuition - now only $95! Learning Activities: This math course consists of small, easy-to-complete lesson assignments. Each lesson requires you to read topics and answer questions based on the assigned readings. You should solve all the problems in the exercise sections before continuing to the next topic. Reciprocals, percentage and powers of numbers - students learn how to change fractions to decimals & the meaning and use of powers of a number. This self-paced program includes easy-to-follow math lessons that you complete at your own pace and instructor tutorial help. Everything you need to graduate is sent to your home and you can take your exams online. Our highly trained instructors are only a phone call away (or e-mail) from providing you with reassuring assisance whenever you need it. Best of all, you'll earn an impressive Certificate of Completion from CIE Bookstore suitable for framing when you're finished! Student Evaluation and Grading Method: Students are required to complete all the lessons. Each of the assignments concludes with an examination comprising of a multiple-choice test. The assignment examinations are open book. The final grade for this course will be determined as follows: two examinations equals 100% of the final grade. You could transfer any completed lessons from this course over to CIE's nationally accredited Electronics Associate Degree program and get full tuition and academic credit. Student Privileges: 1. Instructor Assistance: Use our toll-free Instructor Hot-line to access our faculty and staff if you ever need assistance with your course work. CIE's dedicated staff of instructors do more than just grade your exams; they help guide you, step-by-step, through your studies and hands-on training. They'll encourage you when you're doing well and give you support when you need it. Most importantly they'll see that every question you have receives careful consideration by one or more members of the staff. You can be sure the response, whether it's a simple explanation or an in-depth theoretical discussion, will be prompt, courteous and thorough. We'll make sure that you'll never study alone. 2. Priority Grading - No waiting Your submitted exams will be graded and sent back to you within 24 hours. You can be sure that you will get back almost instantaneous feedback from your exams. Take your exams online on our e-grade web site or mail them in to us. 3. Professional Certificate of Completion from CIE Bookstore After finishing this course you'll receive a certificate of completion suitable for framing! How do I enroll? 1. You can order online with a credit card or PayPal (click the 'Add to Cart' button). 2. Call us at (800) 321-2155 and ask for course 01-FRAC01. 3. You can mail a check or money order for $109.95 (includes $14.95 for shipping/handling) to:
Eighth Edition of this highly dependable book retains its best features-accuracy, precision, depth, and abundant exercise sets-while substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Conics; Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more. For individuals with an interest in learning algebra as it applies to their everyday lives.
The authors believe that a working knowledge of vectors in Rn and some experience with viewing functions as vectors is the right focus for this course. Material on Axiomatic vector spaces appears toward the end so as to avoid the wall of abstraction so many students encounter. All major concepts are introduced early and revisited in more depth later on. This spiral approach to concept development ensures that all key topics can be covered in the course. The text provides students with a strong geometric foundation upon which to build. In keeping with this goal, the text covers vectors first then proceeds to linear systems, which allows the authors to interpret parametric solutions of linear systems as geometric objects. Looking Ahead features provide students with insight into the future role of the material currently being studied. A wide range of applications throughout gives students a sense of the broad applicability of linear algebra. The applications include very modern topics such as global positioning and internet search procedures. Each exercise set is broken into four categories: Basic Exercises progressing in difficulty from drill to challenging. Discussion and Discovery exercises that are more open-ended. Working with Proofs exercises which ask students for precise proofs. Technology Exercises that teach students how to use such tools as MatLab, Mathematica, Maple and Derive. Theorems and proofs are presented with precision, but in a style appropriate for beginning students.
Quick Overview Details Practice and application characterize LIFEPAC's Mathematics series, focusing on the mastery of basic concepts and skills as well as advanced concepts of mathematics. The major content strands are as follows: Grade 10: A Geometry course, which includes Proofs, Congruency, Similar Polygons, Circles, Constructions, Area & Volume, and Coordinate Geometry
The steady increase in the number of undergraduate students studying finite mathematics each year is reflective of the rising standards for college students to select a mathematics course relevant to their major and above the intermediate algebra level. Finite Mathematics by Jeffrey X. Watt, Ph.D. was
Improve Your Math Author: , Date: 10 Jan 2008, Views: , Publisher: Learning Express (NY); 1 edition Language: English ISBN: 157685406X Paperback: 208 pages Data: April 22, 2002 Format: PDF Description: Consider Improve Your Math as a personal tutor: From basic arithmetic to fractions, from decimals to percentages, from algebra to geometry, from graph reading to statistics and probability, your child can get the extra practice necessary to master middle school math. This book includes page after page of problem-solving strategies that really work, in-depth explanations of difficult math concepts right in the lessons, and step-by-step guidance for tackling the different kinds of math problems found on standardized tests and classroom math tests. You'll also find hundreds of practice problems with complete answer explanations and practice word problems that apply the skills learned in each section to situations encountered every day. Plus, there's a pre-test and a post-test to help identify strengths and weaknesses—and to show progress
Latest News Mathematics PORTLAND PLACE SCHOOL MATHEMATICS DEPARTMENT Mathematics is not only an intellectual discipline in its own right, but it also has essential applications in science, engineering, telecommunications, information technology, financial trading and multinational business. The fundamental principles to the aims of the school mathematics course being achieved are to develop, maintain and stimulate students' curiosity, interest and enjoyment in mathematics. To develop students' familiarity with appropriate mathematical concepts, principles, methods and vocabulary and develop students' understanding of mathematics and see how it relates to them outside of the school context. The contents of this Handbook have been determined in consultation with all current members of the Departmental staff. The contents are subject to regular review and are amended as necessary. Each member of the Department has been provided with a copy. AIMS These aims relate directly to the aims of Portland Place School. Fundamental to the aims of the school being achieved is a realisation that the learning and development of a student is a partnership between parents, teachers and student. 1. To development, maintain and stimulate students' curiosity, interest and enjoyment in mathematics.
The Subway Map Symbols The DAU Math Refresher module is navigated by the use of the subway map. The routes, marked on the map by different colors, represent learning journeys. The stations along each route are indicated by circles. (Double circles indicate a stop on more than one route.) The reader is invited to click on any stop on the map to see the material in the tutorial relating to the name for that station. The shaded stations on the subway map indicate the location of an interactive demonstration or workbench for the tutorial user. The Subway Map Button The Subway Map button appears in the material presented at each subway stop. A mouse click on this button will always return to complete Math Refresher SUBWAY MAP to the screen. The Math Home Page Button A mouse click on the "house" button will always return the Math Home Page of the Math Refresher module. The Copyright Button Clicking on this button will display the copyright notice for this module. The Index Button A mouse click on the INDEX button will link to the index of algebra and calculus terms which are linked to their reference pages in the tutorial. The Mailbox Button Click on this button to send a comment. The Question Mark Buttons A mouse click on the black "question mark" button will take you to exercises on the subject of your current station. A mouse click on a colored "question mark" button will take you to a self test on the subway line of that color. Whenever a pop-up diagram, picture or explanation appears in its own window, you may move it or size it like any other window on your screen. If you wish to reduce it to an icon or delete it, click your rightmost mouse button on the small triangle in the bar at the top of the window for the appropriate menu. The Navigation Buttons While the browser buttons BACK and FORWARD keep track of your specific path through this module, individual buttons in the frame at the left of each page are provided to help you navigate within each subway line. To help you remember where you are, these buttons will be the same color as the subway line you are browsing. The left arrow button takes you back to the previous page of your current station or your current subway line. The right arrow button takes you to the next page of your current station or your current subway line. The up arrow button takes you the first page of your current station or the first page of your current subway line.
10 Units 3000 Level Course Not available in 2013 Introduces the most user-friendly of the various spaces occurring in analysis, chosen because their geometry is most like that of familiar two and three dimensional Euclidean space. Hilbert Spaces provide an excellent framework for the study of quantum mechanics, classical subjects like Fourier analysis and the developing theory of wavelets. Consequently they arise frequently in application such as theoretical physics, control theory and image processing. They also underlie much of the research effort of mathematicians in the Functional Analysis Group at Newcastle. Objectives On successful completion of this course, students will have: 1. an awareness of the breadth of mathematics as well as an in depth knowledge of one specific area. 2. an ability to communicate a convincing and reasoned argument of a mathematical nature in both written and oral form. 3. an understanding of what constitutes a rigorous mathematical argument and how to use reasoning effectively to solve problems.
Hi all, I just began my free algebra equation calculator class. Boy! This thing is really difficult! I just never seem to understand the point behind any topic. The result? My grades go down. Is there any guru who can lend me a helping hand? Algebrator is what you are looking for. You can use this to enter questions pertaining to any math topic and it will give you a step-by-step solution to it. Try out this software to find answers to questions in angle-angle similarity and see if you get them done faster. I agree, a good software can do miracles . I tried a few but Algebrator is the best. It doesn't make a difference what class you are in, I myself used it in Pre Algebra and Basic Math too, so you don't have to be concerned that it's not on your level. If you never had a software before I can tell you it's not hard, you don't need to know much about the computer to use it. You just have to type in the keywords of the exercise, and then the software solves it step by step, so you get more than just the answer. I remember having often faced problems with angle-angle similarity, adding numerators and trigonometry. A truly great piece of math program is Algebrator software. By simply typing in a problem homework a step by step solution would appear by a click on Solve. I have used it through many math classes – Remedial Algebra, Algebra 2 and Intermediate algebra. I greatly recommend the program.
Math Professional Development What do the measures of central tendency (mean, median, and mode) tell you about the data? Teach your students how to answer that question and encourage them to look beyond calculations and individual data points. Explain how the measures are related to the whole set and see the data as an aggregate; help students perform higher-order statistical thinking. Develop strategies for teaching students how to represent and manipulate linear equations. Examine the rationale behind the symbol manipulation that maintains an equality or corresponding inequality. Use symbolic and graphic techniques to solve equations. Discover a fresh approach to teaching linear functions through the use of real-world problems that generate varied approaches and solutions. Learn how multiple representations and solutions strengthen students' understanding of functions, equations, and problem solving. Discover techniques to successfully guide your students through the critical transition from elementary mathematics and computing to the more complex, proportional thinking of algebra. Adapt problems from your curriculum to different learning styles using graphing, multimedia technology, and other strategies. Move beyond tried-and-true quadratic equation teaching techniques and look at the big picture: what the results reveal, how to interpret them within the context of a problem, and how to find related information. Manipulate the three symbolic forms of a quadratic function in order to inspect and predict shape, orientation, and location, and connect graphic and symbolic representations
Variables, Constants, and Real Numbers Summary: This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses variables, constants, and real numbers. By the end of the module students should be able to distinguish between variables and constants, be able to recognize a real number and particular subsets of the real numbers and understand the ordering of the real numbers. Links Supplemental links Section Overview Variables and Constants Real Numbers Subsets of Real Numbers Ordering Real Numbers Variables and Constants A basic distinction between algebra and arithmetic is the use of symbols (usually letters) in algebra to represent numbers. So, algebra is a generalization of arithme­tic. Let us look at two examples of situations in which letters are substituted for numbers: Suppose that a student is taking four college classes, and each class can have at most 1 exam per week. In any 1-week period, the student may have 0, 1, 2, 3, or 4 exams. In algebra, we can let the letter xx size 12{x} {} represent the number of exams this student may have in a 1-week period. The letter xx size 12{x} {} may assume any of the various values 0, 1, 2, 3, 4. Suppose that in writing a term paper for a biology class a student needs to specify the average lifetime, in days, of a male housefly. If she does not know this number off the top of her head, she might represent it (at least temporarily) on her paper with the letter tt size 12{t} {} (which reminds her of time). Later, she could look up the average time in a reference book and find it to be 17 days. The letter tt size 12{t} {} can assume only the one value, 17, and no other values. The value tt size 12{t} {} is constant. Variable, Constant A letter or symbol that represents any member of a collection of two or more numbers is called a variable. A letter or symbol that represents one specific number, known or unknown, is called a constant. In example 1, the letter xx size 12{x} {} is a variable since it can represent any of the numbers 0, 1, 2, 3, 4. The letter tt size 12{t} {}example 2 is a constant since it can only have the value 17. Real Numbers Real Number Line The study of mathematics requires the use of several collections of numbers. The real number line allows us to visually display (graph) the numbers in which we are interested. A line is composed of infinitely many points. To each point we can associate a unique number, and with each number, we can associate a particular point. Coordinate The number associated with a point on the number line is called the coordinate of the point. Graph The point on a number line that is associated with a particular number is called the graph of that number. Constructing a Real Number Line We construct a real number line as follows: Draw a horizontal line. Origin Choose any point on the line and label it 0. This point is called the origin. Choose a convenient length. Starting at 0, mark this length off in both direc­tions, being careful to have the lengths look like they are about the same. We now define a real number. Real Number A real number is any number that is the coordinate of a point on the real number line. Positive Numbers, Negative Numbers Real numbers whose graphs are to the right of 0 are called positive real numbers, or more simply, positive numbers. Real numbers whose graphs appear to the left of 0 are called negative real numbers, or more simply, negative numbers. The number 0 is neither positive nor negative. Subsets of Real Numbers The set of real numbers has many subsets. Some of the subsets that are of interest in the study of algebra are listed below along with their notations and graphs. Natural Numbers, Counting Numbers Whole Numbers Integers The integers (ZZ): . . . -3, -2, -1, 0, 1, 2, 3, . . . Notice that every whole number is an integer. Rational Numbers (Fractions) The rational numbers (QQ): Rational numbers are sometimes called fractions. They are numbers that can be written as the quotient of two integers. They have decimal representations that either terminate or do not terminate but contain a repeating block of digits. Some examples are Notice that there are still a great many points on the number line that have not yet been assigned a type of number. We will not examine these other types of numbers in this text. They are examined in detail in algebra. An example of these numbers is the number ππ, whose decimal representation does not terminate nor contain a repeating block of digits. An approximation for ππ is 3.14. Exercise 4 Solution Exercise 5 Solution Ordering Real Numbers Ordering Real Numbers A real number bb size 12{b} {} is said to be greater than a real number aa size 12{a} {}, denoted b>ab>a size 12{b>a} {}, if bb size 12{b} {} is to the right of aa size 12{a} {} on the number line. Thus, as we would expect, 5>25>2 size 12{5>2} {} since 5 is to the right of 2 on the number line. Also, -2>-5-2>-5 size 12{"- 2 ">"-5"} {} since -2 is to the right of -5 on the number line. If we let aa size 12{a} {} and bb size 12{b} {} represent two numbers, then aa size 12{a} {} and bb size 12{b} {} are related in exactly one of three ways: Either Equality Symbol a=ba and b are equal(8=8)a=ba and b are equal(8=8) Inequality Symbols Sample Set B Example 4 What integers can replace xx so that the following statement is true? -3≤ x< 2-3≤ x< 2 size 12{"-3" <= " x"<" 2"} {} The integers are -3, -2, -1, 0, 1. Example 5 Draw a number line that extends from -3 to 5. Place points at all whole numbers between and including -1 and 3. Exercise 7 Solution Exercises For the following 8problems, next to each real number, note all collections to which it belongs by writing NN size 12{N} {} for natu­ral number, WW size 12{W} {} for whole number, or ZZ size 12{Z} {} for integer. Some numbers may belong to more than one collec­tion
## DESCRIPTION ## Matrix Algebra ## ENDDESCRIPTION ## KEYWORDS('Algebra' 'Matrix' 'Matrices' 'True' 'False') ## Tagged by tda2d ## DBsubject('Algebra') ## DBchapter('Systems of Equations and Inequalities') ## DBsection('The Algebra of Matrices') ## Date('') ## Author('') ## Institution('ASU') ## TitleText1('') ## EditionText1('') ## AuthorText1('') ## Section1('') ## Problem1('') DOCUMENT(); loadMacros("PGbasicmacros.pl", "PGchoicemacros.pl", "PGanswermacros.pl", ); TEXT(beginproblem(), $BR,$BBOLD, "True False Problem", $EBOLD, $BR,$BR); # Since this is a true questions, we do not usually wish to tell students which # parts of the matching question have been answered correctly and which are # incorrect. That is too easy. To accomplish this we set the following flag to # zero. $showPartialCorrectAnswers = 0; # True false questions are a special case of a "select list" # Make a new select list $tf = new_select_list(); # $tf now "contains" the select list object. # Insert some questions and whether or not they are true. $tf -> qa ( # each entry has to end with a comma "If A and B are both square matrices such that AB equals BA equals the identity matrix, then B is the inverse matrix of A.", "T", "If A is a square matrix, then there exists a matrix B such that AB equals the identity matrix.", "F", "If \( AX = B \) represents a system of linear equations and \( A^{-1} \) exists, then the product \( A^{-1}B \) gives the solution to the system.", "T", ); # every statement has to end with a semi-colon. # Choose two of the question and answer pairs at random. $tf ->choose(2); # Now print the text using $ml->print_q for the questions # and $ml->print_a to print the answers. BEGIN_TEXT $PAR Enter T or F depending on whether the statement is true or false. (You must enter T or F -- True and False will not work.)$BR \{ $tf-> print_q \} $PAR END_TEXT # Enter the correct answers to be checked against the answers to the students. ANS(str_cmp( $tf->ra_correct_ans ) ) ; ENDDOCUMENT(); # This should be the last executable
Are they related? You must have worked with some (books, lecture notes or internet materials) which make you master the topics. Could you suggest your choice to me? I want to follow your track to study.
- Mechanics and Probability Many students who embark on a GCE A-level course in mathematics choose the combination of pure mathematics with applications to mechanics. The pure ...Show synopsisMany students who embark on a GCE A-level course in mathematics choose the combination of pure mathematics with applications to mechanics. The pure mathematics content of most such syllabuses is covered in "Mathematics - The Core Course for A-Level", while this book provides the companion mechanics course. It also contains a section on probability, a topic included in many A-level mathematics syllabuses. An appreciation of the properties of vectors is introduced at an early stage and, wherever appropriate, problems are solved using vector methods. Worked examples are incorporated in the text to illustrate each main development of a topic, and a set of straightforward problems follows each section. A selection of more challenging questions is given in a miscellaneous exercise at the end of most chapters. Multiple-choice exercise are also included on many topics
Bob Jones Algebra 1 Student Text (2nd ed.) Present algebra topics in a logical order. Bob Jones Algebra 1 develops the student's understanding of algebra by justfiying methods and by explaining how to do the problems. It introduces graphing, solving systems of equations, operations with polynomials and radicals, factoring polynomials, solving rational equations, and graphing quadratic functions. Biographical sketeches of mathematicians are included, as well as features on probability and statistics, Algebra Around Us, and Algebra and Scripture. The Student Text presents concepts with numerous examples and step-by-step explanations. Included at the end of each exercise set is a systematic cumulative review.
CyberLearning When you click the link and enter in the username and password, you will see another link that reads 'san rafael math homework helper'. Once you click on a textbook, for example Geometry, you will see another window open up. Then click on the "search by chapter and section" on the lower right hand side. You will then see links to the chapters of the book. Let's say that I click on a chapter, a section, problem set, and a random problem... When you click on the green arrow pointing down, it will provide hints and guidelines of how to solve the problem. When you click on watch videos, you can click on any of the topics that show up under that tab. If there are no titles that show up then it means that there are no tutorial videos for that topic. You can read lessons on the subject matter, and also try our exercises. Do not click the "Ask A Tutor" button. Instructional Videos Click here to access a free library of over 2,400 science, math, and test prep instructional videos on provided by the Khan Academy. The Khan Academy is a non-profit organization with the goal of changing education for the better by providing a free world-class education to anyone anywhere.
Mathematics Courses MAT 105 FUNDAMENTALS OF MATHEMATICS IN TODAY'S WORLD Campus: This course, recommended for liberal arts students of varying mathematical backgrounds, stresses critical thinking and reasoning. The course includes the study of patterns, set theory, logic, inductive and deductive reasoning, the real number system and topics in geometry. 3 hours a week, 1 semester, 3 credits. Fall, spring and summer. MAT 106 EXCURSIONS IN CONTEMPORARY MATHEMATICS Campus: This course presents an overview of various topics in mathematics with a focus on recent developments and their applications. Designed for those students for whom the profundity of mathematics has often been obscured by its techniques, this course proposes to illustrate and explore the ubiquitous nature of mathematics in the world around us and thereby promote an appreciation for the significance, power and beauty of the discipline. Many topics are considered. They range from some modern applications of graphs to the mathematics of social choices. Not open to students who have credit for any 200-level math course. 3 hours a week, 1 semester, 3 credits. Spring. MAT 107 INTRODUCTION TO PROBABILITY AND STATISTICS Campus: This course offers an introduction to probability and statistics. It is designed to provide a common foundation for the more specialized material presented in the various statistics courses offered in other quantitative departments. Material covered includes: probability models, random variables and probability distributions (both discrete and continuous), descriptive statistics, inference, sampling and hypothesis testing. 3 hours a week, 1 semester, 3 credits. Fall and spring. MAT 111 COLLEGE ALGEBRA Campus: Properties of numbers and expressions; linear and quadratic equations; systems of equations; exponents and logarithms; functions; linear, quadratic, polynomial, exponential and logarithmic. Not open to students who have completed MAT 113 or students with credit for any 200-level math course. 3 hours a week, 1 semester, 3 credits. Fall, spring and summer. MAT 113 ELEMENTARY FUNCTIONS: PRECALCULUS Campus: Introduction to the concept of functions: their graphs, elementary properties, geometric transformations, inverses and algebra of functions. Introduction to the elementary functions and their properties: linear, polynomial, rational, exponential, logarithmic and trigonometric functions. Designed for those who intend to go on to a calculus course. Prerequisite: 11th-year mathematics or equivalent. Not available to students with credit for any 200-level math course. Students will not receive credit for both MAT 111 and MAT 113. 3 hours a week, 1 semester, 3 credits. Fall and spring. MAT 200 MATHEMATICS FOR BUSINESS AND ECONOMICS Campus: This course includes the study of matrices, linear programming, the simplex method and the mathematics of finance. Basic business applications of precalculus mathematics will be discussed. Prerequisite: MAT 111. 3 hours a week, 1 semester, 3 credits. Fall and spring. MAT 203 MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE Campus: The emphasis will be on algorithmic problem solving and discrete mathematical concepts including logic, sets, Boolean algebra, relations, functions, induction and recursion, counting principles and combinatorics, graphs and trees. Use of the computer as a problem-solving tool will be integrated with the theory. Fundamental algorithms including sorting, searching and tree traversal will be introduced. Prerequisite: MAT 113 or equivalent. 4 hours a week, 1 semester, 4 credits. Fall and spring. MAT 204 ANALYTIC TRIGONOMETRY AND GEOMETRY Campus: This course will focus on analytical geometry and the trigonometric functions and their properties. Amongst the topics considered under analytic geometry are the conic sections and the general quadratic equation along with polar and parametric equations. The topics covered under trigonometric functions include the inverse functions, trigonometric identities and the trigonometric representation of the complex numbers. Prerequisite: MAT 113 or equivalent. 3 hours a week, 1 semester, 3 credits. Fall and spring. MAT 206 CALCULUS AND ANALYTIC GEOMETRY II Campus: Differentiation and integration of logarithmic and exponential functions. Techniques for computing integrals are developed and applications of integration such as volumes of various solids are explored. Differentiation and integration of inverse functions, including trigonometric functions, is examined. Maple software will be used in the laboratory component. Prerequisite: MAT 205 with a minimum grade of C-. 3 lecture hours, 1 recitation hour and 1 lab hour a week, 1 semester, 4 credits. Fall and spring. MAT 207 CALCULUS AND ANALYTIC GEOMETRY III Campus: Infinite series and their convergence are explored and the Taylor series expansion for differentiable functions is developed. Parametric equations and polar functions are considered. Vectors in two and three dimensions along with their algebras are explored. Lines, planes and various families of surfaces in three-dimensional space are considered. Maple software will be used in the laboratory component. Prerequisite: MAT 206 with a minimum grade of C-. 3 lecture hours, 1 recitation hour and 1 lab hour a week, 1 semester, 4 credits. Fall and spring. MAT 208 ADVANCED CALCULUS Campus: Functions of several variables are introduced and studied. The calculus is redeveloped in this context. Gradients, directional derivatives, tangent planes and normal lines along with relative and absolute extrema are considered. Line, contour and multiple integration are explored. Vector fields and their calculus are studied. Material is illustrated and enhanced by the use of software packages such as Maple. Prerequisite: MAT 207 with a minimum grade of C-. 4 hours a week, 1 semester, 4 credits. Fall and spring. MAT 241 (HIS 240) HISTORY OF MATHEMATICS Campus: This course presents the development of mathematics from the ancient times to the present. Major advances in the field are examined in some depth and how these advances contributed to the growth of the discipline as a whole. Topics include the birth of the axiomatic system as exemplified by Euclidean geometry, the prescience of Archimedes, the study of roots of polynomials, the development of the calculus and many other breakthrough topics. Prerequisite: MAT 205. Recommended for prospective teachers. 3 hours a week, 1 semester, 3 credits. Spring and summer. MAT 307 REAL ANALYSIS Campus: This course provides a closer and more rigorous look at material covered in Calculus I, II and III. It reviews content from single variable calculus and goes further into the theoretical foundations of the subject. Topics covered include the real number system, sequences, limits, continuity, differentiation, Riemann integration and infinite series of numbers and of functions. Prerequisties: MAT 207 or equivalent with a minimum grade of C. 3 hours a week, 1 semester, 3 credits. Offered when there is sufficient demand. MAT 470 DIRECTED READING Campus: Assigned reading in the mathematical literature. Normally the student is required to demonstrate progress in a paper of significant depth. Approval of associate chair is necessary. 1 semester, 1, 2, or 3 credits. MAT 471 SEMINAR Campus: Special topics in the field of modern mathematics; preparation of written reports. Required of mathematics majors in their last semester. 2 hours a week, 1 semester, 3 credits. Fall and spring.
College Algebra with Modeling & Visualization Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the reader to ...Show synopsisGary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the reader to succeed. Introduction to Functions and Graphs. Linear Functions and Equations. Quadratic Functions and Equations. Nonlinear Functions and Equations. Exponential and Logarithmic Functions. Systems of Equations and Inequalities. Conic Sections. Further Topics in Algebra. Basic Concepts From Algebra and Geometry. For all readers interested in college algebra
The Mathematics GCSE does not just begin in Year 10. Students are building up their knowledge and skills throughout Key Stage 3 and the work then continues with consolidation and further development of these aspects. At present the Mathematics GCSE is modular. This means that students take a GCSE examination at the end of each of three Units, rather than only at the end of Year 11. From September 2012, Year 10 will be following a Linear GCSE course as modular exams will no longer be available. This means that they will not take any external exams until May/June 2014. In both Modular and Linear exams, students can enter Foundation or Higher tier. The decision on which tier to enter is governed only by a student's strengths in the subject. Being in a particular Mathematics set does not necessarily mean entry at a particular tier of the final exam. At Higher Tier, grades A* to D are available. At Foundation Tier, grades C to G are available. Homework is generally set weekly and may take a variety of forms, e.g. worksheets or activities to consolidate or assess understanding, preparation for future lessons, revision for exams, practice exam papers and online tasks. The department has its own dedicated homework website where parents can check the work which has been set. The URL for this is Students also have individual passwords for the MyMaths.co.uk website and can use this to help them review classwork, revise for exams or complete assigned homework.
Algebra Buster is one of the best resources that can offer help to people like you. When I was a novice, I took support from Algebra Buster. Algebra Buster offers all the principles of Remedial Algebra. Rather than utilizing the Algebra Buster as a step-by-step guide to work out all your homework assignments, you can use it as a tutor that can offer the basics of 3x3 system of equations, difference of cubes and function domain. Once you assimilate the basics, you can go ahead and solve any tough assignments on Algebra 1 within minutes.
id: 06145587 dt: j an: 2013b.00625 au: Jiang, Zhonghong; O'Brien, George E. ti: Multiple proof approaches and mathematical connections. so: Math. Teach. (Reston) 105, No. 8, 586-593 (2012). py: 2012 pu: National Council of Teachers of Mathematics (NCTM), Reston, VA la: EN cc: G60 G40 E50 ut: geometric concepts; secondary school mathematics; preservice teachers; mathematical logic; technology; trigonometry ci: li: ab: Summary: One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. To help students see and use the connections among various mathematical topics, the authors have paid close attention to selecting such problems as the Three Altitudes of a Triangle problem. They presented the problem to preservice teachers (referred to here as "students") in their Geometry for Teachers class. Using technology to explore the three altitudes of a triangle problem, students devise many proofs for their conjectures. After all the proof approaches were presented and discussed in class, students were excited about what they had learned and felt ownership of the proofs. They commented that they not only understood how to prove that the three altitude lines of any triangle are concurrent but also saw connections between this problem situation and various mathematical topics. In addition, their explorations of multiple approaches to proofs led beyond proof as verification to more of illumination and systematization in understandable yet deep ways [{\it M. D. de Villiers}, Rethinking proof with the Geometer's Sketchpad. Emeryville, CA: Key Curriculum Press (1999; ME 2000d.02607)]; expanded their repertoire of problem-solving strategies; and developed their confidence, interest, ability, and flexibility in solving various types of new problems. These benefits, in turn, will be passed on to their own students. (ERIC) rv:
This second edition of Maths Quest 11 Mathematical Methods CAS is a comprehensive text designed to meet the requirements of VCE Units 1 and 2 Mathematical Methods CAS course. The student textbook contains the following new features: Areas of studies dot-points; Comprehensive step-by-step CAS calculator instructions, fully integrated into Worked Examples, for the Casio ClassPad CAS calculator. Questions from past VCAA Examination papers; Exam tips to highlight danger areas for students; Exam-practice sections with allocated time and marks. Fully worked solutions to these sections are available to students on the eBookPLUS. show more show less Linear Functions Quadratic functions Cubic and quartic functions Relations and functions Exponential and logarithmic functions Circular functions Matrices Exam practice Rates of change Differentiation Applications of differentiation Introductory probability Combinatorics List price: $107.99 Edition: N/A Publisher: John Wiley & Sons Australia, Limited Binding: Box or Slipcased Pages: N/A Size: Weight: 3
It's a long story but I ended up not taking maths as level in september last year and I wish I'd tried harder to sort the problem out. However I ended up taking physics and honestly I don't find it as hard as people were saying it would be without maths but obviously having maths would help. I am thinking about taking maths this september with the year below. I'm fine with physics and taking physics has meant that my brain has been mathematically active should I say and yes it will be hard with a year out of proper maths but in general how are people finding the course? What did you get at GCSE? Just trying to see if it's worth taking it or not, possibly to A2 if I stay on at school another year (considering doing physics with astronomy at uni) I've have just finished A-level math on the Aqa board, i achieved a grade A a GCSE (edexcel) although i moved from 3rd set target grade C to to first set target grade A/A* in the space of 3 months i also got the highest mark on the last paper in the whole school , but without this senseless bragging my point is that math is a very logical subject and can learnt very quickly, my advice is that if you enjoyed math at GCSE and was working at A/A* You would have already met some of the A/S level topics i.e. coordinate geometry, completing the square etc. So in my opinion some may disagree but an A* GCSE candidate is not far from an A/S level candidate the real step up is A2 when (surprise surprise) they expand on your calculus and trig. However as i've said if you enjoy math and have a talent for recognising patterns and memorising formulae, you should be fine, and yes it is definitely worth taking if you wish to go in to any science including math at uni you will need some knowledge of calculus etc which will make math enormously helpful to you now. (Original post by Nooshkabob)The mechanics modules in applied math goes into far more detail then physics, and is far more effective at preparing for degree level, most people find D1 easy i hated it because id rather do differential equations rather then getting arthritis in my left hand from drawing dot to dot continuously lol but yeah like i said they leave the substance of physics out 'to make it more accessible to students' complete different story at uni, so yeah do math I don't do physics but I'd probably take maths to AS this year if I were you, I wouldn't do the whole A2 in a year. You'd have to put in a serious amount of work and you'd be putting the other subjects at risk. You could do what you mentioned and stay on for another year but is it really worth a year? If you're finding the maths OK at the moment then having AS maths should be enough, it'll give you quite a boost above GCSE. If you do want to do the A2 as well then I would advise against doing it by yourself - it'd probably be OK for maths enthusiasts but really I know a lot of people (some really intelligent) who struggled with lessons.
The example below shows that the problem solving process is the same for puzzles (story problems) and for problems based on subject matter. Using a unified approach to problem solving that is valid across the curriculum removes an important barrier to learning and using mathematics efficiently and effectively. The same linear process is used for solving the puzzle as is used to solve the physics problem. The Mary's Apples structure occurs as a part of a wide variety of problems. The problem solving skills learned in introductory algebra story problems form the basis for problem solving in more advanced courses. If the principles of solving story problems are learned well in middle school and high school, they will serve the student well in later subject matter courses in college and beyond. The words change and the symbols change, but the problem solving process remains the same. Sound problem solving skills make possible the understanding and use of concepts expressed in mathematical form. Solving word problems in any subject that uses mathematical methods consists of satisfying several conditions simultaneously. Doing this consists of using elementary methods of solving simultaneous equations. As the solution comparison shown above demonstrates, this basic process is independent of subject. Common sense, reliable problem solving based on basic concepts inherent in mathematics, introduced at the pre-algebra level, would solve the important objectives expressed in the NCTM standards and those advanced by AAAS in project 2061, Bench Marks for Science Literacy. The problem solution was developed using SureMath. Copyright 1995 Howard C. McAllister
These interactive tutorials from MyMathLab are free, and correspond directly to the current textbooks for Math 099, Math 111, Math 115, Math 116, Math 181, Math 241, and Math 242. The videos from MML are not included in this free software . Emergency Evacuation Procedure: A map of this floor is posted near the elevator marking the evacuation route and the Designated Rescue Area . This is an area where emergency service personnel will go first to look for individuals who need assistance in exiting the building. Students who may need assistance should identify themselves to the teaching faculty . • Number & Operations→ Number Theory→ Sieve of Eratosthenes: Part 1* • Number & Operations→ Number Theory→ Sieve of Eratosthenes: Part 2 • Number & Operations→ Number Theory→ Sieve of Eratosthenes on the Computer: Part 1 • Number & Operations→ Number Theory→ Sieve of Eratosthenes on the Computer: Part 2 • Number & Operations→ Number Theory→ Prime Number Definition • Number & Operations→ Number Theory→ Prime Factorization* • Number & Operations→ Number Theory→ Prime Number Graphics* • Number & Operations→ Number Theory→ Prime Numbers on the Computer
Course Description: An investigation of topics, including the history of mathematics, number systems, geometry, logic, probability, and statistics. There is an emphasis throughout on problem solving. Recommended for general education requirements, B.S. degree. Text: Mathematics in Our World, by Bluman (McGraw-Hill, 2005) CORE SKILL OBJECTIVES: These skills are related to the General Education core abilities document. They are also written to refer to the various INTASC standards for the purposes of the Elementary Education program. Thinking Skills: The students will engage in the process of inquiry and problem solving that involves both critical and creative thinking. Students will (a) ... explore writing numbers and performing calculations in various numeration systems. (INTASC 1) (b) ... solve simple linear algebraic equations. (INTASC 1) (c) ... explore linear and exponential growth functions, including the use of logarithms, and be able to compare these two growth models. (INTASC 1) (d) ... explore a few major concepts of Euclidean Geometry, focusing especially on the axiomatic-deductive nature of this mathematical system. (INTASC 1) (e) ... develop an ability to use deductive reasoning, in the context of the rules of logic and syllogisms. (INTASC 1) (f) ... explore the basics of probability. (INTASC 1) (g) ... learn descriptive statistics, including making the connection between probability and the normal distribution table. (INTASC 1) (h) ... learn the basics of financial mathematics, including working with the formulas for compound interest, annuities, and loan amortizations. (INTASC 1) (i) ... solve a variety of problems throughout the course which will require the application of several topics addressed during the course. (INTASC 1) Life Value Skills: The students will analyze, evaluate and respond to ethical issues from informed personal, professional, and social value systems. Students will (a) ... develop an appreciation for the intellectual honesty of deductive reasoning. (INTASC 9) (b) ... understand the need to do one's own work, to honestly challenge oneself to master the material. (INTASC 1) Communication Skills: The students will communicate orally and in writing in an appropriate manner both personally and professionally. Student will (a) ... write a mathematical autobiography. (INTASC 9) (b) ... do group work (labs and practice exams), involving both written and oral communication. (INTASC 4) (c) ... turn in written solutions to occasional problems. (INTASC 1) Cultural Skills: The students will understand their own and other cultural traditions and respect the diversity of the human experience. Student will (a) ... explore a number of different numeration systems used by other cultures, such as the early Egyptian and the Mayan peoples. (INTASC 1) (b) ... develop an appreciation for the work of the Arab and Asian cultures in developing algebra during the European "Dark Ages". (INTASC 1) (c) ... explore the contribution of the Greeks, especially in the areas of Logic and Geometry. (INTASC 1) It is also worth mentioning the NCTM (National Council of Teachers of Mathematics) "standards" for mathematics education, because they are also a list of some overall goals we strive for in this course: The students shall develop an appreciation of mathematics, its history and its applications. The students shall become confident in their own ability to do mathematics. The students shall become mathematical problem solvers. The students shall learn to communicate mathematical content. The students shall learn to reason mathematically. FURTHER COURSE NOTES: This course is aimed at the needs of elementary education majors and as such is the first part of a three-course, 12-credit sequence (MATH 155-255-355). This is a "content" course rather than a "methods" course (teaching methods are addressed in the latter two courses in the above sequence). This is what people generally call a "Liberal Arts Mathematics Course", meaning that it covers a wide variety of topics, has an emphasis on problem solving, and uses a historical and humanistic approach. Consequently, the course is considered appropriate for the general education requirements and is open to all students. Homework questions 100 pts. (Full credit is given for each completed assignment) Homework will be due one class week after it has been assigned. Any questions regarding how to do particular homework problems will be welcomed in the intervening class meetings or in my office but not in class on the day that the homework is due. Late homework will be penalized by a deduction of 20% of the assigned grade for each schoolday -- including schooldays on which class does not meet – that the work is late, so that, if the work is one week late, it will not receive any points. You may, however, still hand the work in so that you can benefit from corrections and be certain you know how to do a question that could well appear on an exam Examinations 400 pts There will be four in class exams worth 100 pts apiece, and lasting 50 minutes each. Participation 50 pts Participation points are easy to acquire and you probably already know how to get them; don't chat to your neighbors when I'm lecturing (asking a neighbor to help if you didn't understand what I said is, however, always acceptable). General politeness counts. Cheerfulness, engagement, willingness to push buttons on your calculator, asking me to clarify if you are stuck, taking advantage of my office hours, these are all, to quote the Sound of Music, a few of my favorite things. Labs 150 pts Cumulative Final Examination 200 pts Total 900 pts Attendance Policy: You can afford to miss no more than the equivalent of one week of class. Any more absences are a dangerous loss of classtime percentage. Once you have had 3 unexcused absences, every unexcused absence from that point onward will incur a penalty of 10 pts from your participation and attendance score. Make up exams situations will be considered on a case-by-case basis, but invariably they require as much forewarning as possible -- and documentation. You know when the exams are; please do not book flights home, or your wedding, etc, etc on those dates. If your, or your best friend's, or your uncle's hairdresser's poodle's (if you're from the Coast) wedding is already booked for any of those dates, please let me know ASAP. I will not give make up tests without good reason, and if you should miss a test that is not made up, your score for that test will be zero. The sad fact is that it is a rare semester when some student doesn't have to rush home to tend a family crisis, or bury a loved one. Often this interferes with exams. Should such sadness happen to you, I will need to ask you for some sort of verification (obituary, hospital record, etc) and then we will try to get your semester moving again. RESOURCES: Tutoring is available in the Learning Center - third floor, Murphy Center. I also want you to consider coming to see me if you have a problem with some material. Sometimes we can resolve in a few minutes a difficulty that can cause problems for weeks. I don't resent your coming – it's part of my job! I want your success as much as you do. FINAL COMMENTS: I believe firmly that you as the student are the learner, and that "to learn" is an active verb; you must be actively engaged in the learning process, and this is best accomplished by your DOING mathematics. I am not here to show you how much I know - I am here to be "a guide on the side, not a sage on the stage". Please feel free to ask questions in class, either of me or of your group-mates. Please feel free to come to my office to discuss problems you might be having. Please feel free to go visit the learning center for tutoring help if necessary. The bottom line is that you must take responsibility for your own learning. Please believe that "Mathematics is not a spectator sport!"
Year 7 Maths: Course Book Paperback There are no reviews for this book.Read reviews or write your own > Currently out of stock online, please contact your nearest store for availability Description Details Reviews This course book covers topics appropriate for KS3 Year 7 Maths and accurately reflects the language and content of the new Programme of Study. Along with the Year 8 and 9 course books full coverage of the KS3 programme of study is provided. *Clear and concise overviews, examples and 'Key Words' boxes help underpin understanding of the key topics * Tasks and exercises challenge and stimulate pupils at all levels and help develop skills * Pages of practice questions for every topic reinforce learning and test understanding.
Our Apps are not designed as games or drills to simply test or exercise your knowledge. Our lesson Apps are made to fully teach the mathematical concepts presented in an interactive and engaging manner. Animations and Voice Instructions As each lesson takes students through the learning experience, text is accompanied by spoken audio along with professionally developed graphics and animations that visually enhance the understanding of each concept. Available Lessons We have a lot of Algebra lessons, you can download individual or by units
Credit: 0.5 units Lessons: 8 lessons, 8 submitted Exams: 2 exams Grading: Computer and Faculty Evaluated Prerequisites: Full credit for Geometry and Precalculus or Trigonometry (C or better) Description: This course provides students with a college-level foundation in calculus. Coursework emphasizes the relationship between the various forms of a function: graphs, equations, tables, and verbal expressions. Calculus has two main topics: rate of change and area under a curve. The fall semester focuses on finding rates of change, i.e. differentiation. Students will review familiar functions and explore the concept of limits and differentiation. Gifted: This course is academically challenging. Any student who has an interest in the subject and has met the prerequisites (if any), may enroll. Special Instructions: The course content will be viewable prior to the start date. Read more about our online Advanced Placement courses. Our AP courses follow a specific calendar, and the normal 9-month completion policy does not apply to these courses. Therefore, students who have not completed all work by the due date for the course final (listed on the course calendar) will automatically be withdrawn from the course. Students who choose to take the AP exam will need to make their own arrangements. Contact the College Board for assistance in locating a testing site, or contact a local high school to determine whether it administers the test. Lesson assignments need to be created in Microsoft Word or another word processor that saves files as .doc (Word 97–2003 document) or .rtf (Rich Text format). Materials Note: Students will need access to a graphing calculator (e.g. TI-83+ or newer). The same textbook is also used for the fall semester. Preview This Course — A preview includes general information about the course and, if available, one lesson and one progress evaluation.
Learning Outcomes The objective of the course is to introduce students to aspects of personal finance with special emphasis on the student developing their knowledge, skill and understanding of the mathematical and statistical underpinnings of the selected topics. Extensive use will be made of theorems and mathematical proofs. Notes This course will use Beamer presentations in lectures. The slides will be available on LEARN before class in pdf format. You will need to be familiar with material other than the Beamer presentations such as the recommended textbooks, lecture notes, tutorial/problem session material and any other supplementary material.