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Basic Mathematical Skills with Geometry with MathZone:Maintaining its hallmark features of carefully detailed explanations and accessible pedagogy, this edition also addresses the AMATYC and NCTM Standards. In addition to the changes incorporated into the text, a new integrated video series and multimedia tutorial program are also available. Designed for a one-semester basic math course, this successful worktext is appropriate for lecture, learning center, laboratory, or self-paced courses.
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Rent Basic Mathematical Skills with Geometry with MathZone 6th edition today, or search our site for Donald textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by McGraw-Hill Education. | 677.169 | 1 |
Steve Demme, creator of Math U-See, combines hands-on methodology with incremental instruction and continual review in this manipulative-based program. It excels in its hands-on presentation of math concepts that enables students to understand how math works. It is one of the rare multi-sensory math programs that continue to use manipulatives up through Algebra 1.
Manipulative Blocks, Fraction Overlays, and Algebra and Decimal Inserts are used at different levels to teach concepts, primarily using the "rectangle building" principle. This basic idea, consistently used throughout the program—even through algebra—is one of the best ways to demonstrate math concepts.
One of the things I think makes Math-U-See so popular is that many parents and teachers find that author Steve Demme's presentations of math concepts helps them to finally comprehend much that they were taught in math but never understood. Parents and teachers with a new or renewed enthusiasm for math then do a much better job teaching their own children. Math-U-See uses a "skill-mastery" approach, requiring students to demonstrate mastery of each topic before moving on. The program also builds in systematic review for previously learned concepts.
There are eight books for elementary grades titled Primer, Alpha, Beta, Gamma, Delta, Epsilon, Zeta, and Pre-Algebra. The Greek letter designations were chosen particularly to emphasize the order of learning rather than grade level designation. Students should move on to the next level once they've mastered the content of a book. These first eight books are followed by Algebra 1, Geometry, Algebra 2, PreCalculus with Trigonometry, and Calculus. Placement tests for the different levels are available free at the Math-U-See website.
Student books are perfect-bound, and the pages are perforated and punched so they can easily be removed, written upon, and placed in binders. (Test books have been redesigned in this same fashion.) Student books now have much more practice work than they did in earlier editions, and they include many word problems. Honors exercises have been incorporated into the student books for Pre-Algebra through PreCalculus. These optional, additional problems stretch students to higher levels of understanding and application of math concepts covered within the lessons.
Test booklets for each course have tests to be used at the end of each lesson plus four unit tests and a final exam. Neither student worktext pages nor tests are reproducible; you need to purchase books for each student. Student workbooks and test booklets are the only consumable items in each course.
Instruction manuals are printed in hardcover books with full-color covers so they might be used a number of times. Calculus, the only exception, has a softcover, comb-bound book, although that will likely change to hardcover with the next printing. Complete answer keys with solutions are now included for all problems at all levels, an especially helpful feature at upper levels.
All books are printed in black and white with no illustrations other than mathematical ones....
The program covers all basic math concepts and all of those in the elementary-level Common Core Standards, but it does not try to correlate the teaching of concepts at the same grade level or in the same order as the Core Standards. Everything gets covered eventually, but in a more sensible order than the standards, in my opinion.
For each level you need both the student kit and the instruction pack. The student kit for each level includes a student workbook and a test booklet for most levels.
For Primer through Algebra 1, you will also need to purchase the set of Manipulative Blocks, but these are very reasonably priced. Math-U-See's manipulatives are primarily plastic blocks somewhat similar to Base Ten Blocks and Cuisenaire Rods, color-coded to correspond to each number...Fraction Overlays are added at Epsilon level and Algebra/Decimal Inserts are added at the Zeta level. That means, the same sets of manipulatives are each used over at least a few years.
The instruction pack for each level includes an instruction manual plus one or more DVDs that "teach the teacher." Note that DVDs have subtitles for the hearing impaired. Parents must watch the DVDs to understand the basic concepts that are the foundation of the program. On the DVDs, Demme works through each level, lesson-by-lesson, demonstrating and instructing. Demme's presentation is enthusiastic and engaging as he clearly explains why and what he is doing. He throws in lots of math tricks, the kind that make you scratch your head and ask yourself why they never taught us that in school....
There are plenty of practice problems in the latest editions of Math-U-See, but students who need more practice have free access to a computation drill program on the Math-U-See website....
As you move into the high school level books, students are able to work more independently. The instruction manual for each level is written to the student. Students need to watch the DVD presentation then read through the instruction manual before tackling the workbook. Workbooks include extra instruction for unusual problems, especially for some of the honors problems, but they do not serve as complete coursebooks on their own.
The honors exercises provide more challenging practice, more critical thinking, practical applications, more complex word problems, test prep practice, and preparation for the math required in advanced science courses. The addition of the honors exercises largely alleviates concerns I expressed in my review in the first edition of Top Picks about the program's ability to challenge advanced students. Students can also move through the texts more rapidly if they master the lessons quickly....
The DVD instructional component might make a huge difference...since Demme does a great job of explaining and illustrating concepts. However, I very much appreciate the fact that the newest editions' instruction manuals for these and other high school level courses now include a teaching component so that students do not have to rely entirely on the DVDs.
Note: Math U See announced updated editions available March 2013 with a number of improvements. Among them are:
- an extra "Application and Enrichment" activity page added to the student workbook for levels Primer through Zeta
- more thorough coverage of concepts encountered on standardized tests
- more work with word problems
- updated instruction manuals with improved or expanded explanations and answers for new problems
Pricing
Math-U-See is sold only through Math-U-See representatives. Check the Math-U-See website for the distributor in your area and for a free demo | 677.169 | 1 |
Graduate textbooks often have a rather daunting heft. So it's pleasant for a text intended for first-year graduate students to be concise, and brief enough that at the end of a course nearly the entire text will have been covered. This book manages that feat, entirely without sacrificing any materia more...
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility... more...
This Second Edition of a classic algebra text includes updated and comprehensive introductory chapters,. new material on axiom of Choice, p-groups and local rings, discussion of theory and applications, and over 300 exercises. It is an ideal introductory text for all Year 1 and 2 undergraduate students in mathematics. - ;Developed to meet the needs... more...
Praise for the first edition "This book is clearly written and presents a large number of examples illustrating the theory . . . there is no other book of comparable content available. Because of its detailed coverage of applications generally neglected in the literature, it is a desirable if not essential addition to undergraduate mathematics and... more...
This book Abstract Algebra has been written primarily from student's point of view. So that they can easily understand various mathematical concepts, techniques and tools needed for their course. Efforts have been made to explain such points in depth, so that students can follow the subject easily. A large number of solved and unsolved problems... more... | 677.169 | 1 |
Although few mathematicians would quarrel with the
proposition that the algebraic notation taught
in high school is a language
(and indeed the primary language of mathematics),
yet little attention has been paid to the possible
implications of such a view of algebra.
This paper adopts this point of view to illuminate
the inconsistencies and deficiencies of conventional
notation and to explore the implications of analogies
between the teaching of natural languages
and the teaching of algebra.
Based on this analysis it presents a simple
and consistent algebraic notation, illustrates its power
in the exposition of some familiar topics in algebra,
and proposes a basis for an introductory course in algebra.
Moreover, it shows how a computer can, if desired,
be used in the teaching process, since the language
proposed is directly usable on a computer terminal.
A.2 Arithmetic Notation
We will first discuss the notation of arithmetic,
i.e., that part of algebraic notation which does not involve
the use of variables. For example, the expression 3-4
and (3+4)-(5+6) are arithmetic expressions,
but the expressions 3-X and (X+4)-(Y+6) are not.
We will now explore the anomalies of arithmetic notation
and the modifications needed to remove them.
Functions and symbols for functions.
The importance of introducing the concept of "function"
rather early in the mathematical curriculum is now widely recognized.
Nevertheless, those functions which the student encounters first
are usually referred to not as "functions" but as "operators".
For example, absolute value (|-3|)
and arithmetic negation (-3) are usually referred to as operators.
In fact, most of the functions which are so fundamental
and so widely used that they have been assigned some graphic symbol
are commonly called operators
(particularly those functions such as plus and times
which apply to two arguments),
whereas the less common functions which are usually referred to by
writing out their names (e.g. Sin, Cos, Factorial) are called functions.
This practice of referring to the most common
and most elementary functions as operators is surely an unnecessary
obstacle to the understanding of functions
when that term is first applied to the more complex functions encountered.
For this reason the term "function" will be used here
for all functions regardless of the choice of symbols used to represent them.
The functions of elementary algebra are of two types,
taking either one argument or two.
Thus addition is a function of two arguments (denoted by X+Y)
and negation is a function of one argument (denoted by -Y).
It would seem both easy and reasonable to adopt one form
for each type of function as suggested by the foregoing examples,
that is, the symbol for a function of two arguments occurs
between its arguments, and the symbol for a function of one argument
occurs before its argument.
Conventional notation displays considerable anarchy on this point:
1.
Certain functions are denoted by any one of several symbols
which are supposed to be synonymous but which are, however,
used in subtly different ways.
For example, in conventional algebra X×Y and XY
both denote the product of X and Y .However,
one would write either 3×Y or 3X or X×3 or 3×4 ,but
would not likely accept X3 as
an expression for X×3 ,nor 3 4
as an expression for 3×4 .
Similarly, X÷Y and X/Y are supposed to be synonymous,
but in the sentence "Reduce 8/6 to lowest terms",
the symbol / does not stand for division.
2.
The power function has no symbol, and is denoted by position only,
as in XN .The
same notation is often used to denote the Nth element
of a family or array X .
3.
The remainder function (that is, the integer remainder of
dividing X into Y) is used very early in arithmetic
(e.g., in factoring) but is commonly not recognized as a function on par
with addition, division, etc., nor assigned a symbol.
Because the remainder function has no symbol and is commonly
evaluated by the method of long division,
there is a tendency to confuse it with division.
This confusion is compounded by the fact that the term
"quotient" itself is ambiguous,
sometimes meaning the quotient and sometimes the integer part
of the quotient.
4.
The symbol for a function of one argument sometimes occurs
before the argument (as in -4) but may also occur
after it (as in !4 for factorial 4)
or on both sides (as in |X| for absolute value of X).
Table A.1 shows a set of symbols which can be used
in a simple consistent manner to denote the functions
mentioned thus far,
as well as a few other very useful basic functions
such as maximum, minimum, integer part, reciprocal, and exponential.
The table shows two uses for each symbol, one to denote
a monadic function (i.e. a function of one argument),
and one to denote a dyadic function
(i.e. a function of two arguments).
This is simply a systematic exploitation of the example set
by the familiar use of the minus sign,
either as a dyadic function (i.e., subtraction as in 4-3)
or as a monadic function (i.e., negation as in -3).
No function symbol is permitted to be elided;
for example, X×Y may not be written as XY .
Monadic form f b
f
Dyadic form a f b
Definition or example
+3 ↔ 0+3
-3 ↔ 0-3
×3 ↔ (3>0)-(3<0)
÷3 ↔ 1÷3
⌈ 3.14 ↔ 4
⌈¯3.14 ↔ ¯3
⌊ 3.14 ↔ 3
⌊¯3.14 ↔ ¯4
*3 ↔ (2.71828...)*3
⍟*5 ↔ 5 ↔*⍟5
|¯3.14 ↔ 3.14
Name
Plus
Negative
Signum
Reciprocal
Ceiling
Floor
Exponential
Natural
logarithm
Magnitude
+
-
×
÷
⌈
⌊
*
⍟
|
Name
Plus
Minus
Times
Divide
Maximum
Minimum
Power
Logarithm
Remainder
Definition or example
2+3.2 ↔ 5.2
2-3.2 ↔ ¯1.2
2×3.2 ↔ 6.4
2÷3.2 ↔ 0.625
3⌈7↔ 7
3⌊7↔ 3
2*3↔ 8
10⍟3 ↔ Log 3 base 10
10⍟3 ↔ (⍟3)÷⍟10
3|8 ↔ 2
Table A.1
A little experimentation with the notation of Table A.1 will show
that it can be used to express clearly a number of matters
which are awkward of impossible to express in conventional notation.
For example, X÷Y is the quotient of X divided
by Y ;either ⌊(X÷Y) or ((X-(Y|X))÷Y
yield the integer part of the quotient of X
divided by Y ;
and X⌈(-X) is equivalent to |X .
In conventional notation the
symbols < , ≤ , = , ≥ , > ,
and ≠ are used to state relations among quantities;
for example, the expression 3<4 asserts
that 3 is less than 4 .
It is more useful to employ them as symbols for dyadic functions defined
to yield the value 1 if the indicated relation actually holds,
and the value zero if it does not.
Thus 3≤4 yields the value 1 ,
and 5+(3≤4) yields the value 6 .
Arrays.
The ability to refer to collections or arrays of items
is an important element in any natural language
and is equally important in mathematics.
The notation of vector algebra embodies the use of arrays
(vectors, matrices, 3-dimensional arrays; etc.)
but in a manner which is difficult to learn
and limited primarily to the treatment of linear functions.
Arrays are not normally included in elementary algebra,
probably because they are thought to be difficult
to learn and not relevant to elementary topics.
A vector (that is, a 1-dimensional array) can be represented
by a list of its elements (e.g., 1 3 5 7)
and all functions can be assumed to be applied element-by-element.
For example:
In addition to applying a function to each element of an array,
it is also necessary to be able to apply some specified function
to the collection itself.
For example, "Take the sum of all elements",
or "Take the product of all elements", or
"Take the maximum of all elements".
This can be denoted as follows:
+/2 5 3 2
12
×/2 5 3 2
60
⌈/2 5 3 2
5
The rules for using such vectors are simple and obvious
from the foregoing examples.
Vectors are relevant to elementary mathematics in a variety of ways.
For example:
1.
They can be used
(as in the foregoing examples) to display the patterns produced
by various functions when applied to certain patterns of arguments.
They can be used
to represent rational numbers. Thus if 3 4 represents the fraction three-fourths,
then 3 4×5 6 yields 15 24 , the product
of the fractions represented
by 3 4 and 5 6 .Moreover, ÷/3 4 and ÷/5 6 and ÷/15 24 yield
the actual numbers represented.
4.
A polynomial can be represented by its vector
of coefficients and vector of exponents.
For example, the polynomial with coefficients 3 1 2 4 and exponents 0 1 2 3 can
be evaluated for the argument 5 by the following expression:
+/3 1 2 4 × 5 * 0 1 2 3
558
Constants.
Conventional notation provides means for writing any positive constant
(e.g., 17 or 3.14) but there is no distinct notation
for negative constants, since the symbol - occurring in a number
like -35 is indistinguishable from the symbol for the negation function.
Thus negative thirty-five is written as an expression,
which is much as if we neglected to have symbols for five and zero
because expressions for them could be written in a variety of ways
such as 8-3 and 8-8 .
It seems advisable to follow Beberman
[1]
in using a raised minus sign to denote negative numbers.
For example:
3 - 5 4 3 2 1
¯2 ¯1 0 1 2
Conventional notation also provides no convenient way to represent numbers
which are easily expressed in expressions of the
form 2.14×108or 3.265×10¯9 .A
useful practice widely used in computer languages is
to replace the symbols ×10 by the symbol E (for exponent)
as follows: 2.14E8 and 3.265E¯9 .
Order of execution.
The order of execution in an algebraic expression is commonly specified by parentheses.
The rules for parentheses are very simple,
but the rules which apply in the absense of parentheses are complex and chaotic.
They are based primarily on a hierarchy of functions
(e.g., the power function is executed before multiplication,
which is executed before addition) which has apparently arisen
because of its convenience in writing polynomials.
Viewed as a matter of language,
the only purpose of such rules is the potential economy
in the use of parentheses and the consequent gain
in readability of complex expressions.
Economy and simplicity can be achieved by the following rule:
parentheses are obeyed as usual
and otherwise expressions are evaluated from right to left
with all functions being treated equally.
The advantages of this rule and the complex and ambiguity
of conventional rules are discussed in Berry
[2],
page 27 and in Iverson
[3],
Appendix A.
Even polynomials can be conveniently written without parentheses
if use is made of vectors.
For example, the polynomial in X with
coefficients 3 1 2 4 can be written
without parentheses
as +/3 1 2 4 × X * 0 1 2 3 .Moreover,
Horner's expression for the efficient evaluation of this same
polynomial can also be written without parentheses as follows:
3+X×1+X×2+X×4
Analogies with natural language.
The arithmetic expression 3×4 can be viewed as an order
to do something, that is,
multiply the arguments 3 and 4 .Similarly,
a more complex expression can be viewed as an order to perform
a number of operations in a specified order.
In this sense, an arithmetic expression is an imperative sentence,
and a function corresponds to an imperative verb in natural language.
Indeed, the word "function" derives from the Latin verb
"fungi" meaning "to perform".
This view of a function does not conflict with the usual
mathematical definition as a specified correspondence
between the elements of domain and range,
but rather supplements this static view with a dynamic view
of a function as that which produces the corresponding value
for any specified element of the domain.
If functions correspond to imperative verbs,
then their arguments (the things upon which they act)
correspond to nouns.
In fact, the word "argument" has (or at least had)
the meaning topic, theme, or subject.
Moreover, the positive integers, being the most concrete of arithmetical objects,
may be said to correspond to proper nouns.
What are the roles of negative numbers, rational numbers,
irrational numbers, and complex numbers?
The subtraction function, introduced as an inverse to addition,
yields positive integers in some cases but not in others,
and negative numbers are introduced
to refer to the results in these cases.
In other words, a negative number refers to a process
or the result of a process, and is therefore analogous to an abstract noun.
For example, the abstract noun "justice"
refers not to some concrete object
(examples of which one may point to) but to a process or result of a process.
Similarly, rational and complex numbers refer to the results of processes;
division, and finding the zeros of polynomials, respectively.
A.3 Algebraic Notation
Names.
An expression such as 3×X can be evaluated only
if the variable X has been assigned an actual value.
In one sense, therefore, a variable corresponds to a pronoun
whose referent must be made clear before any sentence including it
can be fully understood.
In English the referent may be made clear by an explicit statement,
but is more often made clear by indirection
(e.g., "See the door. Close it."),
or by context.
In conventional algebra, the value assigned to a variable name
is usually made clear informally by some statement such as
"Let X have the value 6 "
or "Let X=6 ".
Since the equal symbol (that is, '=') is also used in other ways,
it is better to avoid its use for this purpose
and to use a distinct symbol as follows:
X←6
Y←3×4
X+Y
18
(X-3)×(X-5)
3
Assigning names to expressions.
In the foregoing example, the expression (X-3)×(X-5) was written
as an instruction to evaluate the expression
for a particular value already assigned to X .
One also writes the same expression for the quite different notation
"Consider the expression (X-3)×(X-5) for any value
which might later be assigned to the argument X ."
This is a distinct notion which should be represented by distinct notation.
The idea is to be able to refer to the expression
and this can be done by assigning a name to it.
The following notation serves:
∇ Z ← G X
Z←(X-3)×(X-5)∇
The ∇'s indicate that the symbols between them
define a function;
the first line shows that the name of the function is G .The
names X and Z are dummy names standing
for the argument and result, and the second line shows how they are related.
Following this definition, the name G may be used as a function.
For example:
G 6
3
G 1 2 3 4 5 6 7
8 3 0 ¯1 0 3 8
Iterative functions can be defined with equal ease
as shown in Chapter 12.
Form of names.
If the variables occurring in algebraic sentences
are viewed simply as names, it seems reasonable to employ names
with some mnemonic significance as illustrated by the following sequence:
LENGTH←6
WIDTH←5
AREA←LENGTH×WIDTH
HEIGHT←4
VOLUME←AREA×HEIGHT
This is not done in conventional notation,
apparently because it is ruled out by the convention that
the multiplication sign may be elided; that is, AREA
cannot be used as a name because it would be interpreted
as A×R×E×A .
This same convention leads to other anomalies as well,
some of which were discussed in the section on arithmetic notation.
The proposal made there (i.e., that the multiplication sign
cannot be elided) will permit variable names of any length.
A.4 Analogies with the Teaching of Natural Language
If one views the teaching of algebra as the teaching of a language,
it appears remarkable how little attention is given
to the reading and writing of algebraic sentences,
and how much attention is given to identities, that is,
to the analysis of sentences with a view to determining
other equivalent sentences;
e.g., "Simplify the expression (X-4) × (X+4) ."
It is possible that this emphasis accounts
for much of the difficulty in teaching algebra,
and that the teaching and learning processes in natural languages
may suggest a more effective approach.
In the learning of a native language one can distinguish
the following major phases:
1.
An informal phase, in which the child learns to communicate in a combination
of gestures, single words, etc., but with no attempt to form grammatical sentences.
2.
A formal phase, in which the child learns to communicate in formal sentences.
This phase is essential because it is difficult or impossible to communicate
complex matters with precision
without imposing some formal structure on the language.
3.
An analytics phase, in which one learns to analyze sentences
with a view to determining equivalent
(and perhaps "simpler" or "more effective") sentences.
The extreme case of such analysis is Aristotelian Logic,
which attempts a formal analysis of certain classes of sentences.
More practical everyday cases occur
every time one carefully reads a composition
and suggests alternative sentences which convey the same meaning
in a briefer or simpler form.
The same phases can be distinguished in the teaching of algebraic notation:
1.
An informal phase
in which one issues an instruction to add 2 and 3
in any way which will be understood. For example:
2 + 3 Add 2 and 3
2 2
3 +3
--- ---
Add two and three
Add // and ///
The form of the expression is unimportant,
provided that the instruction is understood.
2.
A formal phase
in which one emphasizes proper sentence structure and would not
accept expressions such as
2
6 × 3 or 6 × (add two and three)
---
in lieu of 6×(2+3) .Again, adherence
to certain structural rules is necessary to permit the
precise communication of complex matters.
3.
An
analytic phrase in which one learns to analyze sentences
with a view to establishing certain relations (usually identity)
among them.
Thus one learns not only that 3+4 is equal to 4+3
but that the sentences X+Y and Y+X are equivalent,
that is, yield the same result whatever the meanings are assigned
to the pronouns X and Y .
In learning a native language, a child spends many years
in the informal and formal phrases (both in and out of school)
before facing the analytic phrase.
By this time she has easy familiarity with the purpose of a language
and the meanings of sentences which might be analyzed and transformed.
The situation is quite different in most conventional courses in algebra
— very little time is spent in the formal phase
(reading, writing and "understanding" formal algebraic sentences)
before attacking identities such as commutativity, associativity,
distributivity, etc.).
Indeed, students often do not realize that they might quickly
check their work in "simplification" by substituting
certain values for the variables occurring in the original
and derived expressions and comparing the evaluated results
to see if the expressions have the same "meaning",
at least for the chosen values of the variables.
It is interesting to speculate on what would happen
if a native language were taught in an analogous way,
that is, if children were forced to analyze sentences at a stage
in their development when their grasp of the purpose and meaning
of sentences were as shaky as the algebra student's
grasp of the purpose and meaning of algebraic sentences.
Perhaps they would fail to learn the converse,
just as many students fail to learn the much simpler task of reading.
Another interesting aspect of learning the non-analytic aspects
of a native language is that much (if not most) of the motivation
comes not from an interest in language,
but from the intrinsic interest of the material
(in children's stories, everyday dialogue, etc.)
for which it is used.
it is doubtful that the same is true in algebra —
ruling out statements of an analytic nature (identities, etc.),
how many "interesting" algebraic sentences
does a student encounter?
The use of arrays can open up the possibility
of much more interesting algebraic sentences.
This can apply both to sentences to be read
(that is, evaluated) and written by students.
For example, the statements:
produce interesting patterns
and therefore have more intrinsic interest than similar expressions
involving only single quantities.
For example, the last expression can be construed as yielding
a set of possible areas for a rectangle
having a fixed perimeter of 12 .
More interesting possibilities are opened up
by certain simple extensions of the use of arrays.
One example of such extensions will be treated here.
This extension allows one to apply any dyadic function
to two vectors A and B so as to obtain
not simply the element-by-element product produced by the
expression A×B but a table of all products
produced by pairing each element of A
with each element of B .For example:
The following analysis suggests the development
of an algebra curriculum with the following characteristics:
1.
The notation used is unambiguous, with simple and consistent rules of syntax,
and with provision for the simple and direct use of arrays.
Moreover, the notation is not taught as a separate matter,
but is introduced as needed in conjunction with the concepts represented.
2.
Heavy use is made of arrays to display mathematical properties
of functions in terms of patterns observed in vectors and matrices (tables),
and the make possible the reading, writing, and evaluation
of a host of interesting algebraic sentences before approaching
the analysis of sentences and the concomitant development of identities.
Such an approach has been adopted in the present text,
where it has been carried through as far as the treatment
of polynomials and of linear functions and linear equations.
The extension to further work in polynomials,
to slopes and derivatives, and to the circular and hyperbolic functions
is carried forward in Chapters 4-8 of Iverson
[3].
It must be emphasized that the proposed notation,
though simple, is not limited in application to elementary algebra.
A glance at the bibliography of Rault and Demars
[4]
will give some idea of the wide range of applicability.
The role of the computer.
Because the proposed notation is simple and systematic
it can be executed by automatic computers
and has been made available on a number of time-shared
computer terminal systems.
The most widely used of these
is described in Falkoff and Iverson
[5].
It is important to note that the notation is executed directly,
and the user need learn nothing about the computer itself.
In fact, each of the examples in this appendix are shown
exactly as they would be typed on a computer terminal keyboard.
The computer can obviously be useful in cases
where a good deal of tedious computation is required,
but it can be useful in other ways as well.
For example, it can be used by a student to explore
the behaviour of functions and discover their properties.
To do this a student will simply enter expressions
which apply the functions to various arguments.
If the terminal is equipped with a display device,
then such exploration can even be done collectively
by an entire class.
This and other ways of using the computer
are discussed by Berry et al
[6]
and in Appendix C.
Rault., J. C., and G. Demars, "Is APL Epidemic? Or a study of its growth
through an extended bibliography",
Fourth International APL User's Conference,
Board of Education of the City of Atlanta, Georgia, 1972. | 677.169 | 1 |
Calculators are allowed within each mathematics classroom as a tool to facilitate calculations within complex problems. However, if the intent of the problem is a simple calculation such as a typical number sense problem found on an AIMS test review, calculators are not allowed.
To support this policy:
* Calculators ARE NOT ALLOWED within the Algebra 1/2 classes.
* A basic scientific calculator may be used within the Geometry classes.
All Geometry classes use the "AIMing for Success" program to incorporate daily practice on AIMS performance objectives within their regular activities.
All juniors and seniors have the option to enroll in individualized AIMS tutoring sessions held after school.
Help
All mathematics teachers encourage students to seek additional on any concepts causing confusion or if an assignments requires an individual more than 30 minutes to complete. Regular office hours are held both before anf after school.
Categories
Students can expect to receive daily homework assignments (including Fridays) designed to practice curriculum objectives. Assignments will generally be started during the class period, but students should expect to be responsible for up to 30 minutes of daily work outside of the class period. | 677.169 | 1 |
This course will be a gentle introduction to the basic concepts of number
theory: prime numbers, factorization, and congruences. Using these
concepts we will be able to investigate such diverse topics as 2,000-year-old
word problems, "casting out nines" to check arithmetical calculations,
perpetual calendars, and the Pythagorean Theorem. A highlight of
the course will be a thorough discussion of the RSA (public key) cryptography
system, which is still widely used by government and industry. By
the end of the course, students will be able to understand what the RSA
system is, how it works, and why it is so difficult to crack.
Use of the Web
Every enrolled student will be given an account on the Mathematics department
undergraduate computer lab located in the MSRC building. The computer
lab is open 24 hours a day. As part of your account, you will have
a quota of 100 pages of free printouts. You may also access the course
web page on any public terminal at UBC, or via your own internet connection.
All documents will be posted in PDF format and can be read with the
free Acrobat reader. This software is already installed on the computers
in the Math lab. You may also download
the free Acrobat reader at no cost.
Evaluation
There will be two midterm exams and one final exam as well as weekly homework
assignments. The course mark will be computed as follows:
Final exam
: 50 percent
Midterm exams (in class) : October 5th, November 9th : 40 percent
Homework: 10 percent
You are required to be present at all examinations. No makeup
tests will be given. Non-attendance at an exam will result in a mark
of zero being recorded. Unavoidable, documented medical emergencies
are the only exception to this policy.
Homework will be assigned on Fridays and due the following Friday
in class. Late homework will not be accepted. Students are allowed
to consult one another concerning the homework problems, but your submitted
solutions must be written by you in your own words. If two students submit
virtually identical answers to a question, both can be found guilty of
plagiarism. The lowest assignment grade will be dropped.
Course syllabus
We will cover a variety of standard topics in Number theory and will, if time permits,
touch on additional themes such as deterministic primality testing and Diophantine
equations. | 677.169 | 1 |
books.google.com - The Oxford Users' Guide to Mathematics is one of the leading handbooks on mathematics available. It presents a comprehensive modern picture of mathematics and emphasises the relations between the different branches of mathematics, and the applications of mathematics in engineering and the natural sciences.... Users' Guide to Mathematics | 677.169 | 1 |
Customer Reviews for TMW Media Group Fundamentals of Probability DVD
The Probability & Statistics Tutor: Learning By Example DVD Series teaches students through step-by-step example problems that progressively become more difficult. This DVD covers the fundamentals of probability in Probability and Statistics, including what the concept of probability really means and why it is important. Grades 9-12. 69 minutes on DVD.
Customer Reviews for Fundamentals of Probability DVD
This product has not yet been reviewed. Click here to continue to the product details page. | 677.169 | 1 |
Textbooks, Teachers' Guides, Workbooks, Workbook Teacher's Guides, and
Question Banks are available in this series. The textbooks in this series are
formatted in the same manner. Each chapter has features such as opener,
activities, examples, exercises, and more. In the right margin are features that
enhance the lessons. The format is colorful, pleasing, and not over busy which
is a plus for visual students.
Update
NAME CHANGE: Levels 7 and 8 are now called Singapore Math®
Dimensions (Discovering) Mathematics Common Core Series
Very few of the components of Level 2 are available at this time. We haven't heard if
these will be back in publication. Since they are changing the name of the new
series to Dimensions, we can't help but wonder.
Levels 3 and 4 will remain the same at this time.
The main differences in
the new Common Core Standards edition is the addition of the topics that
apply to the CCS. It looks like the topics may be moved around a bit, but
all of the material covered in the DM Levels 1 and 2 will still be covered
in the new CCS Levels 7 and 8.
Discovering Mathematics 1 Question Bank
Teachers can use Question Bank 1 Banks 7A and
7B.
Discovering Mathematics Textbook 2B
This book is being replaced with Discovering Mathematics CCS Textbook
8B. It will be available in late 2012.
Grade 8
ISBN-10: 9814176699
Price $20.50
Discovering Mathematics Teacher's Guide 2B
Publisher: Singapore Math
This book is being replaced with Discovering Mathematics CCS Teacher
Notes and Solutions 8B and will be available in late 2012.
Grade 8
ISBN-13: 9789814236577
Price $30.00
One Copy Available
Discovering Mathematics Workbook 2
This book is being replaced with Discovering Mathematics CCS Workbook
8. It will be available in late 2012.
Grade 8
ISBN-13: 9789814249201
Price $14.50
One Copy Available
Discovering Mathematics Workbook 2 Teacher's Edition
This book is being replaced with Discovering Mathematics CCS Workbook
Solutions 8. It will be available at the end of 2012
Grade 8
ISBN-13: 9789814249218
Price $30.00
One Copy Available
Discovering Mathematics Textbook 2A
Publisher: Singapore Math
This book is being replaced with Discovering Mathematics CCS Textbook 8A. It will be available in late 2012.
Grade 8
ISBN-10: 9814176680
Price $20.50
Unavailable at this time
Discovering Mathematics Teacher's Guide 2A
Publisher: Singapore Math
This book is being replaced with Discovering Mathematics CCS Teacher
Notes and Solutions 8A and will be available in late 2012.
Grade 8
ISBN-13: 9789814236553
Price $30.00
Unavailable at this time
Discovering Mathematics Question Bank 2A
Teachers can use Question Bank 2AA.
Grade 8
ISBN-13: 9789814236539
Price $17.00
Unavailable at this time
Discovering Mathematics Question Bank 2B
Teachers can use Question Bank 2BB. | 677.169 | 1 |
Many students face problems when doing algebra factoring. Although they know the basics of factoring and many more advance equations, when they do their homework, or face exams, they experience difficulties even with simple questions related to factor finding.
Now students have a great solution to this problem. The Algebra factoring calculator can find factors for them. Students just have to key the equations and the algebra-factoring calculator displays the right answers very fast. With this gadget, they can spare considerable time from their homework and spend more time on other subjects. Many professionals also use algebra factoring calculators to do many work related equations.
The algebra-factoring calculator can simplify advance algebraic expressions. People use the algebra factoring calculator to simplify polynomials, exponential expressions, roots and fractions giving it absolute values and radicals as well. It can find LCM and GCF as well as simplify complex numbers.
The Algebra factoring calculator can also find factors of quadratic, and linear equations. It gives you inequalities of them including exponential equations and logarithmic equations. It could easily solve problems with two and three equation in the linear equations and Cramer's rule. The algebra-factoring calculator help work with lines, parabolas, hyperbolas, circles, ellipses, equation and inequality problems.
Furthermore, the algebra-factoring calculator is well versed with typical graphic function such as composition, inverse, domain and range. Students can simplify logarithms and find similarities of basic geometry and trigonometry and calculate trig functions. It also helps to do arithmetic and pre-algebra lessons such as ratios, proportions and measurements.
You can find many algebra factoring calculators online. They display step-by-step instruction on how to do equation and get factors of them. Many reviews, articles, and details immensely help students to find correct answers for their complex problems.
Many students and professionals who use algebra factoring calculators have put reviews on these software applications online. These reviews help you to understand their functions and limits.
You can download factoring software such as Algebra Buster. With this type of calculators, you can do all your homework with zero problems. You don't have to join an Algebra class and this means you save the money. You just have to enter your homework algebra problem and you will get the answer. If there are areas, where you cannot understand, the Algebra Buster can produce correct answers. A great number of other algebra factoring software is also available from Internet. Some are really good products while others sometime produce erroneous answers. | 677.169 | 1 |
Author comments
Stan Gibilisco is one of McGraw-Hill's most diverse and best-selling authors. His clear, friendly, easy-to-read writing style makes his electronics titles accessible to a wide audience and his background in mathematics and research make him an ideal handbook editor. He is the author of The TAB Encyclopedia of Electronics for Technicians and Hobbyists Teach Yourself Electricity and Electronics, and The Illustrated Dictionary of Electronics. Booklist named his book, The McGraw-Hill Encyclopedia of Personal Computing, one of the Best References of 1996.
Back cover copy
LEARN GEOMETRY FROM AN ALL-NEW ANGLE!
Now anyone with an interest in basic, practical geometry can master it -- without formal training, unlimited time, or a genius IQ. In Geometry Demystified, best-selling author Stan Gibilisco provides a fun, effective, and totally painless way to learn the fundamentals and general concepts of geometry.
With Geometry Demystified you master the subject one simple step at a time -- at your own speed. This unique self-teaching guide offers multiple-choice questions at the end of each chapter and section to pinpoint weaknesses, and a 100-question final exam to reinforce the entire book.
Simple enough for beginners but challenging enough for advanced students, Geometry Demystified is your direct route to learning or brushing up on this essential math subject. | 677.169 | 1 |
Inductive and deductive thinking skills will be used in problem solving situations, and applications to the real world. Emphasizing on proofs to solve (prove) properties of geometric figures. I will cover topics in Algebra ranging from polynomial, rational, and exponential functions to conic sections.The student learns to develop skills in problem solving dealing with rates of change and develops skills to use differential calculus with integral calculus to attack differential equations of various types. Also, differentials become the basis for some fundamental equations used in every day mathematics. Chemistry involves more than just boring theories and difficult lab experiments. | 677.169 | 1 |
Browse
What is a Group? Groups are mathematical structures which are central to abstract algebra and in fact form their own subject known as Group Theory. They are very simple to understand, as they only have four true requirements, and we will see examples that point back to our days in junior high school algebra class. […] | 677.169 | 1 |
Intermediate Algebra - 2nd edition
Summary: This student-focused text addresses individual learning styles through the use of a complete study system that starts with a learning styles inventory and presents targeted learning strategies designed to guide students toward success in this and future college-level courses.
Students who approach math with trepidation will find that Intermediate Algebra, Second Edition, builds competence and confidence. The study system, introduced at the outset and used c...show moreonsistently throughout the text, transforms the student experience by applying time-tested strategies to the study of mathematics. Learning strategies dovetail nicely into the overall system and build on individual learning styles by addressing students' 'big picture' of algebra. ...show less
032135835X60 | 677.169 | 1 |
Math Study Skills Workbook
Math Study Skills Workbook, 4th Edition
Summary
This workbook helps learners identify their strengths, weaknesses, and personal learning styles--and then presents an easy-to-follow system to increase their success in mathematics. With helpful study tips and test-taking strategies, this workbook can help reduce "math anxiety" and help readers become more effective at studying and learning mathematics. | 677.169 | 1 |
HMH FUSE: Algebra 1
Description
WHAT
The award-winning and revolutionary HMH Fuse™ is a highly interactive and engaging curriculum designed for the Apple iPad. HMH Fuse Algebra 1 gives every student a personalized learning experience. Students and Teachers use video tutorials, StepReveal- the award winning way we guide students through step-by-step examples, homework help, quizzes, tips, hints, and many other integrated feat... | 677.169 | 1 |
...The GED Mathematics Test assesses an understanding of mathematical concepts such as problem-solving, analytical, and reasoning skills; focuses on Numbers Operations and Number Sense, Measurement and Geometry, Data Analysis, probability, and algebra. ACT Math is a collection of pre-algebra, eleme... | 677.169 | 1 |
Sum Rule Teacher Resources
Find Sum Rule educational ideas and activities
Title
Resource Type
Views
Grade
Rating
Twelfth graders explore the concept of limits. In this calculus lesson plan, 12th graders investigate the limit rules for both finite and infinite limits through the use of the TI-89 calculator. The worksheet includes examples for each rule and a section for students to try other examples.
Students practice calculating and analyzing Riemann sums and illustrate when Riemann sums will over/under-approximate a definite integral. They view how the convergence of Riemann sums as the number of subintervals get larger.
Students explore the area under a curve. In this calculus lesson plan, students investigate Riemann sums as they employ technology to discover that if enough Riemann sums are used. Students then determine whether the area under a curve can be calculated with the required degree of precision. TI-nspire and appropriate applications are required.
Students find patterns in a sequence. In this sequences and series instructional activity, students use their calculator to find the sequence of partial sums. They graph functions and explore convergent series. Students approximate alternating series.
Students read an article on how calculus is used in the real world. In this calculus lesson plan, students draw a correlation between the Battle of Trafalgar and calculus. The purpose of this article is the show everyday uses for calculus in the real world.
In this numerical integration worksheet, students approximate the value of an integral using the methods taught in the class. They use left-hand Riemann sums, right-hand Riemann sums, the midpoint method and the trapezoidal ruleStudents use the derivative and integral to solve problems involving areas. In this calculus lesson, students calculate the area under a curve as they follow a robot off road making different curves along the drive. They use Riemann Sums and Trapezoidal rules to solve the problem.
Students read about AP calculus online. For this calculus lesson, students learn real life usage for calculus. They read about instructors and their experience teaching and incorporating calculus into the real world.
Twelfth graders investigate derivatives. For this calculus lesson, 12th graders use technology to explore the basic derivatives and how to choose the proper formula to use them. The lesson requires the use of the TI-89 or Voyage and the appropriate application.
Pupils practice the concept of graphing associated to a function with its derivative. They define the concepts of increasing and decreasing function behavior and explore graphical and symbolic designs to show why the derivative can be used as an indicator for the behavior.
Students assess transformations to remove integral symbols as well as to simplify expressions. They explore the Symbolic Math Guide to assist them in solving indefinite integration by parts. This lesson includes partial fractions, sum/difference and scalar product transformations.
In this electrical worksheet, students draw a schematic design circuit board to grasp the understanding amplification in linear circuitry before answering a series of 35 open-ended questions pertaining to a variety of linear circuitry. This worksheet is printable and there are on-line answers to the questions. An understanding of calculus is needed to complete these questions. | 677.169 | 1 |
Basic Math, Math for the Trades, Occupational Math, and similar basic math skills courses offered by trade or technical departments at the undergraduate/graduate level.Now in its sixth edition, Mathematics for the Trades provides the practical mathematical skills needed in a wide variety of trade and technical areas, including electronics, auto mechanics, construction trades, air conditioning, machine technology, welding, and drafting. The authors use a clear and easy to follow format which provides immediate feedback for each step the student takes to ensure understanding and continued attention. There is an emphasis on explaining concepts rather than simply presenting them. | 677.169 | 1 |
books.google.co.jp - This volume provides a comprehensive, up-to-date survey of inequalities that involve a relationship between a function and its derivatives or integrals. The book is divided into 18 chapters, some of which are devoted to specific inequalities such as those of Kolmogorov-Landau, Wirtinger, Hardy, Carlson,... Involving Functions and Their Integrals and Derivatives | 677.169 | 1 |
Casio scientific calculator
Casio scientific calculator
Students and professionals from the engineering and science field, perform lot of calculations. Very often, these calculations involve large digit-ed numbers and using many mathematical functions. Remember the Sin, Cos, Tan functions? Those involved in statistical calculations, also require functions such as Random, Log etc. These calculations are time consuming and due to the probability of human error, there are chances, that the calculated figure may be wrong. A single error can result in a cumulative error; especially, if the calculation is part of a long chain of calculations. Casio scientific calculators offer a solution to such calculation problems. Casio scientific calculators are identified by the familiar ìFXî in its model name. These calculators can perform scores of different functions in a blink of an eye and one can be certain that the answers are always correct. The wide range of mathematical functions, which the Casio scientific calculator can handle, makes these calculators suitable for scientific and statistical calculations. These calculators generally have an 8+2 or 12+2 LCD display. Casio scientific calculators are slim, sleek and light weight. Most of Casio calculators are enclosed in a hard case, to protect it from damage. In some models the hard case can be used as a base for the calculator. Casio scientific calculators consume very little power, making the battery last for a long, long time. In most models, the battery can last for up to 2 years of continuous operation. Some of the popular models of scientific calculators are FX 100s, FX 115 MS, FX 260 solar calculator, and FX 300 MS. Casio scientific calculators are very popular with students and professionals alike. | 677.169 | 1 |
Math 197S: Symmetry, Geometry, and Optimization
What is this Document?
This page contains information about the Fall 1998 version of
Math 197S, entitled "Symmetry, Geometry, and Optimization" being
taught by
Robert L. Bryant.
Course Synopsis
We will look at some classical problems involving soap bubbles and films,
curves of shortest descent (Brachistochrone problems), shortest paths on
curved surfaces, and the motion and shape of elastic rods and strings.
All of these will be used as motivation for introducing the ideas
of the calculus of variations and studying how they interact with geometric
notions, such as symmetry, both in problems and solutions. If time permits,
we may study some higher dimensional problems, such as Poincaré's famous
analysis of the three-body problem in celestial mechanics.
More description
If you are interested in learning something about the field
of optimization, particularly as it applies to problems in geometry
and physics, I'd like to encourage you to consider taking a new
course, Math 197S, that is being taught this fall by Professor Bryant.
If you've ever wondered what mathematics can be applied to such
diverse problems as:
finding the shortest graph connecting a specified set
of vertices, in the plane or in space,
finding the shortest path between two points that lies
on a given surface containing the points,
determining the shape of soap films and soap bubbles,
figuring out why and how rivers meander and what this
has to do with the shape an elastic wire takes when
you clamp the ends in any given position,
how we can most effectively use symmetry in a given
problem involving differential equations to help us
solve it,
what physicists mean when they say space is `curved'
and how do we observe and predict these effects.
All this and more will be treated in Math 197S this fall. If
you enjoyed Frank Morgan's DUMU talk this spring, and are looking
for some way to follow up on the sort of issues that he raised,
this would be a good place ot start.
The background that Professor Bryant will be assuming is a
facility with vector calculus and some familiarity with the basics
of linear algebra and differential equations. (Don't worry, you
won't be required to know all sorts of tricks for solving differential
equations. In fact, one of the subjects of the course will be
just where these tricks come from, so Professor Bryant will be
going over this material anyway when it comes up in the course.)
There's no textbook to buy, instead Professor Bryant will
be handing out lecture notes every week. What you should bring to
the course is plenty of curiosity and a willingness to share in
the work.
What, when, and where
Lectures: 2:15--3:30, Tuesday and Thursday, in Physics 218
Text: None. Lecture notes will be provided by the professor.
Grading Policies
You'll be assigned problems on a regular basis and will
be expected to present your solutions in class. You'll also
have to write-up an extended project (about 15 to 20 pages) by the end of the
term, explaining and giving your solution to a problem selected by
you in consultation with Professor Bryant.
Robert L. Bryant <[email protected]> | 677.169 | 1 |
Beginning Pre-Calculus for Game Developers
9781598632910
ISBN:
1598632914
Edition: 1 Pub Date: 2006 Publisher: Course Technology
Summary: Beginning Pre-Calculus for Game Developers provides entertaining, hands-on explanations of topics central to calculus as related to game development. It explains the mathematics and programming involved in developing nine computer programming applications furnished with the book's CD-ROM. Begin by working your way through first semester calculus topics and then use your new math skills to create programs that apply e...ach topic. Beginning Pre-Calculus presents math topics in a method that is direct, easy-to-understand, and pertinent to all studies related to calculus math.
Flynt, John P. is the author of Beginning Pre-Calculus for Game Developers, published 2006 under ISBN 9781598632910 and 1598632914. Five hundred forty two Beginning Pre-Calculus for Game Developers textbooks are available for sale on ValoreBooks.com, one hundred ten used from the cheapest price of $10.09, or buy new starting at $12.49 | 677.169 | 1 |
Calcula = THE CALCULATOR ... but not limited to the calculator. Calcula is not a scientific calculator. Calcula is a tool 'all-in-one': instead of having 1, 2, 5, 10, 20 applications that serve as 'technical means' we have only one: Calcula, indeed!So, what is and what makes Calcula?. calculator with the 4 operations, percentage, square root, exponentiation of x, a fraction of 1, form, and factor accumulation and subtraction in memory ... what they do all the calculators, some (not quite all, actually!). storing the list of all the transactions like a roll of paper with its zoom. button to cancel last input CI, C key to cancel the entire operation and key 'tearing paper' to delete all memorized transactions. selection of the number of decimal places, from 0 to 5, with which to develop. currency conversion online, in real time and then, leaning on a free service of common good (the result can be integrated in the operation in progress). conversion between many units of measurement: length, weight, volume, area, etc.. (The result can be integrated in the operation in progress). conversion between different number systems: decimal, octal, hexadecimal and binary (the result, of course decimal) can be integrated in the operation in progress). calculating perimeter, area and volume of many geometric shapes with a list of requests for images and input context to the figure (within the perimeter of the circle or to calculate the volume of the cylinder, or more or less according to your traps, etc..)(The result can be integrated in the operation in progress). expression processing up to 26 variables and many functions available, such as cos, sin, tan, etc.. (The result can be integrated in the operation in progress). development of algebraic proportions of the type: b = x: c-fit of the 3 known values and the processing of the result in 4 combinations (the result can be integrated in the operation in progress). generation of random numbers indicating the amount of numbers to be generated and the minimum and maximum limits (ability to select whether the numbers generated should all be different or with repetitions). elaborations of summations, differences between dates with even numbers add or subtract days. elaboration of summations, differences between zones with even add or subtract a preset time. stopwatch with lap times list the possibility of. flashlight (beam) with a selection of different colors. in cm and inch ruler, and color-changing background and calibration lines for even better viewing of the backlit. compass needle or rotary dial with digital indication of the degree. level graphics and digital indication of the degree of vertical tilt and horizontal. selection if it beeps when you press any buttons or voice with repetition of numbers typed and conducting operations in. ability to change the background color. appropriate option for the configuration settings. Detailed help on all aspects. Calcula the program is released with 2 screens, others are making and will be issued free of charge even after the purchase) to have more or fewer buttons then more or less the same size buttons. In version 1.1.00 there are 2 screens: the no. 0 with all the buttons available, some with 2 or 3 functions enabled via special button shift, the no. 1 instead of the calculator and all transactions with a button that serves as a menu to call up all the other functions.. all the screens are operated by the minimum resolution is 320x480 portrait or landscape (480x320). ON / OFF switch!The program is released in Italian, English | 677.169 | 1 |
The Algebra 2 Tutor DVD Series teaches students the core topics of Algebra 2 and bridges the gap between Algebra 1 and Trigonometry, providing students with essential skills for understanding advanced mathematics.
This lesson teaches students how to solve a system of equations that contain three independent variables. Students are shown how to simplify the equations and substitute them in such a way to cancel one or more variables which then leads to the solution. Grades 8-12. 23 minutes on DVD. | 677.169 | 1 |
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular, their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. This book comprehensively covers all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. The text is based on courses taught successfully over many years at the University of Michigan, Imperial College, London and Pennsylvania State University.
Large collection of stimulating problems associated with each section
Extensive references to both historical background and further development of subject
Based extensively on the material used successfully at the University of Michigan, Imperial College London, and Penn State University
Reviews & endorsements
"The monograph is a very readable, concise presentation of classical prime number theory, giving techniques as well as the underlying ideas, and describing an incredibly large range of topics. A study of this monograph seems to be a must for every number theorist. Hopefully this volume will be available as soon as possible, to renew and broaden the interest in this highly interesting field of analytic prime number theory."
Wolfgang Schwarz, Mathemat | 677.169 | 1 |
The Town lab is looking for motivated undergraduate students who are interested in gaining lab experience as a research assistant. Our lab focuses on the interface between two main systems of the body, the central nervous system and immune system. More specifically, our lab is interested in the innate immune system in Alzheimer's disease. There are projects focused on immune drug deliveries in Alzheimer rats, immune reactions to neural stem cell engraftments, and the basic cellular biology of microglia (the resident immune cells of the brain).
Freshmen and sophomores looking for multiple years of experience are highly encouraged to apply. Juniors with lab experience are also encouraged to apply. Animal handling experience is a bonus. Drosophila experience is also a bonus. We are asking students to dedicate at least 15 hours per week.
If you are interested, please send an email with a one paragraph description of your reasons for wanting to join the Town lab along with your CV to Allan Jensen [email protected]
What does e + π mean and how can we evaluate it? What is the difference in the meaning of the equals sign between x2 −1 = 0, x2 −1 = (x−1)(x+1), (x2 −1)/(x−1) = x+1 and √x2 = x? What does it mean for a line to be straight? Are there lines that are not straight? In Math 499 we will be addressing these questions and more!
In this class we will explore the foundations of mathematics and how we acquire and process mathematical knowledge. We will revisit K-12 mathematics from the point of view of a mathematician. We will explore the roles of metaphors, models, and definitions. We will discuss the use of symbols and see that even in mathematics their meanings are often contextual. We will compare and contrast proofs and convincing arguments and think about the roles they play in developing and understanding mathematics. We will discuss the relationship between mathematics and our physical world and how we use mathematics to understand the physical world. We will consider various algorithms common in K- 12 mathematics and discuss why and how they work. We also will read and discuss the literature on how K-12 mathematics is taught and how we learn and process that knowledge. Throughout the semester, you will also the opportunity to observe and participate in classes at AUGUSTUS HAWKINS High School. This is a new school with a modern curriculum implementing an initiative called the Algebra Project.
This class has no prerequisites. In particular, it is not necessary to have taken any college level math classes; you are only expected to know how to count (albeit fairly well!). However, students must be willing to engage with the material at a mathematically sophisticated level. There will be very little lecturing. There will be a lot of discussion, group work, and both oral and written presentations. This class will be valuable for math majors, anyone with an interest in teaching mathematics, and sociology and psychology majors interested in the science of learning.
The MS in Applied Psychology program at the University of Southern California (formerly known as MHB program) is organizing the event Psyched4Jobs taking place on October 25th, 2013 from 9:00 AM to 1:00 PM. This event is focused on providing undergraduate psychology students who are not seeking careers in clinical training, with the chance to hear first-hand about the opportunities available to them after graduation.
The event will encompass speakers from various fields of study in psychology including: Marketing, Human Resources/Organizational, Mental Health, Applied Behavioral Analysis, with job market and graduate school prep as additional resources for students. The students will be exposed to experts in this field through a series of presentations and get a chance to network and personally discuss their potential interestsWe are looking for a part-time volunteer research assistant for an IRB-approved study on the Genetics of Posttraumatic Stress Disorder (Colin P. Dias, M.D., Principal Investigator, IRB #HS-10-00623). This exciting study is being conducted at the Keck School of Medicine, USC. Recruiting is being done on-site in the Department of Emergency Medicine at LAC + USC Medical Center.
This is an opportunity to cultivate research and clinical skills in a stimulating environment while receiving research training and supervision from our professional research team members.
Undergraduate students majoring in psychology will have opportunities to: Support the study by preparing clinical interview materials and entering data in SPSS. Oversee the entire study process and provide support for the clinical interviewers. Interact with research participants to manage scheduling of interviews.
No cost training and certification in HIPAA, Human Subjects, and Good Clinical Practice compliance.
Participation in monthly clinical supervision with Dr. John Briere, a world expert in treatment of trauma.
Attend research team meetings.
Support in developing your own research project that may be presented at professional conferences.
Advanced undergraduate students may apply for PSYC 391 course credit.
If you are interested in being part of our energetic and skilled research team, please email your CV to Dr. Semple along with a brief cover letter that includes a statement of interest.
Assistantships are available as part of a Directed Research Course or can be done on a volunteer basis. Assistants work on studies examining the role of emotional factors that influence tobacco, alcohol and drug use, as well as other behaviors that impact health (e.g. exercise and diet). Undergraduate assistantships are a great way to gain initial exposure to research in preparation for medical school and graduate school in psychology, neuroscience and public health.
We are currently looking for research assistants who are either fluent in Spanish or have a full day of availability in fall 2013. To get a better understanding of our lab, please check out our website (
3 paid URAP internships: Seeking 3 talented undergrads (biology/pre-med, math/engineering, and computer science/engineering) for a multidisciplinary cancer simulation team. The team will work to make powerful 3-D computer models of cancer user friendly enough for diverse research teams, while testing and refining simulations of invasive breast cancer, stem cell biology, and chemotherapy. Publication and indepdendent study opportunities available. Applications due May 10, interviews May 13-17, and project to run summer 2013-spring 2014. See details in the attached flyer or at MathCancer.org, and apply as instructed to [email protected].
Requirements: Should be a junior or advanced sophomore with a 3.5+ GPA. One position in biology, pre-med or related. One position in math or engineering or related. One position in computer science or engineering or related. Same flyer for all 3 positions. | 677.169 | 1 |
There is a newer edition of this item:
Designed as a companion to The Economist Style Guide, the best-selling guide to writing style, The Economist Numbers Guide is invaluable to anyone who wants to be competent and able to communicate effectively with numbers.
In addition to general advice on basic numeracy, the guide points out common errors and explains the recognized techniques for solving financial problems, analysing information of any kind, and effective decision making. Over one hundred charts, graphs, tables, and feature boxes highlight key points. Also included is an A–Z dictionary of terms covering everything from amortization to zero-sum gameA handy reference to stay on top of global economic trends. In today's global arena it is imperative that business people keep abreast of the economics of nations around the world. Every day features the release of a new barrage of updated economic indicators and figures that carry often hidden messages about the direction of segments of the economy. This pocket reference enables readers to quickly revisit the meaning and impact of late breaking economic news and to make better decisions based on the looming economic terrain.
--This text refers to an out of print or unavailable edition of this title.
From the Inside Flap
Crucial to business success, numerical methods are often viewed as too complex to understand, much less use. They are, in fact, far less complicated, able to be broken down into stepby-step instructions and processed by basic computing devices. This invaluable resource from the publishers of The Economist, the leading international business journal, simplifies and demystifies the numbers game, illustrating just how straightforward—and relatively easy—it really is. Taking you clearly and concisely through numerous fundamental functions, both elementary and advanced, The Economist Numbers Guide arms you with the tools necessary to not only approach numbers with more confidence, but solve financial problems more easily, analyze information more accurately, and make decisions more effectively. Covering finance and investment, forecasting techniques, hypothesis testing, linear programming, and a host of other important topics, it shows you how to handle everything from figuring interest and quantifying risk to projecting inflation and evaluating investment opportunities. In addition to the basic mechanics of numerical techniques, the Guide takes a look at their practical applications, including their role in stock control, simulation, and project management. To help you sidestep potentially costly mistakes, it also highlights common errors to avoid, such as rounding incorrectly and bypassing time series selection. Along with sample calculations, concise definitions, and clear explanations, as well as more than 100 charts, graphs, and tables, The Economist Numbers Guide features an A-to-Z dictionary that encompasses key terms—from autocorrelation to zero sum game—and provides useful reference material on such essentials as conversion factors and formulae for calculating areas and volumes. In-depth and easy-to-use, this is an indispensable reference for business and numbers success.
--This text refers to an out of print or unavailable edition of this title.
Most Helpful Customer Reviews
I have read cover-to-cover a previous edition of this book (when it was published by Wiley in 1998) and recently had an opportunity to carefully peruse this current edition (5th ed. by Bloomberg Press???). What I found is that this is a strange case of how a great book (the 1998 edition) turned into merely a good book (this 5th edition). Because of this regression toward the average, I deducted one star from my review (but still feel that it is good enough for 4 stars).As you may have noticed, I really loved the older edition of The Economist Numbers Guide that I thankfully own. It is a great overview and introduction of mathematics as it relates to business. There are a lot of great things about that edition of this book. One of the things I admired about it was the range of topics covered, from interest rates and basic probability/statistics all the way up to Markov Chains, linear programming, and marginal analysis. It is hard to find the breadth of topics covered in that book elsewhere - whether all in one book or in any combination of books.So I found it perplexing that this 5th edition dedacted some materials and topics covered in older editions. Gone are the interesting discussion of descriptive statistics for sets of data that do not easily conform to any of the standard probability distributions (e.g., where median is the best measure of the 'average' and substitutes must be used for the more common parameters such as standard deviation). I have a hard time finding anything coherent much less accessible on those topics elsewhere so it is a shame that they were left off of the 5th edition.The only new material (not previously present) is a short blurb on public-key cryptography.Read more ›
This book provides concise and clear definitions of business analytics with practical applications. Excellent for the neophyte in business math. Helpful index and glossary to get started. Good guide to use if learning stats or marketing research.
I've been looking for an easy to read, understand and all rounder book in business math and finally i found it. Number Guide is, in most part what I've been looking for. I've been looking for a quick reference that would help me in recalling many math basics especially statistics basics and to be honest was a little lazy in going through a complete course again, however, this book did a great job and served as a compromise for me. I enjoy reading this book everywhere and whenever I have time. Even reading it early morning in the rest room before going to work. This book is an excellent starting point for a more comprehensive, easy to understand number guide detailed book which I hope the author think of writing it as I assure him it would be a best seller and a must have reference for both students and practitioners.
Thanks economist for the excellent serious of books that I became one of its fans.
Appreciative readers (they tend to be long-term readers as well) of the ECONOMIST sometimes wonder why misspellings and non sequiturs are virtually absent from that superb weekly magazine.
The answer?: an obsessive dedication to editorial rigor, nowhere better exemplified than in this 'style guide' for the numbers set. It doubles as a methodological guide, for it sets out near canonical equations and means for solving economic problems.
Nine chapters cover:
Key concepts
Finance and investment
Descriptive measures for interpretation and analysis
Tables and charts
Forecasting techniques
Sampling and hypothesis testing
Incorporating judgments into decisions
Decision-making in action
Linear programming and networking
This guide should be required reading for everyone who manages from a numbers-intensive platform. | 677.169 | 1 |
Mathematical Reasoning Writing And Proof
9780131877184
ISBN:
0131877186
Edition: 2 Pub Date: 2006 Publisher: Prentice Hall
Summary: Focusing on the formal development of mathematics, this book shows readers how to read, understand, write, and construct mathematical proofs. Uses elementary number theory and congruence arithmetic throughout. Focuses on writing in mathematics. Reviews prior mathematical work with " Preview Activities" at the start of each section. Includes " Activities" throughout that relate to the material contained in each sectio...n. Focuses on Congruence Notation and Elementary Number Theorythroughout. For professionals in the sciences or engineering who need to brush up on their advanced mathematics skills. Mathematical Reasoning: Writing and Proof, 2/E Theodore Sundstrom
Sundstrom, Ted is the author of Mathematical Reasoning Writing And Proof, published 2006 under ISBN 9780131877184 and 0131877186. One hundred forty eight Mathematical Reasoning Writing And Proof textbooks are available for sale on ValoreBooks.com, twenty five used from the cheapest price of $53.45, or buy new starting at $12477184-4-0-3 Orders ship the same or next business day. Expedited shipping within U.S. [more]
May include moderately worn cover, writing, markings or slight discoloration. SKU:9780131877184 | 677.169 | 1 |
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Maple Ta
Maple T.A. is an online assessment tool that is built into Blackboard. Although any instructor can use the application to build online tests, it may be most appealing to faculty in math and science due to its built-in math functions and mathematical versatility. Faculty can use this software to display mathematical notation in their questions and students can create free-form mathematical responses. Hundreds of sample questions, that can be used as-is or modified, are available within the software.
Maple T.A. also provides an abundance of statistical information at both the course level and individual student level. For example, on the entry exams, in addition to a list of students' final scores, faculty can access the dates on which students took the exam and the amount of time they spent on it. The percentage of students who answered each question correctly as well as an individual student's answers can be determined. This type of information is extremely useful in identifying weaknesses in the calculus sequence, as well as weaknesses for individual students.
Maple T.A. ™ has partnered with the Mathematics Association of America (MAA) in order to maintain the functional standard of the product. | 677.169 | 1 |
MATH 74
Transition To Upper Division Mathematics
Course info & reviews
The course will focus on reading and understanding mathematical proofs. It will emphasize precise thinking and the presentation of mathematical results both orally and in written form. The course is intended for students who are considering majoring in mathematics but wish additional training. | 677.169 | 1 |
Galois' Theory of Algebraic Equations gives a detailed account of the development of the theory of algebraic equations, from its origins in ancient times to its completion by Galois in the nineteenth century. The main emphasis is placed on equations of at least the third degree, i.e. on the developments during the period from the sixteenth to the... more... | 677.169 | 1 |
Sc in Mathematical Finance This part-time, modular MSc is flexibly designed for those in full-time employment in the UK and overseas. It covers the most important technical and quantitative aspects of finance in regular use in financial institutions.
Nice and Noughtie Numbers This course shows how numbers are fundamental to many aspects of our civilization. It covers topics such as counting systems, prime numbers, the importance of zero, musical scales, bell ringing, the calendar and seasons, and encryption of messages.
Mathematical finance This flexible, part-time Programme is designed to allow those working full-time to develop expertise in mathematical finance without compromising their professional work.
Basic Statistics for the Social Sciences The aim of this course is to provide a good grounding in the basic statistical methods used in the social sciences - in particular in Business Studies, Economics, Psychology and their applications.
You Can Count on It - Maths in Finance In this brief course we shall look at how mathematics contributes to finance and business. Our course is suitable for people with previous experience of mathematics at the sixth-form level and aims to provide an elementary introduction to the mathematics.
Alternatively you can perform a keyword search on all our courses using the 'Find courses' box on this page. | 677.169 | 1 |
If you provide us with a few extra details when you register you will receive a free publication and become an Associate of ATM.
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Mathematics for Primary and Early Years: Developing Subject Knowledge
How the publisher describes it:
"This task-driven text emphasizes strategies and processes and is very different from the usual style of mathematics textbooks. For example, algebra is treated as a way of thinking mathematically, rather than merely manipulating symbols. Each of the sections is designed to stand alone so that they can be studied in any order or dipped into as needed."
Review by Matthew Reames
In brief:
Unfortunately misnamed, this book is not a guide to primary and early years mathematics. Instead, it is a self-study text for people hoping to improve their mathematical understanding and confidence.
"A useful resource for people wishing to brush up on their knowledge of mathematical ideas and concepts up to GCSE level."
Mathematics for Primary and Early Years: Developing Subject Knowledge is not a guide to primary mathematics at all. Instead, it is part revision book, part refresher course of maths to GCSE level.
Written as part of the series Developing Subject Knowledge, this book is one of several used in an Open University course as part of the Foundation Degree in Early Years. Each chapter covers a different mathematical strand: number, measures and proportion, statistics, algebra, geometry, chance, and proof. The book is designed to be a self-study text for people who are trying to build their confidence in mathematics.
While the book seems rather useful as a basic mathematical reference text (if encountering gradians, for example, turn to page 53 for a description), it seems that the title is unfortunately misleading: those looking for a maths revision guide will miss it while those hoping for help developing their knowledge of primary and early years maths will be rather disappointed.
Matthew Reames • Former Head of Mathematics, St Edmund's Junior School, Canterbury, now PhD student in mathematics education at the University of Virginia | 677.169 | 1 |
Vector Calculus and Applications
Module aims:
This module is an introduction to vector calculus and its applications especially fluid dynamics. It lays down some basic principles using a number of simplifying assumptions. It examines how one can use vector formalism and calculus together to describe and solve many problems in two and three dimensions. For example, the rules that govern the flow of fluids and the motion of solids can be described using vector calculus, with resulting laws of motion described by partial differential equations rather than ordinary differential equations. The emphasis will be on inviscid, incompressible flows: viscous flow is the subject of later modules. Applications include the design of aeroplanes, car body shapes and the flows of liquids and gases through pipes. These problems raise important questions, such as: How is flight possible? How can one minimise drag? How do vortices form? What is pressure and how does it interact with the flow? Physical applications include meteorology (fluid dynamics applied to weather forecasting and events such as tornadoes and hurricanes) and oceanography (fluid dynamics applied to ocean currents, tides and waves). This module is a prerequisite for a number of more specialist modules in the third year.
Please note that full specifications are not currently available for download. This usually indicates that the module isn't being taught in this current academic year and details will be available soon. Please get in contact if you have any further questions about this module or programme structure. | 677.169 | 1 |
This second, updated edition of the admired introduction to discrete mathematics is a detailed guide both to the subject itself and to its relationship with other topics including set theory, probability, cryptography, graph theory... | 677.169 | 1 |
College Teachers -
Internet Projects
The Math Forum hosts a project called Ask Dr. Math. It provides students (primarily K-12) all over the world with a place to pose their questions
about mathematics. Not only is this a great service to the students, but it
is also a lot of fun for the "doctors."
As this project becomes more and more popular, the demand for doctors
increases too. If you know of any college students who would like to spend
a little time answering fun and challenging math questions on the Internet,
please let us
know.
Stan Wagon, a professor in the Mathematics and Computer Science Department
at Macalester College, poses a
mathematics problem to his students every week. The problems are meant to be
accessible to first-year college
students, so very little background is needed to understand or solve them.
They are also sent out by electronic
mail and an archive of some older Problems of the Week is also maintained at
Macalester. The archives of the Macalester Problems of the Week are housed
at the Math Forum.
A database containing materials designed to help teach a CHANCE course
or a more standard introductory probability or statistics course. The aim of
CHANCE is to make students more informed, and critical, readers of current
news that uses probability and statistics as reported in daily newspapers
such as "The New York Times" and the "The Washington Post" and current
journals and magazines such as "Chance," "Science," "Nature," and the "New
England Journal of Medicine."
Chance News, a biweekly news letter that provides abstracts of
articles in current newspapers and journals. Links are made
to the full text of the article when it is available and to resources at
other Web sites. Discussion questions are provided for
many of the articles.
Syllabi of previous CHANCE courses and articles that have been written
about the CHANCE course.
Teaching aids by topic, descriptions of activities, data sets,
videotapes, and other resources that may be useful in teaching a CHANCE
course and/or other introductory statistics or probability courses. | 677.169 | 1 |
Trigonometry - 2nd edition
Summary: Engineers trying to learn trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous Parallel Words and Math...show more examples are included that provide more detailed annotations using everyday language. Your Turn exercises reinforce concepts and allow readers to see the connection between the problems and examples. Catch the Mistake exercises also enable them to review answers and find errors in the given solutions. This approach gives them the skills to understand and apply trigonometry45 +$3.99 s/h
Acceptable
BookCellar-NH Nashua, NH
0470222719 Has heavy shelf wear, corner wear, highlighting, underlining & or writing. CD-ROM or supplement may not be included. The book is still a good reading copy.A portion of your purchase of this...show more | 677.169 | 1 |
Discrete Mathematics For Computer Science
9781930190863
ISBN:
1930190867
Pub Date: 2005 Publisher: Key College Publishing
Summary: "Discrete Mathematics for Computer Science" is the perfect text to combine the fields of mathematics and computer science. Written by leading academics in the field of computer science, readers will gain the skills needed to write and understand the concept of proof. This text teaches all the math, with the exception of linear algebra, that is needed to succeed in computer science. The book explores the topics of bas...ic combinatorics, number and graph theory, logic and proof techniques, and many more. Appropriate for large or small class sizes or self study for the motivated professional reader. Assumes familiarity with data structures. Early treatment of number theory and combinatorics allow readers to explore RSA encryption early and also to encourage them to use their knowledge of hashing and trees (from CS2) before those topics are covered in this course.
Bogart, Kenneth P. is the author of Discrete Mathematics For Computer Science, published 2005 under ISBN 9781930190863 and 1930190867. One hundred twenty four Discrete Mathematics For Computer Science textbooks are available for sale on ValoreBooks.com, nine used from the cheapest price of $4.50, or buy new starting at $23.31 | 677.169 | 1 |
Special Functions of Mathematics for Engineers, Second Edition
Modern engineering and physical science applications demand a thorough knowledge of applied mathematics, particularly special functions. These typically arise in applications such as communication systems, electro-optics, nonlinear wave propagation, electromagnetic theory, electric circuit theory, and quantum mechanics. This text systematically introduces special functions and explores their properties and applications in engineering and science.
Publishers' note: This new softcover printing of the Second Edition of Special Functions of Mathematics
for Engineers, originally published by McGraw-Hill in 1992, includes known corrections to the
text and formulas. Because of the importance of this material in modern engineering, SPIE The
International Society for Optical Engineering and Oxford University Press are republishing it to
make it available to the engineering, science, and mathematics communities.
Modern engineering and physical science applications demand a more thorough knowledge of
applied mathematics particularly special functions than ever before. These functions typically
arise in applications such as communication systems, electro-optics, nonlinear wave propagation,
electromagnetic theory, electric circuit theory, and quantum mechanics, among others. This book
systematically introduces important special functions and explores their properties and
applications in engineering and science.
The book is suitable as a classroom textbook in courses dealing with higher mathematical
functions or as a reference text for practicing engineers and scientists. The second edition includes
numerous applications drawn from a variety of fields, including fiber optics, statistical
communication theory, vibration phenomena, and fluid mechanics. Whenever possible, related
applications are discussed in the chapter introducing the special function. The volume includes a
brief review of calculus concepts, such as infinite series and improper integrals, because of their
close association with special functions. Each chapter includes exercises to facilitate learning.
Larry C. Andrews is a professor of mathematics at the University of Central Florida and a
member of the Department of Electrical and Computer Engineering. Dr. Andrews is also an
associate member of the Center for Research and Education in Optics and Lasers (CREOL).
Along with special functions, his research interests include laser beam propagation through
random media, detection theory, and signal processing. | 677.169 | 1 |
Michael Hunt on Scheme and algebra
High school math teacher Michael Hunt reports on his first three weeks
of class:
Class periods are 40 minutes twice a week and 45 minutes three times a week.
We've completed day 12 (that is, 9.5 instructional days) and completed the
area-of-ring problem today. We've also done convert3 along the way. My
goal is to finish the first extended exercise with the ping-pong game
(hopefully by Christmas).
For context, the majority of my students "took" Algebra One at various
(mostly private) schools in and around Houston last year in eighth grade,
but did not score well enough on our diagnostic test to place out of Algebra
One and into Geometry in ninth grade. A small minority of my students took
Pre-algebra in eighth grade. A still smaller minority are repeating Algebra
One, having failed it here as ninth graders last year. The pace
deliberately favors these minorities of students and appears to be as
fast as about 50% of the students can go. At the start, most of these
students were unfamiliar with the word "function" and many could not either
remember or apply the order of operations rules, for examples. Many are
challenged to correctly compute arithmetic expressions without the use of a
calculator.
In fairness, students here historically have not been exposed to the
word "function" in Algebra One until the last several weeks of the course.
I am enthusiastically pleased so far with the results we've achieved in
Algebra One, using Scheme. Nearly all of the students are now
appropriately
using words like "function" (and even composite function), "evaluate,"
and
"substitute." I was thrilled to have been able to introduce the word
"function" on the first instructional day, particularly with these
students, without overwhelming them with all of the usual conceptual and
notational
overhead as well as I was thrilled to see so many students grasp this
fundamental mathematical concept so effortlessly! | 677.169 | 1 |
TI's first graphing calculator that operates like a computer. Simpler
keypad with separated alpha keys makes navigation through screens, menus and the math objects easier. It includes computer algebra system (CAS) that performs symbolic and numeric calculations seamlessly. | 677.169 | 1 |
027368180X
9780273681809
Essential Mathematics for Economic Analysis:"The book is by far the best choice one can make for a course on mathematics for economists. It is exemplary in finding the right balance between mathematics and economic examples."Dr Roelof J Stroeker, Erasmus University, Rotterdam."The writing style is superb…it manages to allow intuitive understanding whilst not sacrificing mathematical precision and rigour."Dr Steven Cook, University of Wales SwanseaEssential Mathematics for Economic Analysis provides an invaluable introduction to mathematical analysis and linear algebra for economists. Its main purpose is to help students acquire the mathematical skills they need in order to read the less technical literature associated with economic problems. The coverage is comprehensive, ranging from elementary algebra to more advanced material, whilst focusing on all the core topics usually taught in undergraduate courses on mathematics for economists.
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Rent Essential Mathematics for Economic Analysis 2nd edition today, or search our site for Knut textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. | 677.169 | 1 |
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10th maths guide pdf – samacheer kalvi maths guide for tenth free pdf
10th maths guide pdf is given by our site kinindia for the students reference purpose. many students feels difficulty in solving probelms given in the textbooks.The complete samacheer kalvi maths guide for tenth is given here in the pdf format.
The students can download it freely of sslc maths guide pdf. This premier maths guide for class 10 provides the easy way to solve the mathematical problems in the tenth textbooks. Even for the examples sums the samacheer kalvi sslc Xth guide for maths gives the detailed explanation to understand the problem.
This samacheer kalvi tenth class maths guide deals with all the sums in the textbooks. samacheer kalvi maths study material also provides answers for the objective type questions in all the units. The download link of this guide for class 10 maths pdf free download is given below.
10th Maths samacheer kalvi guide – Tamil Nadu state board
The above link of samacheer kalvi tenth maths guide pdf is taken from the government official site.If you come across any problem in PTA (DPI) sslc maths guide for samacheer kalvi download link please leave a comment below. | 677.169 | 1 |
Middle School Course Offering will be posted shortly, please check back
Math
The 21st century takes us into a new era in mathematics education. Changes in technology have made mathematics an alive and dynamic science in itself, as well as an integral part of our daily lives. Now, more than ever before, educating students for life requires that we provide all students with a strong mathematical background.
Elementary Program
The mathematical instructional approach implemented in kindergarten and first grade classrooms and is based on the recognition of mathematical concepts in the everyday experiences of children. Beginning in elementary school, the mathematics program focuses on the development of critical thinking and problem solving strategies. The use of various manipulatives enables children to enjoy a hands-on approach to learning. Computer software is used to facilitate the acquisition of math skills. Students participate in small group activities where they learn to listen and consider the ideas of others in solving problems. Students continually communicate mathematical ideas and solutions and explain their reasoning.
Middle School Program
At the middle school level, students continue to use manipulatives, calculators and computer software, as well as paper and pencil, mental math, and estimation where appropriate. Real-life applications and cooperative learning are incorporated into the program. Communication skills of reading, writing and discussion are further developed.
Grades six, seven and eight are taught by interdisciplinary teams and students are able to connect mathematics to other disciplines. Honor students accelerate in grade eight and take the NYS regents course, Integrated Algebra, culminating with a regents exam in June. All other eighth grade students take a pre-algebra course in preparation for Integrated Algebra in grade nine. Additionally, seventh graders take the Math Seminar course, which introduces students to explorations of mathematics that extend and enrich the current curriculum with topics such as origami, fractals and Sierpinski's Triangle, and magic squares.
High School Program
At the high school level, the mathematics department follows the new New York State curriculum of Integrated Algebra, Geometry and Algebra 2 Trigonometry. Students completing the required sequence of courses are offered electives, highlighted by our AP Statistics and Computer Science classes.
Within the department, over 200 students are enrolled in Advanced Placement courses, including AP Calculus AB, AP Calculus BC, AP Statistics, and AP Computer Science. Those who do not wish to take Advanced Placement math courses may choose from Honors College Calculus, Advanced Computer Programming, Pre-Calculus or College Prep Algebra. The high percentage of students taking four or more years of mathematics is a measure of the success of our program.
Technology
The use of technology is expanding throughout the district. Since graphing calculators are allowed on state assessments, students receive instruction on the use of these devices. Graphing calculators are also used to enhance teaching in calculus, pre-calculus and elective mathematics courses.
Teacher Workshops
Mathematics teachers are continously staying up to date with the ever changing standards our students are accountable for understanding. All along, we continue to keep a focus on instruction that fosters perseverence, critical and logical thinking while also enfusing joy within our practice.
The accomplishments of the mathematics department are the result of dedicated professionals, involved parents, and motivated students striving for excellence | 677.169 | 1 |
Guys, I need some help with my algebra assignment. It's a really long one having almost 30 questions and it covers topics such as 10th std state syllabus maths very important objectives with answers and steps, 10th std state syllabus maths very important objectives with answers and steps and 10th std state syllabus maths very important objectives with answers and steps. I've been trying to solve those questions since the past 4 days now and still haven't been able to solve even a single one of them. Our teacher gave us this assignment and went on a vacation, so basically we are all on our own now. Can anyone show me the way? Can anyone solve some sample questions for me based on those topics; such solutions would help me solve my own questions as well.
I have a way out for you and trust me it's even better than buying a new textbook. Try Algebrator, it covers a rather elaborate list of mathematical topics and is highly recommended. With it you can solve various types of problems and it'll also address all your enquiries as to how it came up with a particular answer. I tried it when I was having difficulty solving questions based on 10th std state syllabus maths very important objectives with answers and steps and I really enjoyed using it.
Thanks for the detailed instructions, this sounds great. I wished for something just like Algebrator, because I don't want a software which only solves the exercise and gives the final result, I want something that can actually show me how the exercise has to be solved. That way I can understand it and after that solve it without any help, not just copy the answers. Where can I find the program? | 677.169 | 1 |
The student uses numerical and computational concepts and procedures in a variety of situations.
1.1
The student demonstrates number sense for real numbers and algebraic expressions in a variety of situations.
1.1.A1
generates and/or solves real-world problems using equivalent representations of real numbers and algebraic expressions (2.4.A1a) ($), e.g., a math classroom needs 30 books and 15 calculators. If B represents the cost of a book and C represents the cost of a calculator, generate two different expressions to represent the cost of books and calculators for 9 math classrooms.
compares and orders real numbers and/or algebraic expressions and explains the relative magnitude between them (2.4.K1a) ($), e.g., will (5n)² always, sometimes, or never be larger than 5n? The student might respond with (5n)² is greater than 5n if n > 1 and (5n)² is smaller than 5 if o < n < 1.
1.1.A2
determines whether or not solutions to real-world problems using real numbers and algebraic expressions are reasonable (2.4.A1a) ($), e.g., in January, a business gave its employees a 10% raise. The following year, due to the sluggish economy, the employees decided to take a 10% reduction in their salary. Is it reasonable to say they are now making the same wage they made prior to the 10% raise?
1.1.K3
knows and explains what happens to the product or quotient when a real number is multiplied or divided by (2.4.K1a):
1.1.K3A
a rational number greater than zero and less than one,
1.1.K3B
a rational number greater than one,
1.1.K3C
a rational number less than zero.
1.2
The student demonstrates an understanding of the real number system; recognizes, applies, and explains their properties, and extends these properties to algebraic expressions.
1.2.A1
generates and/or solves real-world problems with real numbers using the concepts of these properties to explain reasoning (2.4.A1a) ($):
1.2.A1A
commutative, associative, distributive, and substitution properties, e.g., the chorus is sponsoring a trip to an amusement park. They need to purchase 15 adult tickets at $6 each and 15 student tickets at $4 each. How much money will the chorus need for tickets? Solve this problem two ways.
1.2.A1B
identity and inverse properties of addition and multiplication, e.g., the purchase price (P) of a series EE Savings Bond is found by the formula ½ F = P where F is the face value of the bond. Use the formula to find the face value of a savings bond purchased for $500.
1.2.A1C
symmetric property of equality, e.g., Sam took a $15 check to the bank and received a $10 bill and a $5 bill. Later Sam took a $10 bill and a $5 bill to the bank and received a check for $15. $ addition and multiplication properties of equality, e.g., the total price for the purchase of three shirts in $62.54 including tax. If the tax is 3.89, what is the cost of one shirt, if all shirts cost the same?
1.2.A1D
addition and multiplication properties of equality, e.g., the total price for the purchase of three shirts is $62.54 including tax. If the tax if $3.89, what is the cost of one shirt?
1.2.A1E
zero product property, e.g., Jenny was thinking of two numbers. Jenny said that the product of the two numbers was 0. What could you deduct from this statement? Explain your reasoning.
1.2.K1
explains and illustrates the relationship between the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] using mathematical models (2.4.K1a), e.g., number lines or Venn diagrams.
1.2.K2
identifies all the subsets of the real number system [natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers] to which a given number belongs (2.4.K1m).
1.2.A2
Jenny said that the product of the two numbers was 0. What analyzes and evaluates the advantages and disadvantages of using integers, whole numbers, fractions (including mixed numbers), decimals or irrational numbers and their rational approximations in solving a given real-world problem (2.4.A1a) ($), e.g., a store sells CDs for $12.99 each. Knowing that the sales tax is 7%, Marie estimates the cost of a CD plus tax to be $14.30. She selects nine CDs. The clerk tells Marie her bill is $157.18. How can Marie explain to the clerk she has been overcharged?
1.2.K3
names, uses, and describes these properties with the real number system and demonstrates their meaning including the use of concrete objects (2.4.K1a) ($):
addition and multiplication properties of equality (if a = b, then a + c = b + c and if a = b, then ac = bc) and inequalities (if a > b, then a + c > b + c and if a > b, and c > 0 then ac > bc);
1.2.K3E
zero product property (if ab = 0, then a = 0 and/or b = 0).
1.2.K4
uses and describes these properties with the real number system (2.4.K1a) ($):
1.2.K4A
transitive property (if a = b and b = c, then a = c),
1.2.K4B
reflexive property (a = a).
1.3
The student uses computational estimation with real numbers in a variety of situations.
1.3.A1
adjusts original rational number estimate of a real-world problem based on additional information (a frame of reference) (2.4.A1a) ($), e.g., estimate how long it takes to walk from here to there; time how long it takes to take five steps and adjust your estimate.
uses various estimation strategies and explains how they were used to estimate real number quantities and algebraic expressions (2.4.K1a) ($).
1.3.A2
estimates to check whether or not the result of a real-world problem using real numbers and/or algebraic expressions is reasonable and makes predictions based on the information (2.4.A1a) ($), e.g., if you have a $4,000 debt on a credit card and the minimum of $30 is paid per month, is it reasonable to pay off the debt in 10 years?
1.3.A3
determines if a real-world problem calls for an exact or approximate answer and performs the appropriate computation using various computational strategies including mental math, paper and pencil, concrete objects, and/or appropriate technology (2.4.A1a) ($), e.g., do you need an exact or an approximate answer in calculating the area of the walls to determine the number of rolls of wallpaper needed to paper a room? What would you do if you were wallpapering 2 rooms?
1.3.K3
knows and explains why a decimal representation of an irrational number is an approximate value (2.4.K1a).
1.3.K4
knows and explains between which two consecutive integers an irrational number lies (2.4.K1a).
1.3.A4
explains the impact of estimation on the result of a real-world problem (underestimate, overestimate, range of estimates) (2.4.A1a) ($), e.g., if the weight of 25 pieces of paper was measured as 530.6 grams, what would the weight of 2,000 pieces of paper equal to the nearest gram? If the student were to estimate the weight of one piece of paper as about 20 grams and then multiply this by 2,000 rather than multiply the weight of 25 pieces of paper by 80; the answer would differ by about 2,400 grams. In general, multiplying or dividing by a rounded number will cause greater discrepancies than rounding after multiplying or dividing.
1.4
The student models, performs, and explains computation with real numbers and polynomials in a variety of situations.
applications from business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and square roots when the formulae are given as part of the problem and variables are defined (2.4.A1a) ($), e.g., given F = ma, where F = force in newtons, m = mass in kilograms, a = acceleration in meters per second squared. Find the acceleration if a force of 20 newtons is applied to a mass of 3 kilograms.
1.4.A1B
volume and surface area given the measurement formulas of rectangular solids and cylinders (2.4.A1f), e.g., a silo has a diameter of 8 feet and a height of 20 feet. How many cubic feet of grain can it store?
1.4.A1C
probabilities (2.4.A1h), e.g., if the probability of getting a defective light bulb is 2%, and you buy 150 light bulbs, how many would you expect to be defective?
1.4.A1D
application of percents (2.4.A1a), e.g., given the formula A = P(1+rdivided by n) to the nt, when A = amount, P= principal, r = annual interest, n = number of compounding periods per year, t= number of years. If $1,000 is placed in a savings account with a 6% annual interest rate and is compounded semiannually, how much money will be in the account at the end of 2 years?
1.4.A1E
simple exponential growth and decay (excluding logarithms) and economics (2.4.A1a) ($), e.g., a population of cells doubles every 20 years. If there are 20 cells to start with, how long will it take for there to be more than 150 cells? or If the radiation level is now 400 and it decays by ½ or its half-life is 8 hours, how long will it take for the radiation level to be below an acceptable level of 5?
1.4.K1
computes with efficiency and accuracy using various computational methods including mental math, paper and pencil, concrete objects, and appropriate technology (2.4.K1a) ($).
1.4.K2
performs and explains these computational procedures (2.4.K1a):
1.4.K2A
addition, subtraction, multiplication, and division using the order of operations
1.4.K2B
multiplication or division to find ($):
1.4.K2Bi
a percent of a number, e.g., what is 0.5% of 10?
1.4.K2Bii
percent of increase and decrease, e.g., a college raises its tuition form $1,320 per year to $1,425 per year. What percent is the change in tuition?
1.4.K2Biii
percent one number is of another number, e.g., 89 is what percent of 82?
1.4.K2Biv
a number when a percent of the number is given, e.g., 80 is 32% of what number?
1.4.K2C
manipulation of variable quantities within an equation or inequality (2.4.K1d), e.g., 5x – 3y = 20 could be written as 5x – 20 = 3y or 5x(2x + 3) = 8 could be written as 8/(5x) = 2x + 3;
simplification or evaluation of real numbers and algebraic monomial expressions raised to a whole number power and algebraic binomial expressions squared or cubed;
1.4.K2F
simplification of products and quotients of real number and algebraic monomial expressions using the properties of exponents;
1.4.K2G
matrix addition ($), e.g., when computing (with one operation) a building's expenses (data) monthly, a matrix is created to include each of the different expenses; then at the end of the year, each type of expense for the building is totaled;
1.4.K2H
scalar-matrix multiplication ($), e.g., if a matrix is created with everyone's salary in it, and everyone gets a 10% raise in pay; to find the new salary, the matrix would be multiplied by 1.1.
1.4.K3
finds prime factors, greatest common factor, multiples, and the least common multiple of algebraic expressions (2.4.K1b). | 677.169 | 1 |
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for). | 677.169 | 1 |
Introduction To Graph Theory
9780073204161
ISBN:
0073204161
Pub Date: 2004 Publisher: McGraw-Hill College
Summary: Written by one of the leading authors in the field, this text provides a student-friendly approach to graph theory for undergraduates. Much care has been given to present the material at the most effective level for students taking a first course in graph theory. Gary Chartrand and Ping Zhang's lively and engaging style, historical emphasis, unique examples and clearly-written proof techniques make it a sound yet acc...essible text that stimulates interest in an evolving subject and exploration in its many applications.This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Chartrand, Gary is the author of Introduction To Graph Theory, published 2004 under ISBN 9780073204161 and 0073204161. Two hundred forty Introduction To Graph Theory textbooks are available for sale on ValoreBooks.com, eleven used from the cheapest price of $37.90, or buy new starting at $152.21 464 p. Contains: Illustrations. Walter Rudin Student Series in Advanced Mathematics. Audience: General/trade. BOX # 3812. (Media mail takes 5-14 days) Special note(Used book)I check each pages of this book it is in Very Good Condition. CDs is (not included): This book has Approximate(0)pages contains Answers of all Questions, Notes, Highlight, or Under-lines. This Hard Cover book: Jacket cover is (Good) Stem binding, and all 4 tips cover are (Good): Old(Ex library s Book contains marker s mark, library s logo and Jacket cover cutting ). Jacket cover is ( N/A). Email me before you Return it, If its not in better condition I described | 677.169 | 1 |
The key to doing well on the SAT Math is knowing how to set up and solve word problems.
The SAT Math Review Book for People Who Hate Math differs from the other books on the market because it gives... More > you in-depth teaching on word problems. By studying this book, you will learn how to set up and solve different kinds of word problems: distance, rate of work, mixture, age, money, Pythagorean Theorem problems and many more.
In addition to word problems, the book contains a complete review of arithmetic, algebra, and geometry
Instead of spending four years at your "safety school," get into the college of your dreams by scoring well on the SAT.< Less
New nonlinear concepts for data analysis in life and biomedical sciences are introduced. Biological science is loaded with data with various curves: C-curves, S-curves, and symmetric and asymmetric... More > bell curves, etc,; these curves are nonlinear curves. Different types of cuves are outcome of different nonlinear physical phenomena that can have different degree of nonlinearity and different ways of meauring nonlinearity. All these nonlinear phenomena can be assembled into groups and described by simple nonlinear equations.
A nonlinear phenomenon needs to be described by multiple graphs in association with nonlinear equations. The book discusses the fundamentals of nonlinearity followed by describing the methodoogy for analyzing the nonlinear data. The book is based on two mathematical axioms and two universal standards for linear and nonlinear measurements. A series of Proportionality laws along wth the GVP (graph based, true value compared, and proportionality oriented) math system are discussed.< Less | 677.169 | 1 |
Fourth Edition of Numerical Methods for Engineers continues the tradition of excellence it established as the winner of the ASEE Meriam/Wiley award for BestTextbook. Instructors love it because it is a comprehensive text that is easy to teach from. Students love it because it is written for them—with great pedagogy and clear explanations and examples throughout. This edition features an even broader array of applications, including all engineering disciplines. The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods. What's new in this edition? A shift in orientation toward more use of software packages, specifically MATLAB and Excel with VBA. This includes material on developing MATLAB m-files and VBA macros. In addition, the text has been updated to reflect improvements in MATLAB and Excel since the last edition. Also, many more, and more challenging problems are included. The expanded breadth of engineering disciplines covered is especially evident in the problems, which now cover such areas as biotechnology and biomedical | 677.169 | 1 |
Added 01/03/2008
With this applet you can explore the impact on a graph of a standard function when you change the parameters. You can also change the graph (using the so called hotspots) and see the impact on the parameters. Also, you can take a look at the effects that operations have on one function or on two fucntions.
Added 01/03/2008
This site includes more than 40 tutorials in Intermediate Algebra topics with practice tests and answer keys. The site is designed to assist the user in preparing for math placement tests and the math portion of the GREGrapher allows the user to enter a function of a single variable with up to three parameters, then vary the parameter values with sliders and watch the resulting changes in the function's graph. This applet is part of the National Library of Virtual Manipulatives | 677.169 | 1 |
Most instructors are willing to look the other way if you get a piece of software that will fulfill the same functions as a graphing calculator. There are phone apps, Windows programs, etc which mimic and sometimes perfectly emulate a TI-8X calculator.
There is some worry about cheating during a test, but, there are many way of cheating with graphing calculators alone. It's even easier when you are taking online classes... At some point even cheaters are going to have to show they are competent. If they are paying for college and not learning the material, they are just wasting their money. | 677.169 | 1 |
Limits at a Glance
When looking at limits, precalculus books briefly explain the concept and how to calculate basic problems. Regarding limits, Precalculus helps us understand how to calculate the value of a function at infinity. Particular types of functions, such as certain rational functions, have easier methods for calculating limits. With the introduction to limits, Precalculus gives us our first taste of Calculus. | 677.169 | 1 |
Splines and Variational Methods
by P M Prenter Publisher Comments
One of the clearest available introductions to variational methods, this text requires only a minimal background in linear algebra and analysis. It explains the application of theoretic notions to the kinds of physical problems that engineers regularly... (read more)
Logic in Elementary Mathematics
by Robert M Exner Publisher Comments
This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Topics include axiomatic structure and the relation of theory to interpretation. No... (read more)
Algebra II Practice Pack [With CDROM] (CliffsNotes)
by Mary Jane Sterling Publisher Comments
Your guide to a higher score in Algebra II Why CliffsNotes? Go with the name you know and trust Get the information you need-fast! About the Contents: Pretest Helps you pinpoint where you need the most help and directs you to the corresponding sections... (read more)
Algebra II Workbook for Dummies (For Dummies)
by Mary Jane Sterling Publisher Comments
From radical problems to rational functions -- solve equations with ease Do you have a grasp of Algebra II terms and concepts, but can't seem to work your way through problems? No fear -- this hands-on guide focuses on helping you solve the many types of... (read more)
Why Beauty Is Truth: A History of Symmetry
by Ian Stewart Publisher Comments
Hidden in the heart of the theory of relativity, quantum mechanics, string theory, and modern cosmology lies one idea: symmetry. Symmetry has been a key concept for artists, architects, and musicians for centuries, but as a mathematical principle it... (read more)
Letters to a Young Mathematician (Art of Mentoring)
by Ian Stewart Publisher Comments
Mathematician Ian Stewart tells readers what he wishes he had known when he was a student. He takes up subjects ranging from the philosophical to the practical-what mathematics is and why its worth doing, the relationship between logic and proof, the... (read more)
Let's Review Algebra 2/Trigonometry (Barron's Review Course)
by Bruce C Waldner Publisher Comments
This review book offers high school students in New York State advance preparation for the Regents Exam in Algebra 2/Trigonometry. Fourteen chapters review all exam topics and include practice exercises in each chapter. The book concludes with a sample... (read more)
Smoot's Ear: The Measure of Humanity
by Robert Tavernor Publisher Comments
Measures are the subject of this unusual book, in which Robert Tavernor offers a fascinating account of the various measuring systems human beings have devised over two millennia. Tavernor urges us to look beyond the notion that measuring is strictly a... (read more)
Logic for Mathematicians
by J Barkley Rosser Publisher Comments
Hailed by the Bulletin of the American Mathematical Society as "undoubtedly a major addition to the literature of mathematical logic," this volume examines the essential topics and theorems of mathematical reasoning. No background in logic is assumed | 677.169 | 1 |
Calculus essentially takes the fundamentals of algebra and extends them to include rates of change between quantities. The This lesson teaches students how to apply the concept of the integral in order to calculate the volume of an object. Problems of this type involve a function that is revolved around the x-axis to make a three dimensional shape. The goal is to find the volume of this shape. The student is taught how to set up the problem and solve the integrals accordingly. Teachers User Instruction & Resource Guide - Includes Recommended books & Calculus Websites. | 677.169 | 1 |
I'm a student putting together a slide geared towards freshmen level students who are trying to understand what the importance of various classes in the CS curriculum are. Would it be safe to say that this list is fairly accurate?
2 Answers
I don't think it's fair to characterize discrete math as "how to think logically". All math (or most of it, anyway) involves logical thinking, but discrete math isn't any more or less about logic than is algebra or calculus. It's about things like learning the properties of fields and rings, that you generally won't have been exposed to in previous math classes. To make a long story short, while there's certainly logical thinking involved, there's quite a bit that's pretty basically just a type of math you (probably) haven't done much of previously. It's probably also worth mentioning that a fair amount of programming is based fairly directly on various forms of discrete math -- for example, public key cryptography is mostly based on rings and/or fields, and symmetric cryptography tends to be based mostly on group theory.
I think the characterization of data structures as just how to store stuff is a bit short-sighted as well. Although they generally try to do so, it's really quite difficult to separate algorithms from data structures -- many algorithms are dedicated to building and maintaining specific data structures, so what's called a "B tree" (for example) refers as much or more to the algorithm than the data structure itself. Likewise, the computations involved in a fair number of algorithms depend intimately on specific data structures (or at least data structures with specific properties).
Thank you very much for your response. I did feel that I was over-generalizing discrete math and I'm glad you pointed that out.
–
AvinashNov 12 '11 at 16:08
@JerryCoffin All your examples (groups, rings, fields) are drawn from abstract algebra, but what most people would call discrete math is much broader than that. Discrete math describes pretty much any sort of math that deals with countable things, including: graph theory, set theory, combinatorics, number theory, game theory, etc. Logic would certainly be included since it generally involves a limited number of discrete states. Thinking logically might not properly describe discrete math, but it likely squares with many students' experience in taking those courses.
–
CalebNov 13 '11 at 20:06 | 677.169 | 1 |
Differential Equations 2ND Edition Schaums
by Richard Bronson Publisher Comments
Confusing Textbooks? Missed Lectures? Tough Test Questions? Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and... (read more)
Fractals
by John Briggs Publisher Comments
Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them... (read more)
Algebraic Number Theory (2ND 94 Edition)
by Serge Lang Publisher Comments
This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic... (read more)
Essence of Chaos
by Edward Lorenz Publisher Comments
Chaos surrounds us. Seemingly random events -- the flapping of a flag, a storm-driven wave striking the shore, a pinball's path -- often appear to have no order, no rational pattern. Explicating the theory of chaos and the consequences of its principal... (read more)
Rapid Math Tricks & Tips: 30 Days to Number Power
by Edward H Julius Publisher Comments
Demonstrates a slew of time-saving tips and tricks for performing common math calculations. Contains sample problems for each trick, leading the reader through step-by-step. Features two mid-terms and a final exam to test your progress plus hundreds of... (read more)
Understanding Basic Statistics (Textbooks Available with Cengage Youbook)
by Charles Henry And Corrinne Pellillo Brase. Brase Publisher Comments
A condensed and more streamlined version of Brase and Brase's bestselling UNDERSTANDABLE STATISTICS, Tenth Edition, this book offers an effective way to learn the essentials of statistics, including early coverage of regression, within a more limited... (read more)
Linear Algebra Demystified (06 Edition)
by David McMahon Publisher Comments
QUICK and DEPENDABLE review of a typical LINEAR ALGEBRA course
Brings ABSTRACT concepts down to EARTH
Hundreds of SOLVED PROBLEMS show you how to get answers, step by step
Lots of QUIZZES, test questions, and a "final EXAM"
GET A LINE ON LINEAR ALGEBRA!... (read more)
Sphere Packing, Lewis Carroll and Reversi (09 Edition)
by Martin Gardner Publisher Comments
P... (read more)
Basic Practice of Statistics (Cloth) & CD-ROM
by David S Moore Publisher Comments
The Basic Practice of Statistics has become a bestselling textbook by focusing on how statistics are gathered, analyzed, and applied to real problems and situations—and by confronting student anxieties about the courses relevance and... (read more)
Calculus Demystified (Demystified)
by Steven G Krantz Publisher Comments
LEARNING CALCULUS JUST GOT A LOT EASIER! Heres an innovative shortcut to gaining a more intuitive understanding of both differential and integral calculus. In Calculus Demystified an experienced teacher and author of more than 30 books puts all the math... (read more)
Elementary Statistics (11TH 12 Edition)
by Robert R. Johnson Publisher Comments
Succeed in statistics with ELEMENTARY STATISTICS! With its down-to-earth writing style and relevant examples, exercises, and applications, this book gives you the tools you need to make the grade in your statistics course. Learning to use MINITAB, Excel | 677.169 | 1 |
When it comes to learning linear algebra, engineers trust Anton. The tenth edition presents the key concepts and topics along with engaging and contemporary applications. The chapters have been reorganized to bring up some of the more abstract topics and make the material more accessible. More theoretical exercises at all levels of difficulty are integrated throughout the pages, including true/false questions that address conceptual ideas. New marginal notes provide a fuller explanation when new methods and complex logical steps are included in proofs. Small-scale applications also show how concepts are applied to help engineers develop their mathematical reasoning.
Highlights Relationships among Concepts – By continually revisiting the web of relationships among systems of equations, matrices, determinants, vectors, linear transformations, and eigenvalues, Anton helps students to perceive linear algebra as a cohesive subject rather than as a collection of isolated definitions and techniques.
Proof Sketches – Students sharpen their mathematical reasoning skills and understanding of proofs by filling in justifications for proof steps in some exercises.
Emphasizes Visualization – Geometric aspects of various topics are emphasized, to support visual learners, and to provide an additional layer of understanding for all students. The geometric approach naturally leads to contemporary applications of linear algebra in computer graphics that are covered in the text.
Mathematically Sound – Mathematical precision appropriate for mathematics majors is maintained in a book whose explanations and pedagogy meet the needs of engineering, science, and business/economics students. | 677.169 | 1 |
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So is it worth it? Not really, in my opinion. You should expect more for a textbook costing $55+.
Personally, I prefer the book "How to Prove It" by Daniel Velleman, as it is not only less expensive, but much more thorough in teaching someone about discrete and abstract mathematics. It's abundant with more explanations, examples, exercises, and solutions. Here's what I'm talking about: How to Prove It: A Structured Approach
Check that out. It might be more worth your time. As for my copy of "Sets, Functions, and Logic," I'm probably going to sell it in the near future. It's just not that valuable to my math library.
Keith Devlin's book is an excellent introduction to proofs, an important part of one's mathematics education, which is missing in the US educational system at high school level. The problems left to solve by the reader are without solutions, hints or answers, which is author's intention, but is somewhat controversial. I think that, at least, hints should be provided for the more difficult problems. | 677.169 | 1 |
You are here
Math & Stats Help
The Math/Stats Help service of the University Learning Centre is located in the Murray (Main) Library, Room 144 (map).
The service is free of charge to all University of Saskatchewan students for help with University of Saskatchewan courses.
Services
Math/Stats help staff help students with a variety of mathematical or statistical topics, with a focus on first-year or introductory courses. Our service is primarily a drop-in service: students are welcome to drop in and work on homework, and ask questions when needed. Our service is designed for current University of Saskatchewan students looking for help with U of S courses. We also offer workshops or review sessions on certain topics in mathematics. These will be announced on this page and on PAWS.
Unfortunately, we do not have the resources to provide help with research-level statistics at this time. Please contact the Department of Mathematics and Statistics for advice on research-level statistics. You may also find the resources at the Murray Library page on Numeric Data helpful.
Announcements
We will be open for Term 1 of Regular Session 2013-2014 on Thursday, September 5. See below ("Hours of Operation") for schedule.
December final exam period: Yes, we will be open during the final exam period - please see below ("Hours of Operation") for the detailed schedule. Please note that the schedule is tentative.
- Math Placement Test (for students registered in certain 100-level mathematics courses): For more information about the placement test, go to . If you still have questions, please contact Amos Lee in the Department of Mathematics and Statistics (lee at math.usask.ca - replace the 'at' with @). To try a sample version of the placement test that you will write in September, please go to:
- Math Readiness evening course - A fall evening course for Math Readiness is in progress. For more information, please call Holly Fraser at 306-966-2742. To register, please call the Centre for Continuing and Distance Education at 306-966-5539.
- Math help for physics - If you are looking for help with the mathematics used in physics, you may want to consider registering in the "Math for Physics" course being offered by the Department of Physics and Engineering Physics through CCDE (the Centre for Continuing and Distance Education). For more information, please visit the "Math for Physics" website here: . Alternatively, you may want to seek help at your physics tutorial, at the Structured Study Sessions for physics, or at Math/Stats Help. Please note that Math/Stats Help tutors are not necessarily prepared to help with physics concepts, but can help with math calculations involved.
Hours of Operation
Hours during Term 1 of Fall Session, 2013-2014
Hours of Operation during the final exam period (Dec. 5-20, 2013)
Thurday Dec. 5: 10am-6pm & 7-9pm
Friday Dec. 6: 10am-6pm & 7-9pm
Saturday Dec. 7: 12noon-4pm
Sunday Dec. 8: 1-5pm
Monday Dec. 9: 10am-6pm & 7-9pm
Tuesday Dec. 10: 10am-6pm & 7-9pm
Wednesday Dec. 11: 10am-6pm & 7-9pm
Thursday Dec. 12: 10am-5pm
Friday Dec. 13: 10am-5pm
Saturday Dec. 14: 11am-5pm
Sunday Dec. 15: 1-5pm
Monday Dec. 16: 10am-6pm & 7-9pm
Tuesday Dec. 17: 10am-6pm & 7-9pm
Wednesday Dec. 18: 10am-6pm & 7-9pm
Thursday Dec. 19: 10am-6pm & 7-9pm
Friday Dec. 20: 10am-2pm
Sat. Dec. 21-January 5: closed
This schedule is subject to change. If these hours are not compatible with your schedule, please email Holly at holly.fraser at usask.ca (replace the 'at' with the appropriate symbol).
Schedule: Math/Stats Help is generally open whenever the U of S is in session; that is, during Regular Session (September-April) and Spring and Summer Session (mid-May until mid-August). We are not able to open on statutory holidays. We often hold exra hours during the final exam periods.
U of S students seeking help with non-U of S courses should be aware that students needing help with U of S courses have priority. Unfortunately, we usually do not have the capacity at this time to answer questions from people who are not University of Saskatchewan students. | 677.169 | 1 |
GCE1040: Math Detective uses topics and skills drawn from national math standards to prepare your students for advanced math courses and assessments that measure reasoning, reading comprehension, and writing in math | 677.169 | 1 |
0131577050
9780131577053
Prealgebra & Introductory Algebra: Elayn Martin-Gay believes every student can succeed and that is the motivating force behind her best-selling texts and acclaimed video program. With Martin-Gay you get 100% consistency in voice from text to video! Prealgebra and Introductory Algebra 2e is appropriate for a 2-sem sequence of Prealgebra (Basic Math with very early introduction to algebra) and Introductory Algebra (aka Elementary Algebra). This text was written to help students effectively make the transition from arithmetic to algebra and provide a strong foundation for success in their next, intermediate algebra course. To reach this goal, Martin-Gay introduces algebraic concepts early and repeats them as she treats traditional arithmetic topics, and then further develops their exposure to elementary-level algebra topics. The material from this text is also available split out into two separate textbooks, Prealgebra 5e and Introductory Algebra 3e, if you prefer to use split textbooks, rather than one combined textbook for your 2-sem sequence. | 677.169 | 1 |
Technology is changing the face of education. An obvious statement, of course. Everybody from students to instructors to parents will agree. Over 40 years ago, the introduction of the pocket calculator allowed us to change the focus from menial calculations to applying our knowledge to solve problems and discover the power of mathematics.
Since then we have seen leaps from innovation to innovation. The personal computer. Computer Algebra systems. Tablet computing....
Never before has the educational landscape been changing as fast as it is today, driven by a new generation of students who are growing up with instant access to on-demand information. This generation relies on ubiquitous network access and takes for granted technology that permeates every aspect of their lives. Phones and tablets are everyday companions and are used to connect with their peers, take classroom notes and research school projects. Beyond being mere consumers...
I am currently working on my final project in high school. This project is about mathematical modelling within epidemology and i am currently working on the mathematical models based on the SIR model.
The basis models for the SIR model were pretty easy, but i cant figure out how to fit data to my models. My first idea was to use the method of Leastsquare and/or Nonlinearfit but i cant figure out how to do this in maple.
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The 'Anthem Junior Mathematics Book 3 Answer Book' provides a complete set of answers to all the exercises and questions featured in both the 'Anthem Junior Mathematics Book 3' and the 'Anthem Junior Mathematics Book 3 Test Papers'. An indispensable classroom resource, this teacher's companion text also offers an array of additional exercises and activities, suitable for pupils of all abilities. With its rich, differentiated content and linear structure, the 'Anthem Junior Mathematics Book 3 Answer Book' will make organising lesson plans, teaching materials and preparatory work simple - thus facilitating a complete coverage of the subject.
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Summary: Finally there s an easy-to-follow book that will help readers succeed in the art of proving theorems. Sibley not only conveys the spirit of mathematics but also uncovers the skills required to succeed. Key definitions are introduced while readers are encouraged to develop an intuition about these concepts and practice using them in problems. With this approach, they ll gain a strong understanding of the mathematical ...language as they discover how to apply it in order to find proofs.
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The widespread use of computers and the rapid growth in computer science have led to a new emphasis on discrete mathematics, a discipline which deals with calculations involving a finite number of steps. This book provides a well-structured introduction to discrete mathematics, taking a self-contained approach that requires no ancillary knowledge of mathematics, avoids unnecessary abstraction, and incorporates a wide rage of topics, including graph theory, combinatorics, number theory, coding theory, combinatorial optimization, and abstract algebra. Amply illustrated with examples and exercises.
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Exploring Numerical Methods is designed to provide beginning engineering and science students, as well as upper-level mathematics students, with an introduction to numerical analysis that emphasizes insight and hands-on experience. To serve the needs of both the younger and the more experienced audience, each chapter begins with an intuitive presentation of motivation and simple algorithms. Topics are developed progressively within each chapter and the advanced material, which reveals underlying theory and discusses complicated methods, is clearly marked. The text takes a focused approach to introducing the more important numerical algorithms and exposes students to partial differential equations by using simple prototypes. This text provides a strong experiential basis for future | 677.169 | 1 |
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PROFESSOR STRANG: Okay. Hi. So, our goal, certainly, to reach next week is partial differential equations. Laplace's equation. Additional topics still to see clearly in 1-D. So one of those topics, these will both come today, one of those topics is the idea, still in the finite element world, of element matrices. So you remember, we saw those, that each bar in the truss could give a piece of A transpose A that could be stamped in, or assembled, to use the right word -- I think assembled is maybe used more than stamped in, but both ok -- into K. For graphs, an edge in the graph gave us a little [1, -1 ;-1, 1] matrix that could be stamped in. And now we want to see, how does that process work for finite elements. Because that's how finite element matrices are really put together out of these element matrices. Okay, so that's step one, that's half today's lecture.
Step two, problem two now, coming from the next section, is fourth order equations. Up to now, all our differential equations have been second order. Are there fourth order equations that are important? Yes, there are. For beam bending. So I'll describe that application, which leads to fourth order equations. Do they fit our A transpose C A framework? You bet. You know they will. Each additional application in the framework kind of get us comfortable, familiar with that framework, what it can do. The A transpose C A.
So let me start with element matrices. I'll get the homework, those numbers will get posted on the website later today. I just thought I'd put them down, and I have to figure out what would be a suitable MATLAB question. So my idea for this homework, as it really was for the last homework, was that you get some, not a large number of ordinary questions, paper and pencil questions, and one MATLAB question. When I wrote MATLAB last, people interpreted that as last MATLAB. But those words are not commutative. Right? I just meant -- and it doesn't really matter, it was a dumb thing to say -- I meant you to put the MATLAB question at the end after the regular questions. Sorry. So that MATLAB is due. Maybe a bunch of those turned in on Monday didn't include the MATLAB. No penalty. I'm talking now about the MATLAB for the trusses. How many have still got a MATLAB for the truss still to turn in? A number. Oh, not too many. Okay. Anyway, just when you can. In my envelope is good. Okay. So it'll be a similar thing for this week, and because it's short I said okay, let's get that cleaned up by Monday. And then we're ready for vector calculus, partial differential equations, two and three dimensions, the next big step.
If I want to illustrate element matrices, the best place I could do it would be to go back to our piecewise linear elements in 1-D, and see how an element now is just one of those little intervals. Little pieces of the whole structure. If it's a bar, or whatever it is, I've cut it into pieces. Here's one piece, here's another piece. With finite differences, if I gave you unequally spaced meshes, if my little h is different from my big H, we'd have to think again. I mean there would be some three point, instead of minus one, two, minus one for the second difference. It would be a little lopsided, of course, when the mesh is unequal. We would have to think that through for finite differences; for finite elements, the system thinks for us. So I just want to show how that happens.
So I'll take this. What's the element matrix for our standard equation for that element? Okay. And then it would fit into the big matrix K. I'm going to come up with a matrix K that I could do in any other way, but this is the way it's really done. So I look in that interval. I'm focusing on that interval. So here I've drawn the basis function. But now I'm not going to operate so much with basis function. Let me just think about that interval again. That's the same interval. So those were the basis functions that went up to height one. One started at height one and went down, one started at height zero and went up. But it's their combination, of course. Let me number this node number zero and this node number one.
So we have some height, U_0, here. This is coming from U_0 times that hat. And some other height, U_1, here, which is coming from U_1 times that hat. But inside this interval, my U in this interval is U_0 times that first hat function, the phi_0, the coming down hat. Plus U_1 times the phi_1 function, the going up hat. It's a linear function, so it's going to be there. That's my graph -- no, yes. This is U(x). U(x). Okay. Right? I'm focusing inside one element. One interval. I've numbered them zero to one, but of course that distance is H.
Okay, so there's my function. Right? Everybody agrees that this combination, it starts out right, it ends up right, at height U_1, and it's linear. So that's got to be right. So really, what's the contribution from that element? I look at the quantity, and I'm always taking the phi functions to equal the V functions. So I can write this as c(x) times dU/dx squared, dx. Over the whole thing, over the whole interval, that would be the U transpose K U. This, everybody remembers the K part, of course, comes from the left side of the problem. It comes from integrations. And this dU is now a combination of all the -- with weights U_0, U_1, U_2, U_3 -- if I plug in for capital U and do all the integrals, I'll see what K is.
Now what's the point? The point is, when I did those integrals, the question is, how am I going to do the integrals? Do I do them the way I did before, was I watched what phi_0, one phi times another phi and I integrated. That was successful. But the new way is, integrate it an interval at a time. Do the integrals. So this would be K global. Now I'm going to go just from zero to H. If I go from just zero to H, that's going to give me the K element piece. The little piece that comes from this little interval. And on that little interval, this is my formula for U. I'm just hoping you'll sort of see this as a reasonable idea, and then when we do the integral you'll see it. It clicks.
Okay, how does it click? So what's my plan? My plan is, here's my function. There is its picture. I'm just going to plug it into here. Oh, it's going to be simple, isn't it? What's the slope of that function in that element? On that interval? What's the dU/dx? So instead of doing every full integral for each separate phi, I'm doing every element integral for both phis. See, these two phis are both coming in to that element. Okay, so what's dU/dx.
I didn't realize how neat this that's going to be. So what's dU/dx in this element? I'll use a different board here. So it's an integral, then, from zero to H of whatever my c(x) might be. And I'll make a comment on that. But my focus here is, what's dU/dx? What's the derivative? And then I'm going to square it. For this function, for that picture, the slope is obviously (U_1-U_0)/H Right? The slope is (U_1-U_0)/H. And I'm squaring it. dx.
Okay. Let me take c(x)=1. Just to see clearly what's going on. So c(x) is just going to be one. Okay, so I'm claiming that this is my U transpose. My little piece. Why is it only a little piece? Because it only involves two of the U's. It's going to be a little two by two element matrix, that comes from this element. And then it's going to to be put into the big K, the global K, in its proper place. Okay, well. It's trivial, right? This is a constant, this is a constant, the integral is just H times U_1-U_0, squared, over H squared. Because that's getting squared, the interval was length H. I think I just have a 1/H. So this is my U transpose K element U. And now I want to pick out, what's that matrix? What's that little two by two matrix that only touches these two U's? What's the matrix -- well, since it only touches these two U's, you can tell me. I want a U_0, U_1.
Sorry, let me make a little more space. And you can tell me what matrix goes in there. I want this all to match up. U_0, U_1. Now here is the two by two element matrix, . What's the two by two matrix that will correctly produce this answer? I'm just shooting for that answer. What do I have here? This is U_1 squared minus 2U_0*U_1, plus a U_0 squared. Right? And I have to remember the 1/H, so it's automatically going to come out right. So there's a 1/H, shall I remember that first off. 1/H is part of my element matrix. And then, what are the numbers that go inside that matrix?
We had practice with this. You remember when we talked about positive definite matrices, way back in chapter one? The point was that we could look at eigenvalues, or pivots, or something. But the core idea was energy. The core idea was that energy, that quadratic, and that's what we're looking at again. That's the energy. That's the energy, right there, and this is the energy, this is the energy in the finite element subspace. All I'm saying is, what matrix, what two by two matrix, goes with U_1 squared minus 2U_0*U_1 plus U_0 squared. Just tell me what to put in that matrix.
What do I put in here? One, right. Because it's multiplying U_0 U_0. What do I put there? Minus one. Good. Because I have a minus two, it comes in, minus one comes in twice, and a one goes there. So there, with the 1/H included, is K_e. K element, for that element. For the big H element. You'll say big deal, because we've seen this thing before. Notice what is nice. First of all, notice how nice that is. It's particularly nice, of course, because I took c(x) to be one.
So let me make a comment. Suppose c(x) was not one. What would I do? Suppose c(x), suppose I have some variable stiffness in the material. Suppose the material could be changing width, so its stiffness would change. So in other words, I'd have a variable, c(x), that I should do the integral. Probably finite element systems aren't set up to actually do the exact integral. What would they do? They would take, for that simple integration, they would probably just take c(x) at the midpoint. So there's a numerical integration here in the creation of these element matrices. And numerical immigration is just, take a suitable combination of the values at a few points. You do know Simpson's rule? Simpson's rule, that's a pretty high level rule. My suggestion there was just a midpoint rule. Just take c(x) at the middle of the interval. Then it would factor out.
So I should really put a c here. A c should really be coming in there. And you expected that, right, from the A transpose C A. We always saw a C in the middle. It really should be there. When I took c to be 1, I didn't see it.
So what am I doing? I'm approximating c(x) by c at halfway. Approximately. I would replace this unpleasant, possibly varying, function by c at a point and use that value. So numerical integration is one part of the picture that we won't go into all the different rules. There's a rectangle rule, there's a trapezoid rule, very good. There's the Simpson's rule that's better. As I get higher order elements, like those cubic elements I spoke about, the numerical integration has to keep up. If I was integrating cubic stuff, I wouldn't use such a cheap rule. I would go up to Simpson's rule, or Gauss's rule, or somebody's rule.
Anyway, that's the c part. Here's the part that stamps into the matrix. Notice, by the way, when I stamp it in, tell me how it's going to look stamped in. And then I've completed it. So here's my big K. I wish I had a little more room for it. Okay, here's my big K. So that interval that I drew there, the H interval, will stamp in here, some two by two. Right? Now where will the similar thing coming from this guy -- maybe it has to be numbered minus one. Sorry about that. That's another little interval. I'll do the same thing on that interval. I'll get a little element matrix, two by two guy, for K for that element.
And where will it fit in to the big k? Does it fit in up here, let me just ask you. Does it fit in up there? Yes, no? I'm assembling, stamping in the small two by twos into the full n by n. And if I draw the picture you'll see it. So when I do the two by two for that big H interval, it goes there, let's say, then I just want to say where does the two by two go for the interval to the left? Does it go there? Nope. How does it go? It overlaps. Right? It overlaps.
Why does it overlap? Because the phi_0, this guy, is acting on the right, and also acting on the left. The U_0 is active, is partly controlling the slope this way, and also that way. The U_0 is in common the two intervals. Anytime any unknowns, any mesh points that are in common to two elements, we're going to have an overlap when we assemble. And so it'll just sit, it'll sit right there. And so there is the diagonal guy. And maybe you could tell me what number will go there. What number would actually go there? And then you'll see the whole point of assembly, stamping in.
Well, what number goes there from this? One times the c/H. So in here would be the c, can I call it c right, or c_H, c on the big H interval, divided by the H. Because that one, we had to get it right. And then what will go in that very same spot? So add it in coming from the small h interval. The same thing, it'll be this one, like shifted up, moved over. So it'll be coming from that one, so it'll be a c on the little h interval, divided by little h. That would be the diagonal entry of K. That's what we would see right there.
Over here, should I write a typical row of K? Typical row of K, when I do that, is going to have this c_h/h, plus c_H/H. That's like the two, right? That's like the two. And what goes here? What will the entry be that sits there when I assemble? Just this guy. Right? Just this guy, times that. The entry here will be the minus c_H/H. That'll be the entry. This is the diagonal one, this is the one to the right, and what's the one to the left? What's the one here? Well, you know what it is. It's going to come from the minus and it'll be the minus c_h/h.
Look at that. That just shows you how it works. And again, you can look at that, page 299 to 300 in the book. You see that if the c's are the same, if the h's are the same, then we're looking again at our minus one, two, minus one. Times whatever c over h, to keep it dimensionally right. Do you see that? It's just simple. Simple idea. The point is that each interval can be done separately. It's a simple idea in 1-D. It's a key idea in 2-D, where we have triangles, we have tetrahedra, tets. We'll see this in two dimensions, later in this chapter, when we're doing Laplace's equation. It's just fun to see it work. You'll have different triangles, say column triangles.
So that phi -- do you want me to look ahead? Just ten seconds, to triangles? So imagine we have triangles here, so we have piecewise, we have little pyramids. Instead of hat functions, they grow to pyramids. So there's a pyramid guy whose height is one there, and drops to zero in all these places. And that's our phi. Our trial function, test function, will be pyramid function, then. And I can do integrals that way, or I can take the integral over a typical triangle. So a typical triangle is involved with three, now I've three functions, in the linear case, controlling inside that triangle. So what will be the size of the element matrix? Can you sort of see how the system is going to work? And then we'll make it work in 2-D. Every node, every mesh point, corresponds, has a pyramid function, has a U that goes with it. Those U's are the unknowns. And how many of those unknowns are operating inside that triangle? Three. So what will be the size of the element matrix, the non-zero part of the element matrix? Three by three. What else could it be? So we'll see what it looks like. And we'll have integrals over triangles.
So that's good. Okay, thanks. Exactly halfway through the hour is exactly that first topic of element matrices. Done. Okay. Let me take two deep breaths, and move to fourth order equations.
Fourth order equations. For the bending of a beam. So I'd better draw a beam. This is a 1-D problem, still. This is a 1-D problem, still. To keep it 1-D, this better be a thin beam. So this is a thin beam. And the loads, what's the difference? What's here? It looks like a bar, pretty much, right? But the difference is, the load is acting this way. The load is acting that way on the beam. Maybe two loads. Maybe a uniform load. Maybe the weight of the beam. But it's transverse. It's in the perpendicular, it's transverse to the beam. It's this way. So the beam bends. Let me do a fixed free. So this'll be a fixed free beam. Fixed free, the word for fixed free would be cantilever beam.
Okay. So what happens if I impose those loads. Well, the beam bends. So the displacement is now downwards, is now not the direction of the rod, the displacement I'm interested in is perpendicular to the beam. Downwards.
Okay, so we can start on our framework. So this is displacement. u(x). I'll stay with the same letters. So you know I'm going to have an A, that will take me to whatever this is going to get called. What's the quantity there? It's going to be, let's see. What happens? So this is just geometric now. Let me put in the easy part, C. That'll be sort of the bending stiffness. Right? This'll be the bending stiffness. Because the beam is going to bend. And over here I'll get a suitable w. So when the beam bends, it's curvature. Curvature of the beam is what's produced. It's not stretching of the beam; it's curving of the beam. So this quantity, e, will be the curvature that comes from the displacement. If I displace these beams, suppose I put a node here, it's going to bend that down. The bar will curve. So the curvature, e. Now then, the question is, what is this A; what is the curvature?
Well, do you remember? You're on the ball if you remember the formula for curvature. It's a horrible formula, actually. But that's only because we're going to make it better. You remember the curvature, it was in calculus. Yes, you all remember this. Suppose I have a graph. I know its slope, that's become easy now, right? Calculus. But the curvature of it, what derivative did it involve? Second derivative. And was it the second derivative exactly? No, unfortunately there's some term which is horrible. One plus the first derivative squared, all square root. But I'm just going to take u double prime. So this is an approximation.
So what is A now? What's my matrix, A, that gets me from u -- or my operator, A, that gets me from u to e? What's the e=Au equation? A is just second derivative. That's something new. A is second derivative. And why do I do that? Because I assume small curvature, small displacement. I assume that u' squared is very small compared to one. So it's just slightly bent. A beam that goes way down here, I'd have to go nonlinear. But if I want to keep things linear, I approximate this will be much smaller than this, so one is fine that term goes.
And now the next step will be easy. What's the bending moment? This will be called the bending moment. And let me use the letter w again. I should really capital M for bending moment. That will be the stiffness times the curvature. So that's the force, the way the spring had a restoring force by Hooke's law. This is the equivalent of Hooke's law. But this restoring force is not pulling back, it's bending back. It's torquing back.
And then, of course you know, there'll be an equilibrium equation to balance the load. So this load is the f(x). And you know what that'll be. Because you know it'll involve A transpose. And the transpose of that, do you want to just make a guess? I shouldn't use transpose, of course, but I'll use it again. It'll be the same; it'll be second derivative. I mentioned we had a minus sign with the first derivative, but now we're going to have two minus signs, so it's going to come out symmetric, second derivative, and the equation here will be w''=f(x).
Our framework is working. We have plus boundary conditions on u. And here we have plus boundary conditions on w. So those parts we have not yet mentioned. And of course, that depends on my picture. While we're at it, why don't we figure out, what do you think is the boundary condition here? And how many boundary conditions am I going to look for all together? Four all together. Because I have a fourth order equation. There will be four arbitrary constants until I plug in boundary conditions. So I'm looking for four boundary conditions, two at this end, two at that end now. And what will be the two at the fixed end? At the fixed end, obviously, it's built in. Built in. Slightly different words sometimes for the beam problem. Here I'll have u=0 and u'=0. Those apply with A; those go with A. Those are the essential conditions, the Dirichlet conditions, the ones I must impose all the way. And now at this free end, what do you think?
Well, it's great. It's w=0, and w'=0. It's just beautiful, the way it all works. So that's a completely fixed free. Then why don't I draw in, just while we're talking about boundary conditions, an alternative. So here's my beam. And now you see, it's under a load, f(x), transverse load. Now that would be different boundary conditions. Anybody know the name of a beam that's set up like that? Simply supported. You don't need beam theory, and I don't know beam theory, to tell the truth, to do these problems. So that's a simply supported beam.
And what are the boundary conditions that go with that? Well this is u=0. No displacement, it sits there on that support. And what else is happening at that support? There's no bending moment. Nobody's here. Right? So it's w=0. And at this end, too. Also at this end, u(1) is sitting there, and w(1) is zero. Yeah. That would be the boundary conditions, four of them, for a fourth order equation that we'll just write down in a minute, for simply supported.
And we could have a mix. This could be simply supported here, free here. I think. Or maybe, could it be, or maybe that's too risky. Would that be a singular case, simply supported? Huh. So as always with boundary conditions, some are unstable. Some are not going to determine all four constants. Just the way free free didn't work, right? Free free for a rod didn't determine anything, it left a whole rigid motion. Maybe u=0, w=0 at one end, and free at the other end; it sounds risky to me. But we can see.
Okay. So, do you get the general picture of the beam? So what's the equation? What's A transpose C A, when I put it all together? I'll use that space to put in A transpose C A. Continuous, we're talking here. Right now we've got differential equations. So what's the differential equation, A transpose C A? So it's the second derivative. I'm just going backwards around the framework, as always. The second derivative of this, and this is c(x) times e(x), and e(x) is second derivative of u=f(x).
Good. In ten minutes, we've written down the framework, some possible boundary conditions, and the combined A transpose C A equation. I mean, we're ready to go. We've got the pattern to think about this. So let's see, what should we do first? I would say the first thing to do is, let c be one and solve some problems. Let c be one, and consider -- so if c is one, it's a fourth derivative equation.
Should we take uniform load? Yeah. How does a beam bend under its own weight? So it's just one, or whatever constant. So it's constant load, it's just its own weight, it's going to sag a little in the middle. What's the solution to that equation? And what shall I take as boundary conditions?
Let me do the simply supported one. Because that would be kind of nice. So it's simply supported, it's sagging under its own weight, with u(0)=0, u''(0)=0, because that's the w. And u(1)=0, u''(1)=0. Whatever. I don't know that I'll have the patience to go through and plug in all four boundary conditions to determine all four constants. Just get me to that point. Get me to a solution u(x), the general solution here that's got four constants in it is what? Okay.
Okay, think again. What are we looking at? We're looking at a linear differential equation. Linear problem. I'm asking for the general solution to a linear equation. What's the general set up? General set up is, particular solution plus nullspace solution. Right? You see an equation like that, looking for the general solution, tell me one particular solution and then tell me all the solutions when it has zero on the right, and we've got everybody. So that was true for matrices, it was true for Ax=b, it's just as true for differential equations. So what's one particular solution? What's one function whose fourth derivative is one? Yes? What am I looking for here? 1/4 of x to the -- no, what? 1/24, is it? 1/24 of x to the fourth? x to the fourth over 24. Because four derivatives -- so we're thinking we're in the polynomial world here. Just as we were with u''. With the bar it was x squared over two, the particular solution, now we're up to x fourth over 24. So that's the fourth derivative is one, good. So I'm seeing a fourth degree bending there.
And now what about the null space solutions, the homogeneous solutions. This accounts for the one, now what are the possibilities if it was a zero? You're going to tell me the whole bunch, right? A plus Bx plus Cx squared plus Dx cubed. Because all of those have fourth derivatives equal zero. So that's the general solution. Okay. So whatever the boundary conditions are, they determine A, B, C, D. We're not that far away from Monday's lecture on fitting cubics. Actually we're really close to it. When we use finite elements, we're going to use exactly those cubics. I'll get to that point.
Let me take the other model problem, that everybody knows what's coming. What's the other right hand side that this course lives and dies on -- lives on. Delta function. Right. Delta at some point. So that's a point load then. I can make it whatever the boundary conditions are.
Right. Good point. This boring stuff will just repeat, right? That's the null space solution. But now, what is a particular solution? The particular solution has become interesting. The particular solution here was straightforward, simple, a good one to do first. What's a particular solution to a point load? So instead of having distributed load here, I'm putting a heavy weight here at this point, a. And it's heavy weight, I'm multiplying the delta function by one, I could multiply by some l for load or something, but let's just keep it simple.
What's a solution to that? Fourth derivative equals delta. So that means I've now got to integrate, one way to get the answer here would be to integrate four times. Right? If I integrate delta four times, then I've got something whose fourth derivative will match delta. So do you remember the integrals of delta? Okay, so I integrate. First integral is, step. Second integral is, ramp. Third integral is, quadratic, right? This was linear, boop boop, linear pieces. The next integral is going to bring me up to quadratic ramp. And the next, fourth one is going to bring me up to cubic ramp. Cubic. So it's going to be cubic ramp, is what I get there. So one particular solution would be a function that's zero, and then at the point a, it suddenly goes up cubically. So it's zero here, and it's x cubed over six there, I think. If I do integrate three times, I'll be up to x cubed over six. Is that right? Yes, cubic.
So that's an interesting function. Of course, these parts will tilt the function, will change it. So our solution won't look like this, because I've only got one particular function, and I'll need these to satisfy the boundary conditions. So there is one particular solution.
The general solution -- yes, good for us to think out the general solution. What does that picture look like when I add in this stuff? Very, very important. I'm sorry I don't have more space for this highly important picture. Okay, so here's my point a. Keep your eye on that point a. Okay, so to the left of it, I've got some curve, whatever, dut dut dut dut dut, the beam. And to the right of it, I've got some other curve, whatever it is, dut dut dut dut dut. And what's cooking at point a? What's the jump condition at point a? That's the critical question. What changes at point a? You remember, this is the corresponding thing, the analog of our ramp. So what changed for the ramp at point a? What jumped? The slope. Okay, now the question is what's going to jump here? What jumped there? Here, did the function jump? Certainly not. Did the slope jump? Certainly not. Did the second derivative jump? No, no. The second derivative was zero and then zero. What jumped? Third derivative. The third derivative is allowed to jump. And of course. A jump in the third derivative produces a delta in the fourth. Right? It just works.
So this is a cubic of some sort, coming from that jump. This is another, a different cubic, coming from this sort, from this junk, and this. So it's cubic in each piece. Why is it cubic in each piece? Because, what's the equation in the middle of that piece? What's our differential equation if I look here? Here's my equation. What is it in the middle of that piece? u fourth equal zero. The delta function is zero there. And u fourth is zero here. So of course this is a cubic spline. We're meeting that neat word, cubic spline. Those turn out to be very, very handy functions for other things, too. So we see them here as a solution to fourth order equations with point loads are cubic splines. Because the big key point is that there's a jump here in u''', the third derivative. A jump in the third derivative, that's what we saw here. And we'll see it if we have any cubic meeting any cubic.
Let me just say, a jump in the third derivative, your eye probably won't notice it. I mean, it's a discontinuity, somehow. We don't have the same polynomial from here to here. But that discontinuity in u''', it's pretty darn smooth still. The slope is continuous, so your eye doesn't see a ramp. And even more, the curving is continuous, the curvature is continuous. e and w are good. It's just a jump in the third derivative.
Okay, so I want to speak about splines, and more about this, and about finite elements for beam problems on Friday. And then that will take care of 1-D and we'll move into 2-D. Okay | 677.169 | 1 |
Thinking Mathematically, Expanded-/two-term course in liberal arts mathematics, or survey of mathematics. This Expanded Edition of Thinking Mathematically includes additional chapters on Voting and Apportionment, and Graph Theory. More than any other course/text, Liberal Arts Math depends on strong, engaging applications and examples. Bob Blitzer's books are highly acclaimed for their well-conceived, relevant applications and meticulously annotated examples. This highly anticipated revision achieves the difficult balance between coverage and motivation, while helping ... MOREstudents develop strong problem-solving skills. This book provides students with the skill building and practice so crucial at this level as well as the applications and technology necessary to foster an appreciation of the myriad uses of mathematics as they move forward in their college careers and beyond. Provides readers with the skill building and practice that is so crucial as well as the applications and technology necessary to foster an appreciation of the myriad uses of mathematics. For anyone interested in refreshing his/her fundamental math skills. Softcover. | 677.169 | 1 |
Arthur Mattuck: Introduction to Analysis
The book was developed at MIT, mostly for students not in
mathematics having trouble with the usual real-analysis course.
It has been used at large state universities and small colleges,
as well as for independent study. Students evaluate it as
readable and helpful. The current printing, by CreateSpace and
at a reduced price, is the eighth, incorporating all known
significant corrections and a new Appendix F.
General description
This book is meant for those who have studied one-variable
calculus (and maybe higher-level courses as well), generally
skipping the proofs in favor of learning the techniques and
solving problems. Now they are interested in learning to read
proofs, and to find and write up ther own: perhaps because they
will need this for the next steps in their chosen field, or for
intellectual satisfaction, or just out of curiosity.
There are two paths to this. Some books start with a great leap
forward, giving the definitions in n-space. This requires first an
excursion into point-set topology, whose proofs are unlike those
of the usual calculus courses and are a roadblock to many.
The path chosen by this book is to start like calculus does, in
1-space (i.e., on the line) and focus on the basic definitions
and ideas of one-variable calculus: limits, continuity,
derivatives, Riemann integrals, and a few more advanced
topics. It's done rigorously, but also in as familiar a way as
possible.
So from the start it will use as a source of examples what you
know (with occasional reminders): K-12 mathematics and basic
one-variable calculus, including the log, exp, and trig
functions. This takes up about two-thirds of the book, and might
be as far as you wish to go. It sounds like this is just
repeating calculus, but students say that it feels very different
and is not all that easy.
The rest of the book gets into techniques from advanced calculus
based on the notion of uniform convergence, and usually used
in lower-level courses without proof: differentiating infinite
series term-by-term, and differentiating integrals containing a parameter (the
Laplace transform, for instance). For the latter, it's finally
time to learn about point-set topology in the plane (i.e.,
2-space, but n-space is no harder). There's also for the curious
or needy an optional chapter with the most important facts about
point-sets of measure zero on the line, and a more powerful
integral: the Lebesgue integral.
Two appendices respectively provide needed and optional
background in elementary logic, and four more give interesting
applications and extensions of the book's theory.
(See below for the link to the Table of Contents for more details
about the topics and the order in which they are given.
Generally helpful features
--- Leisurely exposiion, with serious comments about proofs, other
possible arguments, writing advice; some semi-serious comments,
too;
--- Attention paid to layout and typography, both for greater
readability, and to give readers models they can imitate;
--- Questions after most sections of a chapter to firm up what
you just read, with Answers of various sorts at the end of the
chapter: single words, hints, complete statements, formal
proofs.
(See below for the link to Sample Text Pages to see examples.)
Mathematically helpful features
--- The language of limits is simplified by suppressing the N and
the delta when their explicit value is not needed in the
argument, replacing them with standard applied math symbols
meaning "for n large" and "for x sufficiently close to a". These
are introduced carefully and rigorously; some caution is needed,
which is described at the end of the Preface (see the link below
to it).
--- The book tries to go back to the roots of real analysis by
emphasizing estimation and approcimation, which use inequalities
rather than the equalities of calculus, but have a similar look,
so that many proofs are calculation-like "derivations" that seem
familiar. But inequalities require more thought than equalities;
they are often mishandled and warnings have to be given and repeated.
Looking at the book
For more details about what's written above, you can use
these links in order to get an idea of how it's written, and
what studying analysis from it will
be like.
These are a few sections, totalling about 15
pages in all, showing text material, Questions, Exercises, and Problems,
to give you a sample of the mathematical writing style and level. They are
selected from the first three chapters:
--- Chapter 1: Real Numbers and Monotone Sequences
--- Chapter 2: Estimations and Approximations
--- Chapter 3: The Limit of a Sequence
Information about earlier printings
PRINTING: There is only one edition so far, but several printings.
The printing is identified by a number sequence like
10 9 8 7 6 5 4
on the left-hand page facing the dedication page; the
sequence shown identifies the fourth printing, for example.
CORRECTIONS: The current inexpensive printing is the eighth; it
incorporates all the significant mathematical corrections needed
from earlier printings.
I would be grateful to hear about any further corrections needed.
as teacher or student;
write to: [email protected]
For those using printings earlier than the eighth, here are lists
of corrections. Bullets indicate the more
significant ones; none are major.
Mathematical corrections to the Third through the Seventh Printing
( pdf file )
Mathematical corrections to the Second Printing
(see also the corrections to printings 3-7 above)
( pdf file )
Mathematical corrections to the First Printing (see also
the corrections to printings 2 and 3-7 above)
( pdf file ) | 677.169 | 1 |
Other Courses
Home Schooling Maths / GCSE Mathematics – The Course
The GCSE Maths course gently guides the student through basic mathematical skills, progressing onto more advanced material as the student's skills and abilities develop. The course is divided into two parts: the first is for all students; the second is for those who will be taking the Higher tier of the examination.
Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall programme of study.
Effective learning is encouraged through frequent activities and self-assessment questions.
There are thirteen tutor-marked assignments and a practice exam paper.The course covers the entire syllabus in 13 modules, with a 14th on the examination.
The Syllabus
Our GCSE Maths course prepares students for AQA GCSE Mathematics syllabus 4365 for exams in 2014 and later years. We have chosen this syllabus as it is the most suited to distance learning.
Assessment for 2012 is by two written papers. Paper 1 (non-calculator) is worth 40% and Paper 2 (calculator) is worth 60% .
Special Requirements
A reasonable level of proficiency in arithmetical skills is assumed.
Coursework
No coursework or controlled assessment is required.
The AQA 4365 specification contains an emphasis on "problem"-solving – that is to say, questions are more likely to be given a "real world" context. This should make them easier to grasp and visualize while the underlying mathematical skills remain the same. | 677.169 | 1 |
0321620917
9780321620910
Intermediate Algebra for College Students:The Angel author team meets the needs of today's learners by pairing concise explanations with the new Understanding Algebra feature and an updated approach to examples. Discussions throughout the text have been thoroughly revised for brevity and accessibility. Whenever possible, a visual example or diagram is used to explain concepts and procedures. Understanding Algebra call-outs highlight key points throughout the text, allowing readers to identify important points at a glance. The updated examples use color to highlight the variables and important notation to clearly illustrate the solution process.
Back to top
Rent Intermediate Algebra for College Students 8th edition today, or search our site for Allen R. textbooks. Every textbook comes with a 21-day "Any Reason" guarantee. Published by Pearson. | 677.169 | 1 |
Algebra One on One 4.0 description
Algebra One on One 4.0 brings an educational game which offers a fun way to learn and practice algebra. This program covers 21 functions, including maximums, minimums, absolute values, averages, squares, and cubes. It has both a practice area and a game area.
The Practice menu lets you practice each function individually. The Game menu lets you choose up to 21 functions. You can choose from Calculate Value, Choose Formula, or Figure Formula and Calculate. You can even compete against another player. It has a great help system that makes it simple for the beginner to understand algebra. It also has an ""Einstein"" level that even algebra experts will find fun and challenging.
Version 4.0 features improved graphics, better help, easier registration, and a registration bonus of eight other programs. This version is a 30-day trial.
his game makes math exciting by allowing a two-player head to head competiton option. Full step by step solution of all problems. For all levels from 4th grade on up - special Einstein level for math Free Download
Algebra Vision is a unique educational software tool to help students develop algebraic problem solving strategies. It provides an environment to play and see algebra in a more tangible light. Free Download
Tired of no-fun, state-of-the-art, all graphics and no fun soccer games? No polygons, no gimmicks, just Soccer. This gmae was designed to be fun and not to be realistic. A one on one soccer game. Requ Free Download | 677.169 | 1 |
In... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof." Charles Ashbacher, Journal of Recreational Mathematics
Book Description
Looking for a head start in your undergraduate degree in mathematics? This friendly companion eases beginning students into real mathematical thinking, unlocking important techniques for effective mathematics so you can communicate with clarity, solve problems, and explore the world of definitions, theorems and proofs with real confidence.
About the Author
Kevin Houston is Senior Lecturer in Mathematics at the University of Leeds. | 677.169 | 1 |
+ By spelslottet.se
Get Graphoid - the graphing scientific calculator with fast and easy zoom. Use the scientific calculator look-alike touch keyboard to enter expressions and functions, all on one screen without "2nd" key. Draw graphs or value tables, zoom in the values of the value table or graph by just touching the screen. Calculate min, max, intersections and more in graph mode as well as in table mode!
* EASY TO ZOOM GRAPHS OF FUNCTIONS Use pinch zoom (two-finger zoom) to zoom graphs on multitouch devices. On older devices you can use one-finger zoom. Just long press the graphs to enter the zoom mode. Then just drag left/right/up/down to zoom. The scale grid is automatically updated. To select the interesting parts of the graphs has never been easier! With Graphoid calculator you can focus on inspecting graphs of functions, not how to use menus.
* ZOOMABLE VALUE TABLE OF FUNCTIONS The functions can be investigated by a value table as well. By dragging the table up/down you move the visible interval of the function. You can even zoom the table values with pinch zoom on multitouch devices or by using the zoom buttons on the screen on non-multitouch devices. The differences between the x-values are auto calculated to be human readable. Rotate the device to portrait format and compare two functions in the table. Of course you can calculate min, max, intersections etc right from the table screen. To inspect functions with a value table is faster, easier and more intuitive than ever with Graphoid!
* SYNTAX HIGHLIGHTING INCREASES READABILITY When you enter expressions or functions they are displayed with colored text; the negative sign has a different color than the subtraction sign, the scientific notation 'E' is highlighted by color so you don't miss it (we all have received answers like 1.394735386937635E9 without notice the 'E'). During the input of an expression matching parentheses are highlighted with color to make multi parentheses input more readable.
* EASY HUMAN READABLE ERROR MESSAGES In case you enter an illegal expression you will get an easy-to-read error message. Also, if a calculation error occur a specific human-friendly error message will tell you what went wrong; 'Division by zero', 'Log of a negative number is illegal' etc. Graphoid is made to help us avoid mistakes!
* STORED VARIABLES AND EXPRESSIONS You can easily store variables with an arbitrary name and use them in future calculations. The last entered expressions are automatically stored and can be reused or edited. | 677.169 | 1 |
Beginning Algebra : Early Graphing - With CD - 06 edition
Summary: Normal 0 false false false MicrosoftInternetExplorer4 John understand each topic, gaining confidence as they move through each section. Knowing students crav...show moree feedback, Tobey has enhanced the new edition with a ''How am I Doing?'' guide to math success. The combination of continual reinforcement of basic skill development, ongoing feedback and a fine balance of exercises makes the first edition of Tobey/Slater Beginning Algebra: Early Graphing even more practical and accessible. Prealgebra Review; Real Numbers and Variables; Equations, Inequalities, and Applications; Graphing and Functions; Systems of Equations; Exponents and Polynomials; Factoring; Rational Expressions and Equations; Radicals; Quadratic Equations For all readers interested in algebra. ...show less
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Ng is very polite but he rushes explanations and his notes don't distinguish scalars/vectors/matrices. He overloads the meaning of various notational terms. Homework is very hard (most TAs don't understand it) and requires you to know magic never taught in class. Great subject but absolutely ridiculous course.
Professional Ng is an amazing lecturer, absolutely top notch. His notes are extremely detailed and refined. But going to his class is still a plus, he's clear, to the point and extremely good with giving examples for anything that might be fuzzy in the notes. The class is not easy however - at least for me, the homework really requires a lot work.
Absolutely amazing! Genuinely interested in the subject, explains concepts with clarity, uses excellent examples and focuses on what's important. Usually you'd need to meet a professor in person to iron out problems and understanding. He managed to teach via lecture videos and STILL got through to most people. Absolutely amazing!
A great teacher who always explains hard-to-understand concept in a easy way. The programming exercises really helps me gain deeper understanding about ML. The course is hard, but Prof really really did a good job!
His lecture notes are very clear, but he's a terrible lecturer in person. He mumbles and writes equations on the board without differentiating useful ones from algebraic derivations. I'm very serious when I say that he draws arrows labeled "magic" when he gets tired of explaining things. | 677.169 | 1 |
...Conic sections is also a familiar area of expertise. As an additional resource I also possess an Algebra II "Teacher's Edition" text. Word problems are a particular challenge for a number of students for whom the following steps must first be modeled: 1) drawing an appropriate diagram, if requ... | 677.169 | 1 |
Fundamentals of Matrix Computations, 2e
Written for advanced undergraduate students, graduate students, and professionals, this book provides a detailed explanation of matrix computations and the accompanying theory. Topics covered include the introduction of new methods for solving large, sparse eigenvalue problems, including the implicitly-restarted Arnoldi and Jacobi-Davidson methods; iterative methods; modern componentwise error analysis; reorthogonalization; and rank-one updates of the QR decomposition. Numerous example problems throughout the book are solved using MATLAB.
Free Mathematical Modeling Technical Kit
Learn how you can quickly build accurate mathematical models based on data or scientific principles. | 677.169 | 1 |
MESA Helps Build Your Future!
We help individuals achieve their academic goals. MESA CCCP (Math Engineering Science Achievement California Community College Program) provides support to community college students who are majoring in math, engineering and science so they can excel academically and transfer to four-year institutions.
This course proceeds at an intense pace. Topics include: functions and graphs, applications of functions, exponential and logarithmic functions, trigonometric functions and analytic trigonometry, right triangle trigonometry, analytic geometry, and roots of polynomial equations. This course is intended for students planning to take calculus.
Math 75
Mondays and Wednesdays 1:00-2:00pm, JM 122
Tuesdays and Thursdays 3:00-4:00pm, JM 124
This is the first course of a three-semester sequence. Topics include limits, continuity, differentiation, and integration involving many types of function with a variety of applications. Primarily for mathematics, physical science, and engineering majors.
Math 76
Tuesdays and Thursdays 11:00am-12:00pm, JM 222
This is the second course of a three-semester sequence. Topics include techniques of integration, improper integrals, infinite series, analytic geometry, polar coordinates and parametric equations, vectors, three-dimensional space, and many applications.
Math 77
Tuesdays and Wednesdays 2:00-3:00pm, JM 207
Math 80
Tuesdays and Fridays 2:00-4:00pm, JM 124
MATH080 Introduction to linear algebra including systems of linear equations, vectors, matrices and determinants, two and three-dimensional vectors, vector spaces, inner product spaces, eigenvalues and eigenvectors, and linear transformations. Intended for mathematics, engineering, or computer science majors. Supplemental learning assistance is available for students to strengthen skills and to reinforce student mastery of concepts. Students enrolled in MATH 80 may access the supplemental learning assistance by enrolling in MATH 400, an open entry/open exit non-credit course. Approved for Distance Learning format.
Physics 6
Tuesdays and Thursdays 10:00am-12:00pm, JM 124
Physics 20
Mondays 11:00-12:00pm, JM 119
Wednesdays 1:00-2:30pm, JM 119
Chem 20
Mondays and Wednesdays 8:00-9:00am, JM 124
Wednesdays and Thursdays 4:00-5:00pm, JM 119
CHEM 20 is a one semester transferable college chemistry course designed to meet the needs of allied-health majors. The course is a study of the fundamental theories and laws of chemistry. The laboratory portion of the course involves experimentation and drawing conclusions from data.
Chem 1
Tuesdays 2:00-4:00pm, JM 223
Fridays 2:00-4:00pm, JM 223
A course for majors and pre-professionals involving the fundamental theories and laws of chemistry. Topics include stoichiometery, atomic structure, bonding theories, ionic reactions and properties of gases. | 677.169 | 1 |
Elementary Statistics - With CD - 6th edition
Summary: Elementary Statistics is appropriate for a one-semester introductory statistics course, with an algebra prerequisite. ES has a reputation for being thorough and precise, and for using real data extensively. Students find the book readable and clear, and the math level is right for the diverse population that takes the introductory statistics course. The text thoroughly explains and illustrates concepts through an abundance of worked out examples201771306 | 677.169 | 1 |
Study for a degree in mathematics and informatics and further the development of new technologies
Most of the technological advances that we use every day (3D graphics, MP3 audio compression, GPS navigation) would have been unthinkable without mathematics and informatics. The applied combination of the two disciplines will be the cornerstone of new technological changes in today's society. On the other hand, there is a growing demand for professionals with knowledge of mathematics and informatics in the business world and industry.
Would you like to be party to the development of new simulation systems applied to the environment? Would you like to generate more realistic graphical tools? Would you like to break new ground developing compression algorithms to support Web searches? Would you like to be party to the biotechnology revolution? Study mathematics and informatics
If you like mathematics and informatics and your are interested in their application to new technologies, study for a degree in mathematics and informatics. No previous knowledge of computers is necessary.
Mathematics and informatics: a world of possibilities
Web search algorithms
For many users all over the world, the most commonly used search engines, Google, for example, are the gateway to the Web. Google's page ranking system is based on linear algebra and statistics. Research with a strong mathematical groundwork is being conducted into techniques for broadening search engine search options, applying artificial intelligence techniques to identify photos that were taken of a particular place or identify a particular voice in an audio recording, for example. Other mathematical techniques, like fractal networks, are used to describe and study Internet traffic for possible improvement. Mathematics and informatics have provided revolutionary solutions for searching vast quantities of data and designing complex hi-tech networks for high-speed data processing.
3D graphics and multimedia systems
Animated films, special effects and 3D graphics in video games are based on mathematics (vectors, matrices, polygonal approximations...) and would be impossible without computers. Listening to music on a CD or iPod or watching films on a DVD is possible thanks to informatics techniques that use the mathematics of signal processing, binary arithmetic, differential equations, linear algebra, trigonometry or calculus. On the other hand, the storage and transportation of such information would be impossible without image processing and data compression techniques that use linear algebra, probability, graph theory, abstract algebra and more recently wavelets to compress audio and video.
Simulation
Research into air and water flows dates back over a hundred years, but not until recently has the phenomenon of turbulence, vital for aerodynamics, begun to be understood. Mathematics and computers are able to simulate these phenomena without having to use wind tunnels. Fractal geometry in conjunction with computers is able to simulate irregular natural structures or output real textures for virtual reality. Fractals are also a component of chaos study. The best known example of chaos theory is the butterfly effect, which refers to the fact that the flapping of a butterfly's wings can affect global weather weeks later. The simulation of galaxies, where many objects have chaotic paths, requires the design of new algorithms that will give us a glimpse of the underlying structure of the universe.
Environment
The equations that describe ocean currents and temperatures, which affect the world's climate, are impossible to solve even using today's computers. Even so, it is possible to make short-term forecasts, for example, to predict the appearance of "El Niño". Weather forecasting, which relies on numerical calculus techniques, has improved over the last 20 years thanks to the increased computational power of computers and the advance in mathematics-based applications.
Security and cryptography
The mathematics of cryptography is vital for trade today. Although based on classical algebraic methods, the encryption techniques used today were developed over the last 25 years. Mathematics are also behind error correction codes, enabling error-free operations or assuring correct bar code or identification number (ID card, ISBN,..) reading. Fingerprint identification involves building databases that are only manageable thanks to the use of computer programs that apply wavelet-based data compression mathematics techniques. Iris recognition is based on pattern recognition, wavelets and statistics.
Biology and medicine
Experimenting with the human heart is out of the question, but, thanks to mathematics and informatics, it has been possible to precisely model this organ leading to a better understanding of how it works. This has improved, for example, the design of artificial valves.To understand how the different parts of the brain work, it has to be mapped in 2D. This is especially complicated in the case of the brain due to the numerous folds and fissures in its surface. Different geometrical and topological techniques are useful for these mapping purposes. Geometry, differential equations and linear integer programming are three fields of mathematics used to process real-time data to locate tumours with the aim of doing maximum damage to the tumour and minimum damage to healthy tissue. Using computer-programmed mathematical models, it is possible to experiment on how to use viruses to destroy cancerous cells, eliminating failed approaches and selecting candidates to run other experiments.
Study mathematics and informatics at the Universidad Politécnica de Madrid
Even if you are convinced that mathematics and informatics are your thing, you might ask
Why study mathematics and informatics at the Universidad Politécnica de Madrid?
Because, according to the annual survey conducted by the El Mundo newspaper, the UPM's Facultad de Informática is the number one Spanish higher educational institution teaching the degree in informatics engineering.
Because it has the faculty with the best reputation. The world-level quality of the research by professors of the UPM's Facultad de Informática keeps tuition at the leading edge of the profession and prepares you for the challenges facing informatics.
Because of its students' service: through the Mentor Project, foundation courses, getting started, open day, text messaged grades, etc.
Because of its student-driven tuition: for the last three years, tuition at the UPM's Facultad de Informática has successfully complied with the Bologna Declaration, and technical training has been combined with the development of the skills most sought after in the business world (communication skills, team work, etc.). | 677.169 | 1 |
Written by Stephen Hake, author of the
Saxon Middle Grades program, Math
Intermediate 3 is ideal for students looking
for a textbook approach that provides a
smooth transition into Math 5/4. It is also
helpful for students who are coming to
Saxon from other programs.
Math Intermediate 3 teaches mathematical
concepts through informative lessons,
helpful diagrams, and interactive activities
and investigations. The Math Intermediate 3 Homeschool Kit includes a Student Textbook, Homeschool Testing Book, Solutions Manual, and Power Up Workbook.
Click here for the Saxon Math Intermediate 3 Lesson Activity Worksheets. (This is a password-protected PDF. The password is the final word on page 8 of the Math Intermediate 3 Homeschool Testing Book.)
<< Use the Product Offers on the left to navigate through this category. | 677.169 | 1 |
Successful students will be able to define, represent, and model using logarithmic functions. Recognition of the inverse relationship between logarithmic and exponential functions is essential to this concept. They will apply the laws of logarithms, solve logarithmic equations, and use logarithms to solve exponential equations. There are a variety of types of test items including some that cut across the objectives in this standard and require students to make connections and solve rich contextual problems.
L1. Logarithmic expressions and equations
a. Apply the properties of logarithms and use them to manipulate logarithmic expressions.
Represent logarithmic expressions in exponential form and exponential expressions in logarithmic form.
Understand that a logarithm is an exponent that depends on the
base used.
The properties of logarithms include those related to powers,
products, quotients, and changing the base. | 677.169 | 1 |
In this study, I developed cases describing three participants – Bob, Jack, and Amy – and their mental imagery, representations, and methods used to create meaning for calculus derivative graphs. Two research questions were investigated: (1) What is the nature of calculus students' understanding of derivative graphs; (2) how do calculus students create meaning for derivative graphs? During the clinical interviews, the participants were presented with a derivative graph of a function and asked to draw a possible antiderivative graph as I sought to gain understanding of their mental processes and representations.
The participants' interpretations and representational schemes for derivative graphs were different because of their preferences for mathematical processing. Bob and Jack relied on visual processing and graphic representations (or mental images). For them, the derivative graph represented the slopes of the antiderivative graph, and their images or graphic representations of the slopes of the tangent lines determined the graph of the antiderivative graph. Without the support of analytic thinking, their images hindered their understanding. Amy relied on analytic processing and algebraic representations. For Amy, the derivative graph represented an equation (or a function presented with an equation), and the equation of the derivative graph determined the equation as well as the graph of the antiderivative graph. Without the support of visual thinking, her analytic approach presented different difficulties.
This study found that since the participants' knowledge was strongly associated with one mathematical processing (or representation) and weakly associated with the other mathematical processing (or the other representations), their one-sided thinking or over-reliance on one representation impeded their understanding of derivative graphs. Their difficulties with derivative graphs indicate the importance of reversibility of thinking processes, synthesis of analytic and visual thinking and the use of multiple representations in the complete understanding of differentiation and integration. Derivative and antiderivative graphs with a cusp, a sharp corner, a vertical tangent line, or a discontinuity should be used to encourage students to use formal definitions of left- and right-hand derivatives, differentiability, and continuity as well as help them construct appropriate mental images and representations that will facilitate their learning and understanding of calculus. | 677.169 | 1 |
I would recommend Nancy Blachman's "Mathematica: A Practical Approach." I
believe that it's in its second edition at this point, and she now has a
coauthor. It seems geared toward the novice user and explains everything
from getting help, numerics and symbolics, graphics, and programming.
There are even problem sets after each chapter to give you practice with
the material. Be certain to do them - you'll learn lots!
Regards,
J. Leko
Please reply to leko*j at cspar.uah.edu
In article <8qhoa2$jc8 at smc.vnet.net>, chuleta2099 at my-deja.com wrote:
> What is a good book to show me how to use mathematica?
>
>
> Sent via Deja.com
> Before you buy. | 677.169 | 1 |
igonometry
Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's best-selling ...Show synopsisGain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's best-selling TRIGONOMETRY 6e, International Edition. This book's proven approach presents contemporary concepts in brief, manageable sections using current, detailed examples and high-interest applications. Captivating illustrations drawn from Lance Armstrong's cycling success, the Ferris wheel, and even the human cannonball show trigonometry in action. Unique Historical Vignettes offer a fascinating glimpse at how many of the central ideas in trigonometry began. TRIGONOMETRY 6e, International Edition, uses a standard right-angle approach with an emphasis on the study skills most important for success both now and in advanced courses, such as calculus. The book's proven blend of exercises, fresh applications, and projects is combined with a simplified approach to graphing and the convenience of new Enhanced WebAssign--a leading, time-saving online homework tool--and the innovative CengageNOW teaching system. With TRIGONOMETRY 6e, International Edition, you'll find everything you need for a thorough understand of trigonometry concepts now and the solid foundation you need for future coursework and career 7th Edition. Used-Acceptable. Text is generally...Acceptable. 7th Edition. Used-Acceptable. Text is generally clean; has used stickers on cover. Does not include online code | 677.169 | 1 |
Mathematics by Computer
The most elementary way to think about Mathctrtati ca is as an enhance calculator — a calculator that does not only numerical computation but also algebraic computation and graphics. Matltcmatica can function much like a standard calt".1a- tor. you type in a question, you get back an answer. But Mat/tctttadca ga's turthcr I ue an ordinary calculator. You can type in questions that require answers that arc longer than a calculator can handle. For example, Matltcmatictt can giv; you thc numerical value of tr to a hundred decimal places, or the exact result for a numerical calculation as complicated as the result of 3)tI0, (m Fig. 1) | 677.169 | 1 |
Mathematics
T
he math program strives to equip each student to think logically and analytically and to effectively communicate strategies for solving problems, particularly those related to math and science. We seek to develop a student's understanding of algebra and other mathematical concepts throughout the curriculum. Topics in each subject are explored visually, symbolically, and verbally. Scientific and graphing calculators and various software applications are used as instruments for exploration and deeper understanding. Our aim is to encourage students to become confident in their math abilities and to recognize math as a powerful subject and tool.
Starting in 8th grade, accelerated courses are offered at each grade level. Placement in accelerated courses is based on student performance, teacher recommendation, and the approval of the department head. These courses move at a faster pace and explore topics in greater depth and breadth. Many 12th grade students complete a college level calculus course.
6th Grade
The sixth grade math curriculum has three main components. In the first trimester, students focus on exploring math concepts with data covering the collection, organization, interpretation and analysis of data through the design and reading of graphs. Students investigate the meaning and application of mean, median and mode and the use of range creating graphs. Through this study, students also explore magnitude of large and small numbers, patterns and concepts in number relationships through a variety of problem solving situations. During the second trimester, students move on to an exploration of concepts, algorithms, interpretations and applications of operations with fractions, decimals and percents. During the third trimester Geometry unit, studies center on the vocabulary, logic and formulas of spatial mathematics and the exploration of properties of two-dimensional polygons using manipulative materials and models. Arriving at formulas for finding perimeter and area, students then apply these formulas to solving problems based on drawings and word problems. In working with circles, students discuss the concept of mathematical constants and apply pi to finding circumference and area.
7th Grade
The primary goal of 7th grade mathematics instruction is to equip all students to reason and communicate proficiently in mathematics. By the end of the year students should have the ability to use the vocabulary, forms of representation, materials, tools & techniques, and intellectual methods of the discipline. The curriculum is designed to impart the basic skills and knowledge to succeed in the study of Algebra in 8th grade.
The approach blends problem-centered instruction with basic skills work to make sure that students are not only successful problem solvers but also have the ability to perform mathematical computations accurately and efficiently. Students are asked to explore engaging problems in number operations, probability and algebra. Modules from the Connected Mathematics Program are used in conjunction with carefully selected outside resources to provide an enriching mathematics curriculum.
8th Grade
A firm grounding in algebra is essential for success in all higher level mathematics and sciences. The eighth grade curriculum is designed to meet the needs of students at different levels based upon a continuum of concrete to abstract thinking abilities. Our students will take a full Algebra I course which incorporates graphical investigations using the TI-84 Plus graphing calculator. One section of eighth grade math will work with algebraic topics at a more accelerated level.
Students who continue taking math each year will complete their senior year with college-level calculus and/or statistics. They should be prepared to take the Advanced Placement exam at the end of their calculus or statistics course, if they choose.
Students taking the accelerated algebra-based course are eligible to take the accelerated course the following year. If they continue at that level, they will stay in the enhanced courses through the twelfth grade when they would prepare for a college-level calculus course and should be prepared to take the BC Advanced Placement exam, if they choose.
131 Intermediate Algebra
required major (if recommended by Department Head)
prerequisite: Algebra I
Grade: 9 (or Grade 10 for 2012-2013 school year)
This course reinforces and builds on algebraic skills and concepts introduced in Algebra I, including work with linear equations, linear systems and quadratic equations. Students will also explore polynomials, rational expressions, laws of exponents, simplifying radicals, factoring, graphing and applications. An emphasis is placed on skill development,problem solving and analytical thinking. The graphing calculator is used to explore and understand concepts.
OR
142 Geometry
required major
prerequisite: Algebra I or Intermediate Algebra
Grade: 9 (or 10)
This course in Euclidean geometry includes the study of geometric figures, shapes, angles, parallel lines, similarity and congruence, area and volume, coordinate geometry, some analytic geometry, and some trigonometry. The deductive thought process is emphasized throughout this course and algebraic skills are reviewed and reinforced.
OR
143 Geometry Accelerated
required major
prerequisite: Accelerated Algebra I or Algebra I /Intermediate Algebra and approval of Department Head
Grade: 9
This course takes a strongly analytical approach to the study of Euclidean geometry. Proofs are emphasized throughout the year to develop strong deductive reasoning. Algebra will be used extensively in the development and solving of problems. Students will begin the study of trigonometry.
152 Algebra II
required major
prerequisite: Geometry
Grade: 10 or 11
This course develops clear, logical thinking as students investigate applications of mathematical concepts and develop their problem solving abilities. Topics include linear and quadratic equations and inequalities, higher degree equations and functions, irrational and complex numbers, exponential and logarithmic functions. The graphing calculator is used for graph exploration.
OR
153 Algebra II/Trigonometry-Accelerated
required major
prerequisite: Geometry-Accelerated and approval of the Department Head
Grade: 10
This course moves at a brisk pace while covering topics in depth. The graphing calculator is used for modeling and analyzing functions. Conventional Algebra II and Precalculus topics are integrated to prepare students for Calculus. Topics include solving algebraic equations and inequalities, function operations, polynomial and rational function analysis, exponential and logarithmic functions and trigonometric functions and trigonometric applications. Upon completion of this course and in consultation with the teacher, students in strong standing may take the appropriate SAT subject area test.
161 Functions and Trigonometry
required major
prerequisite: Algebra II
Grade: 11 or 12
Functions and Trigonometry can be an alternative to Precalculus. This course expands on topics from Algebra II and focuses on enhancing students' skills in problem solving. Topics include exponential and logarithmic functions, polynomial and rational functions, trigonometric functions; and probability, sequences and series. This course is for students who have completed Algebra II and wish to strengthen and broaden their mathematical background before taking Statistics. Students planning to take Calculus must take Precalculus.
162 Precalculus
required major
prerequisite: Algebra II and approval of Department Head
Grade: 11 or 12
This course consolidates Algebra and Geometry skills and emphasizes application and synthesis of those topics to prepare students for Calculus. Topics include solving algebraic equations and inequalities, function operations, polynomial, rational, exponential and logarithmic functions, trigonometric functions and applications, function analysis, and polar graphing. Upon completion of this course and in consultation with the teacher, students in strong standing may take Calculus.
163 Differential Calculus
required major
prerequisite: Algebra II-Accelerated and approval of the Department Head
Grade: 11
This is the first year course of a two-year sequence. Students taking this course are required to take Integral Calculus and Series in their senior year. This course will cover topics including mathematical induction, polar coordinates, the complex plane, and data analysis using the graphing calculator. The students will be taking a rigorous approach to the mathematics and proofs will be emphasized.
171 Statistics
major elective
prerequisite: Algebra II, Functions and Trigonometry or Precalculus
Grade: 12
This course uses exploratory analysis of data to make use of graphical and numerical techniques to study patterns and departure from patterns. Students learn to collect data according to a well-developed plan in order to obtain a valid conjecture about the information. Probability is used to anticipate what the distribution of data should look like under a given model. Statistical inference guides the selection of appropriate models. In general, the AP Statistics curriculum is followed.
172 Calculus
major elective
prerequisite: Precalculus or Algebra II/Trigonometry-Accelerated and approval of Department Head
Grades: 11, 12
This course covers the fundamental concepts of Differential and Integral Calculus. First semester topics include limits, average and instantaneous rate of change, the definition of derivative and techniques of differentiation. The product, power, quotient and chain rules are applied to polynomial, rational, trigonometric, exponential and logarithmic functions. Second semester topics are Riemann sums, integration techniques, area between two curves and volumes of revolution. The topics covered are those included in a college level curriculum.
173 Integral Calculus and Series
major elective
prerequisite: Differential Calculus- Advanced
Grade: 12
This is the second year of a two-year sequence. Upon entering the course, students will have a working knowledge of Differential Calculus, thus we will start with Integral Calculus. The topics covered include those studied in many advanced college-level Calculus curricula. | 677.169 | 1 |
More About
This Textbook
Overview
This book compiles the most widely applicable methods for solving and approximating differential equations.as well asnumerous examples showing the methods use. Topics include ordinary differential equations, symplectic integration of differential equations, and the use of wavelets when numerically solving differential equations.
* For nearly every technique, the book provides:
* The types of equations to which the method is applicable
* The idea behind the method
* The procedure for carrying out the method
* At least one simple example of the method
* Any cautions that should be exercised
* Notes for more advanced users
* References to the literature for more discussion or more examples, including pointers to electronic resources, such as URLs
Audience: Students and practitioners of applied mathematics and engineering, where the solution or approximation of differential equations is necessary.
Editorial Reviews
Booknews
A reference rather than a teaching tool, describing the most widely used techniques for solving both ordinary and partial differential equations. Addressed to students taking courses in such equations at the graduate or undergraduate level and to engineers and scientists who are already familiar with differential equations and their solutions. The only date mentioned for earlier versions is 1989. A version is available with a companion CD-ROM | 677.169 | 1 |
Gateway to Modern Geometry: The Poincare Half-Plane - 2nd edition
Summary: Stahl's Second Edition continues to provide students with�the elementary and constructive development of modern geometry that brings them closer to current geometric research.� At the same time, repeated use is made of high school geometry, algebra, trigonometry, and calculus, thus reinforcing�the students' understanding of these disciplines as well as enhancing their perception of mathematics as a unified endeavor. This distinct approach makes these advanced geometry principle...show mores accessible to undergraduates and graduates178.98 +$3.99 s/h
New
PROFESSIONAL & ACADEMIC BOOKSTORE Dundee, MI
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The fundamental goal in Tussy and Gustafson's PREALGEBRA, Third Edition is to teach students to read, write, and think about mathematics through building a conceptual foundation in the language of mathematics. The book blends instructional approaches that include vocabulary, practice | 677.169 | 1 |
Mathland The Expert Version
9780521468022
ISBN:
0521468027
Publisher: Cambridge University Press
Summary: Mathland is a problem-solving adventure. Pupils are given a problem to solve by an inhabitant of Mathland - the answer determines the next page they go to. The problems come from all areas of maths (apart from statistics) and are intended to stimulate both analytical and empirical approaches.
Norman, L. C. is the author of Mathland The Expert Version, published under ISBN 9780521468022 and 0521468027. Three ...Mathland The Expert Version textbooks are available for sale on ValoreBooks.com, two used from the cheapest price of $35.12, or buy new starting at $229.19.[read more] | 677.169 | 1 |
...
More About
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Related Subjects
Meet the Author
Mary Jane Sterling has been teaching algebra, business calculus, geometry, and finite mathematics at Bradley University in Peoria, Illinois, for more than 30 years. She is the author of Algebra Workbook For Dummies, Algebra II For Dummies, and Algebra II Workbook For Dummies.
Read an Excerpt
Algebra For Dummies
John Wiley & Sons
Chapter One
Assembling Your Tools
In This Chapter
* Nailing down the basics: Numbers
* Recognizing the players: Variables and signs
* Grouping terms and operations together
* Playing the game and following the rules
You probably have heard the word algebra on many occasions and knew that it had something to do with mathematics. Perhaps you remember that algebra has enough information to require taking two separate high school algebra classes - Algebra I and Algebra II. But what exactly is algebra? What is it really used for?
This chapter answers these questions and more, providing the straight scoop on some of the contributions to algebra's development, what it's good for, how algebra is used, and what tools you need to make it happen.
In a nutshell, algebra is a way of generalizing arithmetic. Through the use of variables that can generally represent any value in a given formula, general formulas can be applied to all numbers. Algebra uses positive and negative numbers, integers, fractions, operations, and symbols to analyze the relationships between values. It's a systematic study of numbers and their relationship, and it uses specific rules.
For example, the formula a × 0 = 0 shows that any real number, represented here by the a, multiplied by zero always equals zero. (For more information on themultiplication property of zero, see Chapter 14.)
In algebra, by using an x to represent the number two, for example in x + x + x = 6, you can generalize with the formula 3x = 6.
You may be thinking, "That's great and all, but come on. Is it really necessary to do that - to plop in letters in place of numbers and stuff?" Well, yes. Early mathematicians found that using letters to represent quantities simplified problems. In fact, that's what algebra is all about - simplifying problems.
The basic purpose of algebra has been the same for thousands of years: to allow people to solve problems with unknown answers.
Beginning with the Basics: Numbers
Where would mathematics and algebra be without numbers? A part of everyday life, numbers are the basic building blocks of algebra. Numbers give you a value to work with.
Where would civilization be today if not for numbers? Without numbers to figure the total cubits, Noah couldn't have built his ark. Without numbers to figure the distances, slants, heights, and directions, the pyramids would never have been built. Without numbers to figure out navigational points, the Vikings would never have left Scandinavia. Without numbers to examine distance in space, humankind could not have landed on the moon.
Even the simple tasks and the most common of circumstances require a knowledge of numbers. Suppose that you wanted to figure the amount of gasoline it takes to get from home to work and back each day. You need a number for the total miles between your home and business and another number for the total miles your car can run on one gallon of gasoline.
The different sets of numbers are important because what they look like and how they behave can set the scene for particular situations or help to solve particular problems. It's sometimes really convenient to declare, "I'm only going to look at whole-number answers," because whole numbers do not include fractions. This may happen if you're working through a problem that involves a number of cars. Who wants half a car?
Algebra uses different sets of numbers, such as whole numbers and those that follow here, to solve different problems.
Really real numbers
Real numbers are just what the name implies. In contrast to imaginary numbers, they represent real values - no pretend or make-believe. Real numbers, the most inclusive set of numbers, comprise the full spectrum of numbers; they cover the gamut and can take on any form - fractions or whole numbers, decimal points or no decimal points. The full range of real numbers includes decimals that can go on forever and ever without end. The variations on the theme are endless.
For the purposes of this book, I always refer to real numbers.
Counting on natural numbers
A natural number is a number that comes naturally. What numbers did you first use? Remember someone asking, "How old are you?" You proudly held up four fingers and said, "Four!" The natural numbers are also counting numbers: 1, 2, 3, 4, 5, 6, 7, and so on into infinity.
You use natural numbers to count items. Sometimes the task is to count how many people there are. A half-person won't be considered (and it's a rather grisly thought). You use natural numbers to make lists.
Wholly whole numbers
Whole numbers aren't a whole lot different from the natural numbers. The whole numbers are just all the natural numbers plus a zero: 0, 1, 2, 3, 4, 5, and so on into infinity.
Whole numbersrating integers
Integers allow you to broaden your horizons a bit. Integers incorporate all the qualities of whole numbers and their opposites, or additive inverses of the whole numbers (refer to the "Operating with opposites" section in this chapter for information on additive inverses). Integers can be described as being positive and negative whole numbers: ... -3, -2, -1,0,1,2,3 .... This is the plan in this book, too. After all, who wants a messy answer, even though, in real life, that's more often the case.
Being reasonable: Rational numbers
Rational numbers act rationally! What does that mean? In this case, acting rationally means that the decimal equivalent of the rational number behaves. The decimal ends somewhere, or it has a repeating pattern to it. That's what constitutes "behaving." Some rational numbers have decimals that end in 2, 3.4, 5.77623, -4.5. Other rational numbers have decimals that repeat the same pattern, such as 3.164164164 ... = 3.[bar.164], or .666666666 .[bar.6]. The horizontal bar over the 164 and the 6 lets you know that these numbers repeat forever.
In all cases, rational numbers can be written as a fraction. They all have a fraction that they are equal to. So one definition of a rational number is any number that can be written as a fraction.
Restraining irrational numbers
Irrational numbers are just what you may expect from their name - the opposite of rational numbers. An irrational number cannot be written as a fraction, and decimal values for irrationals never end and never have a nice pattern to them. Whew! Talk about irrational! For example, pi, with its never-ending decimal places, is irrational.
Evening out even and odd numbers
An even number is one that divides evenly by two. "Two, four, six, eight. Who do we appreciate?"
An odd number is one that does not divide evenly by two. The even and odd numbers alternate when you list all the integers.
Varying Variables
Variable is the most general word for a letter that represents the unknown, or what you're solving for in an algebra problem. A variable always represents a number.
Algebra uses letters, called variables, to represent numbers that correspond to specific values. Usually, if you see letters toward the beginning of the alphabet in a problem, such as a, b, or c, they represent known or set values, and the letters toward the end of the alphabet, such as x, y, or z, represent the unknowns, things that can change, or what you're solving for.
The following list goes through some of the more commonly used variables.
An n doesn't really fall at the beginning or end of the alphabet, but it's used frequently in algebra, often representing some unknown quantity or number - probably because n is the first letter in number.
The letter x is often the variable you solve for, maybe because it's a letter of mystery: X marks the spot, the x-factor, The X Files. Whatever the reason x is so popular as a variable, the letter also is used to indicate multiplication. You have to be clear, when you use an x, that it isn't taken to mean multiply.
ITLITL and k are two of the more popular letters used for representing known amounts or constants. The letters that represent variables and numbers are usually small case: a, b, c, and so on. Capitalized letters are used most commonly to represent the answer in a formula, such as the capital A for area of a circle equals pi times the radius squared, A [[pi]r.sup.2] = . (You can find more information on the area of a circle in Chapter 17.) The letter ITLITL, mentioned previously as being a popular choice for a constant, is used frequently in calculus and physics, and it's capitalized there - probably more due to tradition than any good reason.
Speaking in Algebra
Algebra and symbols in algebra are like a foreign language. They all mean something and can be translated back and forth as needed. It's important to know the vocabulary in a foreign language; it's just as important in algebra.
An expression is any combination of values and operations that can be used to show how things belong together and compare to one another. 2[x].sup.2] + x + is an example of an expression.
A term, such as 4xy, is a grouping together of one or more factors (variables and/or numbers). Multiplication is the only thing connecting the number with the variables. Addition and subtraction, on the other hand, separate terms from one another. For example, the expression 3xy + 5x - 6 has three terms.
An equation uses a sign to show a relationship - that two things are equal. By using an equation, tough problems can be reduced to easier problems and simpler answers. An example of an equation is 2[chi square] + 4x = 7. See the chapters in Part III for more information on equations.
An operation is an action performed upon one or two numbers to produce a resulting number. Operations are addition, subtraction, multiplication, division, square roots, and so on. See Chapter 6 for more on operations.
A variable is a letter that always represents a number, but it varies until it's written in an equation or inequality. (An inequality is a comparison of two values. See more on inequalities in Chapter 16.) Then the fate of the variable is set - it can be solved for, and its value becomes the solution of the equation.
A constant is a value or number that never changes in an equation - it's constantly the same. Five (5) is a constant because it is what it is. A variable can be a constant if it is assigned a definite value. Usually, a variable representing a constant is one of the first letters in the alphabet. In the equation a [chi square] bx + c = 0, a, b, and c are constants and the x is the variable. The value of x depends on what a, b, and c are assigned to be.
An exponent is a small number written slightly above and to the right of a variable or number, such as the 2 in the expression [3.sup.2]. It's used to show repeated multiplication. An exponent is also called the power of the value. For more on exponents, see Chapter 4.
Taking Aim at Algebra Operations
In algebra today, a variable represents the unknown (see more on variables in the "Speaking in Algebra" section earlier in this chapter). Before the use of symbols caught on, problems were written out in long, wordy expressions. Actually, using signs and operations was a huge breakthrough. First, a few operations were used, and then algebra became fully symbolic. Nowadays, you may see some words alongside the operations to explain and help you understand, like having subtitles in a movie. Look at this example to see what I mean. Which would you rather write out:
The number of quarts of water multiplied by six and then that value added to three
or
6x + 3?
I'd go for the second option. Wouldn't you?
By doing what early mathematicians did - letting a variable represent a value, then throwing in some operations (addition, subtraction, multiplication, and division), and then using some specific rules that have been established over the years - you have a solid, organized system for simplifying, solving, comparing, or confirming an equation. That's what algebra is all about: That's what algebra's good for.
Deciphering the symbols
The basics of algebra involve symbols. Algebra uses symbols for quantities, operations, relations, or grouping. The symbols are shorthand and are much more efficient than writing out the words or meanings. But you need to know what the symbols represent, and the following list shares some of that info.
+ means add or find the sum, more than, or increased by; the result of addition is the sum.
- means subtract or minus or decreased by or less; the result is the difference.
x means multiply or times. The values being multiplied together are the multipliers or factors; the result is the product. Some other symbols meaning multiply can be grouping symbols: ( ), , { }, ,* : . In algebra, the x symbol is used infrequently because it can be confused with the variable x. The dot is popular because it's easy to write. The grouping symbols are used when you need to contain many terms or a messy expression.
Continues...
Excerpted from Algebra For Dummies by Mary Jane Sterling persons, simple and clear explanations
I am 55 years old and re-taking math classes so I can take Trigonometry and Calculus. I was scared to death (like many other older students) going into my college Elementary Algebra class because I had done so miserably in Algebra in high school 40 years ago. Our college textbook for Elementary Algebra didn't always explain things clearly enough for me. I went to this Dummies book a lot. It is easy to read as well as humorous in places. I found it particularly helpful in learning to solve word problems and I have that chapter in this book marked up as much as my textbook! If you already know Algebra pretty well you may find this book too easy. But, for someone like me who was scared to death because of my past failure this book was a godsend. Like any subject you are trying to conquer, you must put in the study time. I learned many years ago that using supplemental books like this give me a little bit of a different perspective on a subject that just may help tweak something in my gray matter to cement a concept in. Please note that I also used this along with the two other books I recommend below.
11 out of 11 people found this review helpful.
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John21
Posted September 29, 2009
I Also Recommend:
Brilliant guide for both the first time student, and the returning grad looking for review.
This is an absolutely brilliant book for those who desperately need a guide in Algebra II. I have a very bad history with mathematics, to put it simply-my education was pretty badly torn off track somewhere around 7th grade. I'm now a senior in high school, and just got back on track last year. (To give an example of just how badly I was behind-Until my junior year, I didn't know how to distribute or how to solve relatively easy equations.)
My point is, if this book helps *me*, it can help anyone! I'm currently in a Algebra II class, however I want to finish it early and go on to precalc. I went through the Algebra II book, took notes, did problems, and generally studied it. It took me around two months to go through the whole thing and make sure I actually knew it. Tomorrow I'm going to take the test-out option to jump directly into precalc, and I'm very sure I'll pass it.
Not only did this book teach me Algebra II, but it also taught me techniques for doing things I've done before, but in a clumsy way. For example, I've always used a slow method of handling exponents, but the book taught me the proper method to manage exponents quickly and properly.
Finally,the best thing about this book-It makes math FUN. I can't describe how great that is, but trust me, it's wonderful. Having the math explained in a "human" way, with all the relevant information but none of the dry textbook "voice" is brilliant. It lets you jump directly into the math, without feeling like you have to crack a code to understand.
Over all, 5/5, and definitely worth the money.
PS-I'd highly suggest that anyone buying this book get the workbook with the same title. It'll give you problems to try and practice on. This is the absolute best way to learn, so don't pass it up!
5 out of 5 people found this review helpful.
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Anonymous
Posted January 5, 2007
Setting Expectations is Key . . .
note: The '...' in the title are an algebra pun! O) p When I hear or read a book title that includes the phrase, 'for Dummies', I easily pull together the concepts that this book is not likely a foundational text for building one's doctorate upon, and that there might very well be some non-standard methodology in its construct. How is it possible to mistake a book titled, 'Algebra for Dummies' as something other than that?!? p In any event, had my high school algebra teacher(s) approached the subject in this vein, I would have never developed a fear of the subject, and by now, my adult income would [approximate] be about quadruple what it is/was/has been. It took more than twenty years and three math-gifted offspring to discover that I have an aptitude for algebra, but was too afraid to pursue it. I have successfully and convincingly discussed 4-plane time and space theory with literal rocket scientists - naturally figured how to solve for a proportional unknown, blah-blah-blah. In other words, I had the goods, but was delusional about being any good at it. p I say this to point out that most everyone that lives in fear of 'higher mathematics' need not do so. That most all those folks could be and would be hysterically excited to discover that their understanding of math is there, just waiting to be coaxed along a bit. p The author's assertion that the knowledge of algebra is power is not far off the mark, if off at all. Even if you never use it (although you will, or will have the opportunity to do so), the provable fact that you are not a math retard after all is worth considerably more than this book costs. That you will be able to pursue algebraic exploits without fear is just gravy.
4 out of 9 people found this review helpful.
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Anonymous
Posted December 28, 2005
Buy this book but read what I have to say.
I have already learned more within the first week of having this book than I did within the last month. The bad thing is that the author strays too much from what she should be talking about. If you can look past the fact that almost every other paragraph isnt about math then buy the book. If it is going to piss you off, dont buy the book.
2 out of 2 people found this review helpful.
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Anonymous
Posted April 8, 2003
Not worth the money
This book is impossible to understand. It has been 15 years since I have taken an algebra course and bought this to brush up on math, before a chem course this summer. I thought I understood the basics, then I read this and became completely confused. My husband who is a scientist and works with algebra on a daily bases, agreed that the teaching technique in this book does not make sense. There are no examples to test what you have learned. All the examples are worked out for you step by step.
2 out of 4 people found this review helpful.
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Anonymous
Posted January 29, 2012
This book has good math problems
This book has a way of teaching you before you actualy have too do the problem, the math problems are great tooCan someone please reply?
I know this isn't for chatting but I need help with some work. I am in 8th grade algebra 1 but im supose to be in pre-algebra but im in a advanced class . The textbook we're using at my school is Beginning Algebra Sixth Editon; Gustafson Frisk I dont understand alot in it sometimes when the teacher explains it I dont underdstand her clearly. Right now we are learning point-
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Anonymous
Posted March 7, 2013
It's so well written. In a normal textbook you have to spend tim
It's so well written. In a normal textbook you have to spend time trying to decipher what half the material means and how it relates to the rest of the book, but in this book it's almost as though you are listening to a person explain it to you at a party. The book also makes it very easy to understand the way algebraic expressions, equations, and formulae are written.
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Anonymous
Posted December 27, 2012
NEED HELP
Will this help my sis she is in 5 th grade and gets bad grades in math she got an 8% in matg on a 10 qusetion plz tell me if it workz
0 out of 1 people found this review helpful.
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Anonymous
Posted July 6, 2012
I need some feedback please!
I took the advice of some of the reviewers and purchased the hardcopy and the workbook that goes with it. I'm really surprised and proud of how far I'm come in just a few days! I'm on Chapter 9 in the workbook and think/hope I've come across a typo because simplifying and factoring algebraic fractions has caused me to hit a wall. I'm looking at problem #9 in the ninth chapter. They show where they work it out and my answer agrees with that, but what they show as the answer in bold differs by one power in the variable. Can anyone verify this? Many thanks.
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Anonymous
Posted April 3, 2012
Didnt have half the stuff i needed to learn about algebra1
Didnt have enough problems or didnt show me examples so i could get better @mathWhere are the problems?
I, like many people, learn by doing. As far as I can tell this book does not offer any practice problems to test your knowledge. It seems to just spout off concepts and rules but doesn't offer the reader a chance to apply what they've learned. This book could be improved greatly if there were worksheets at the end of each chapter. This book reads more like an informational textbook instead of a lesson book.
0 out of 1 people found this review helpful.
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Anonymous
Posted August 4, 2010
watch out for switch
I recently purchased this book but returned it because I paid $14.36 for it and it came used with a bargain book price of $5.95. Customer service refused to reimburse me the different claiming that it was no longer a bargain book yet if you go to the website it clearly says that you can buy the book used( which I did not) So watch you bill closely because they do not honor their charges or claims
0 out of 1 people found this review helpful.
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Anonymous
Posted April 21, 2009
Should I buy this book???
I am a high school student and I'm currently taking Algebra 1. I am really interested in this book, but I don't know if I should buy this one or the Algebra 2 book. I just need to know the difference so I don't waste my money on buying something I already know a lot about.
-Thank you.
0 out of 2 people found this review helpful.
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Anonymous
Posted May 3, 2005
No Galois theory?
How can you call it an algebra book if it doesn't include Galois theory?
0 out of 1 people found this review helpful.
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Anonymous
Posted July 3, 2004
NOT COMPREHENSIVE ENOUGH
Too general in its explainations. Does not go deep enough to really give reader an understanding of the concepts.
0 out of 1 people found this review helpful.
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Anonymous
Posted May 10, 2004
my review
this book rocks! It really helps me with Algebra! This book is great.
Was this review helpful? YesNoThank you for your feedback.Report this reviewThank you, this review has been flagged. | 677.169 | 1 |
Examples in Mathematics for GCSE: Higher Level
Revised in line with the 1998 syllabuses, this higher-level GCSE maths textbook contains exercises for all syllabus topics, 26 revision papers for ...Show synopsisRevised in line with the 1998 syllabuses, this higher-level GCSE maths textbook contains exercises for all syllabus topics, 26 revision papers for further practice, and ten aural tests for work with a teacher or partner. All numerical answers are included | 677.169 | 1 |
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