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Overview
This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.
The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several variables: the space of several variables and continuous functions, differentiation, multiple integrals, and line and surface integrals, concluding with a selection of related topics. Complete solutions to the problems appear at the end of the text.
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ADVANCED CALCULUS
Dover Publications, Inc.
The positive integers 1, 2, 3, ... are called natural numbers. Since we intend to do things rigorously, we cannot be satisfied with our everyday familiarity with these numbers, and we should try to axiomatize their properties. Let us first write down five statements concerning the natural numbers that we feel should be true:
(I) 1 is a natural number.
(II) To every natural number n there is associated in a unique way another natural number n' called the successor of n.
(III) 1 is not a successor of any natural number.
(IV) If two natural numbers have the same successor, then they are equal.
(V) Let M be a subset of the natural numbers such that: (i) 1 is in M, and (ii) if a natural number is in M, then its successor also is in M. Then M coincides with the set of all the natural numbers.
From now on we consider the statements (I)–(V) to be axioms. They are called the Peano axioms. The natural numbers will be the objects occurring in the Peano axioms. Axiom (V) is called the principle of mathematical induction.
We denote the successor of 1 by 2, the successor of 2 by 3, and so on. Note that 2 ≠ 1. Indeed, if 2 = 1, then 1 is the successor of 1, thus contradicting (III). Note next that 3 ≠ 2. Indeed, if 3 = 2 then, by (IV), 2 = 1, which is false. In general, one can show that all the numbers obtained by taking the successors of 1 any number of times are all different. The proof of this statement, which we shall not give here, is based on induction, that is, on Axiom (V).
We would like to state Axiom (V) in a form more suitable for application:
(V') Let P(n) be a property regarding the natural number n, for any n. Suppose that (i) P(1) is true, and (ii) if P(n) is true, P(n') also is true. Then P(n) is true for all n.
If we define M to be the set of all natural numbers for which P(n) is true, then (V') follows from (V). If, on the other hand, we define P(n) to be the property that n belongs to M, then (V) follows from (V'). Thus (V) and (V') are equivalent axioms.
The Peano axioms give us objects with which to work. We now proceed to define operations on these objects. There are two operations that we consider: addition (+) and multiplication (·). To any given pair of natural numbers each of these operations corresponds another natural number. The precise definition of this correspondence is given in the following theorem.
THEOREM 1. There exist unique operations "+" and "." with the following properties:
n + 1 = n', n + m' = (n + m)', (1)
n · n, n · m' = n · m + n. (2)
The proof will not be given here. We shall often write mn instead of m · n.
THEOREM 2. The following properties are true for all natural numbers m, n, k:
m + n = n + m, mn = nm (the commutative laws) (3)
(m + n) + k = m + (n + k), (mn)k = m(nk) (the associative laws), (4)
m(n + k) = mn + mk, (n +k)m = nm +km (the distributive laws). (5)
The proof of Theorem 2 can be given by induction; it is based on the properties (1) and (2).
We state, without proof, another theorem, known as the trichotomy law:
THEOREM 3. Given any natural numbers m and n, one and only one of the following possibilities occurs:
(i) m = n.
(ii) m = n + x for some natural number x.
(iii) n = m + y for some natural number y.
If (ii) holds, we write m > n or n < m, and we say that m is larger or greater than n and that n is smaller or less than m. If either (i) or (ii) holds, we write m n or n m, and say that m is larger or equal to n and that n is less than or equal to m.
If the solution x of (1) is a positive integer, we write b >a or a< b, and we say that b is larger (or greater) than a and that a is smaller (or less) than b. If x is negative, then the equation b + y = a has the positive solution y = -x. Hence a > b.
We now shall introduce fractions. These are symbols that we write in the form a/b or a/b, where a and b are any integers, and b ≠ 0. These symbols are subject to the following definitions:
a/b = c/d if and only if ad = bc (equality), (2)
a/b + c/d = ad + bc/bd (addition), (3)
a/b · c/d = ac/bd (multiplication). (4)
Note that if a/b = c/d and c/d = e/f, then a/b = e/f.
The last two definitions are acceptable only if we can show that b ≠ 0, d ≠ 0 imply that bd ≠ 0. This, however, can be checked by considering the four possibilities: b positive or negative, d positive or negative.
Definitions (3) and (4) would be most unnatural if it turned out that it is possible to have a/b = a'/b', c/d = c'/d' but a/b + c/d is not equal to a'/b' + c'/d' [or (a/b) · (c/d) is not equal to (a'/b') · (c'/d')]. The following theorem shows that this cannot occur.
THEOREM 2. If a'/b' = a/b and c'/d' = c/d, then
a'/b' + c'/d' = a/b + c/d, (5)
a'/b' · c'/d' = a/b · c/d. (6)
Proof. To prove (5) we have to show that
a'd'/b'd' + b'c'/b'd' = ad + bc/bd
or
a'd'bd + b'c'bd = adb'd' + bcb'd'.
But this follows by multiplying the relation a'b = ab' by dd', the relation c'd = cd' by bb', and adding the resulting equalities. To prove (6) we have to show that
a'c'/b'd' = ac/bd,
or
a'c'bd = acb'd'.
But this follows from
a'c'bd = (a'b)(c'd) = (ab')(cd') = acb'd'.
A fraction a/b is called negative if either a > 0, b< 0 or a< 0, b > 0. It is called positive if either a > 0, b > 0 or a< 0, b< 0. It is called zero if a = 0. It is easily seen that if a fraction c/d is equal to a fraction a/b, then they are either both positive, or both negative, or both zero.
THEOREM 3. The following properties hold for any fractions a/b, c/d, e/f:
It has a solution x = (bc - ad)/bd. If x is positive, then we write a/b< c/d or c/d >a/b, and say that c/d is larger than a/b and that a/b is less than c/d. If x is negative, then the equation
c/d + y = a/b
has the positive solution y = -x, so that a/b >c/d. Note that c/d is positive (negative) if it is larger (smaller) than zero.
The definition of fractions is very intuitive and is, in fact, suggested by our experience with quotients of integers. There is, however, one disturbing feeling about the concept of fractions, due to the fact that fractions having different forms may be equal to each other. This makes it impossible to speak of the zero fraction (since there are many fractions 0/b taking the role of zero). We also cannot assert that Equation (10) has a unique solution. Similarly, the equation
a/b · x = c/d, x fraction (where a ≠ 0) (11)
does not have a unique solution.
To overcome this unpleasant situation, we introduce the concept of a rational number.
DEFINITION. A rational number (a, b) (where a and b are integers, and b ≠ 0) is the class of all the fractions e/f that are equal to a/b.
THEOREM 4. Rational numbers satisfy the commutative laws for addition and multiplication, the associative laws for addition and multiplication, and the distributive laws.
Let us write the analog of Equation (11) for rational numbers:
(a, b) · x = (c, d) x rational (where a ≠ 0). (14)
This equation has a unique solution x = (bc, ad). We write this solution also in the form (c, d)/(a, b) or (c, d)(a, b)-1.
Let us write the analog of (10) for rational numbers:
(a, b) + x = (c, d), x rational. (15)
This equation also has a unique solution: x = (bc - ad, bd). We write it also as (c, d) - (a, b).
Note that there is a one-to-one correspondence between the integers a and the rational numbers (a, 1). This correspondence a -> (a, 1) is preserved under addition and multiplication. Indeed, this follows from the relations
(a, 1) + (b, 1) = (a + b, 1). (a, 1) · (b, 1) = (ab, 1).
Hence, if we write an integer a in the form (a, 1), we see that the integers can be identified with a subset of the rational numbers.
In what follows we shall adopt the definition of rational numbers as classes of fractions a/b. However, for brevity, we shall write the rational numbers (a, b) usually in the form a/b. When we write a/b = c/d, we mean that (a, b) = (c, d), that is, ad = bc. The rational numbers b/1 will also be written, briefly, as b. In particular, the rational number zero will be denoted by 0.
Table of Contents
Contents
Preface,
part one FUNCTIONS OF ONE VARIABLE,
1 NUMBERS AND SEQUENCES,
2 CONTINUOUS FUNCTIONS,
3 DIFFERENTIABLE FUNCTIONS,
4 INTEGRATION,
5 SEQUENCES AND SERIES OF FUNCTIONS,
part two FUNCTIONS OF SEVERAL VARIABLES,
6 SPACE OF SEVERAL VARIABLES AND CONTINUOUS FUNCTIONS ON IT,
7 DIFFERENTIATION,
8 MULTIPLE INTEGRALS,
9 LINE AND SURFACE INTEGRALS,
10 SELECTED TOPICS,
ANSWERS TO PROBLEMS,
Index |
Harold Jacobs's Geometry created a revolution in the approach to teaching this subject, one that gave rise to many ideas now seen in the NCTM Standards. Since its publication nearly one million students have used this legendary text. Suitable for either classroom use or self-paced study, it uses innovative discussions, cartoons, anecdotes, examples, and exercises that unfailingly capture and hold student interest. This edition is the Jacobs for a new generation. It has all the features that have kept the text in class by itself for nearly 3 decades, all in a thoroughly revised, full-color presentation that shows today's students how fun geometry can be. The text remains proof-based although the presentation is in the less formal paragraph format. The approach focuses on guided discovery to help students develop geometric intuition. |
6.24 The method by which mathematics arrives at its equations is the method
of substitution. For equations express the substitutability of two
expressions and, starting from a number of equations, we advance to new
equations by substituting different expressions in accordance with the
equations |
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MATH 1004 - Mathematical Concepts*
Credits:
4
Level:
Lower - Developmental/Remedial Course
Description:
This course will introduce the students to the following topics: order of operations, operations on real numbers, simplifying algebraic expressions, integer exponents, solving linear equations in one variable, graphing linear equations in two variables, and applications such as geometry and modeling. Emphasis is placed on reviewing basic arithmetic skills and elementary algebra topics. Development of arithmetic skills throughout the semester is essential, therefore students will not be allowed to use calculators. Students will work on the development of thinking skills through creative problem solving, writing to explain methods and solutions to problems, and collaborative learning. This is a remedial/developmental course; it will not satisfy any graduation requirements. A grade of C or better is required to register for any subsequent math course. |
Students explore the Fundamental Theorem of Calculus. In the Calculus activity, students investigate indefinite and definite integrals and the relationship between the two, which leads to the discovery of the Fundamental Theorem of CalculusYoung scholars read an article on how calculus is used in the real world. In this calculus lesson, 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.
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Twelfth graders explore functions defined by a definite integral. For this Calculus lesson, 12th graders investigate accumulation functions in which a variable is a limit of integration. The lesson is meant to be an introduction to the Fundamental Theorem of Calculus.
Students compute the longest piece of furniture that can be taken around a corner. In this application of calculus problem, students use their TI-84 calculator to compute the size of the largest piece of furniture that can be taken around two corners. They first ignore all measurements except length, then compute allowing for depth of an object. There are ten exercises with varying degrees of directions that lead the student through the process. |
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The mere thought of having to take a required calculus course is enough to make legions of students break out in a cold sweat. Others who have no ...Show synopsisThe "can" master calculus. It's not nearly as tough as its mystique would lead you to think. Much of calculus is really just very advanced algebra, geometry, and trig. It builds upon and is a logical extension of those subjects. If you can do algebra, geometry, and trig, you can do calculus. "Calculus For Dummies" is intended for three groups of readers: Students taking their first calculus course - If you're enrolled in a calculus course and you find your textbook less than crystal clear, this is the book for you. It covers the most important topics in the first year of calculus: differentiation, integration, and infinite series.Students who need to brush up on their calculus to prepare for other studies - If you've had elementary calculus, but it's been a couple of years and you want to review the concepts to prepare for, say, some graduate program, "Calculus For Dummies" will give you a thorough, no-nonsense refresher course.Adults of all ages who'd like a good introduction to the subject - Non-student readers will find the book's exposition clear and accessible. "Calculus For Dummies" takes calculus out of the ivory tower and brings it down to earth. This "Calculus For Dummies" covers the following topics and more: Real-world examples of calculusThe two big ideas of calculus: differentiation and integrationWhy calculus worksPre-algebra and algebra reviewCommon functions and their graphsLimits and continuityIntegration and approximating areaSequences and series Don't buy the misconception. Sure calculus is difficult - but it's manageable, doable. You made it through algebra, geometry, and trigonometry. Well, calculus just picks up where they leave off - it's simply the next step in a logical progression Calculus for Dummies
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I was in a jugle, a deep, dark, frightening jungle. The jungle of CALCULUS. Suddenly a light came in front. A subtle, fagile one but growing even larger and larger as I slowly crawled towards the middle of this book. Now I walk more confident, steping firmly with a backbone for dummies:-) I strongly |
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This course offers a review of the fundamental concepts of algebra and an introduction to functions. The instruction includes such topics as exponents, radicals, inequalities, absolute value, scientific notation, variation, factoring, linear and quadratic equations, systems of equations, functions and graphs. This course prepares students for the study of pre-calculus. Meets Part I.B. of the GECC. (Shared course in VSC) |
Description: WARNING! If you were enrolled in MATH 8A before April 26, 2012, you will need to enroll in the earlier version of MATH 8B. Please contact a customer service representative to assist you.
Continuation of MATH 8A. Includes solving expressions and equations; graphing points on a coordinate plane; identifying translations, rotations, reflections, and dilations of a graph; and using ratios, proportions, percents, and decimals. Also explores problem-solving strategies and the basic fundamentals of geometry, including angles, triangles, prisms, and cylinders. Note: Due to the nature of the lesson assignments for this course, we are unable to accept assignments via e-mail |
A course designed to review and develop mathematical skills needed for college algebra. Topics include properties of the real number system, graphing, word problems, and selected topics in beginning algebra. Credits are not computed in the grade point average and are not counted toward the 120 semester hour graduation requirement. Offered each semester.
103
Principles of Mathematics
3
A first course in college mathematics focusing on functions and their applications. Topics include equations, graphing, relations, and functions with an emphasis on polynomial, logarithmic, and exponential functions. The TI-89 graphing calculator is required. Prerequisite: MTH 100 or placement. Offered each semester.
111, 112
Theory of Modern Mathematics I, II
3,3
A course designed to develop a basic understanding of mathematical systems (including a development of the natural number system, the integers, and the rational, real, and complex number systems), number theory, probability and statistics, geometry, technology, and the role of deductive and inductive reasoning. Prerequisite: MTH 100 or placement in MTH 103. Offered fall, spring semester, respectively.
151
Precalculus Mathematics
3
A course designed for those students requiring a knowledge of precalculus mathematics with an emphasis on functions and their applications. Topics include advanced algebra, trigonometry, and analytical geometry. This course is intended for those students planning to take MTH 201. The TI-89 graphing calculator is required. Prerequisite: MTH 103 or placement. Offered spring semester.
A study of the basic principles of calculus and their applications. Designed especially for the student desiring a one semester exposure to the fundamental concepts of calculus. Topics include limits, continuity, differentiation of algebraic, logarithmic, and exponential functions. The TI-89 graphing calculator is required. Prerequisite: MTH 103. (NOTE: Credit will not be awarded for MTH 171 after receiving credit for MTH 201.)
Offered each semester.
An introduction to integral calculus and a continued study of calculus as applied to the elementary and transcendental functions. Prerequisite: MTH 201. Offered spring semester.
211
Foundations of Higher Mathematics
3
A course designed to introduce students to basic techniques of writing mathematical proofs as well as fundamental ideas used throughout mathematics. Students will be introduced to the logic needed for deductive reasoning and will use direct and indirect arguments to construct proofs of some elementary theorems. Topics include logic operators and quantifiers, relations, functions, equivalence relations, and Mathematical Induction. Prerequisite: MTH 171 or MTH 201. Offered spring semester.
301
Calculus III
3
A continued study of calculus. Topics include improper integrals, infinite series, power series functions, and differential equations. Prerequisite: MTH 202. Offered fall semester.
An introduction to a systematic study of abstract algebra from a theoretical viewpoint. Topics include the theory of groups, rings, integral domains, and fields. Applications include the construction and description of certain characteristics of the natural numbers, integers, rational, real, and complex numbers. Prerequisite: MTH 202. Alternate years: fall semester, even years and spring semester, odd years, respectively.
315, 316
Theory of Real Variables I, II
3,3
An introduction to a systematic study of analysis from a theoretical viewpoint with an emphasis on real variable theory. Topics include the Archimedean property, set terminology, topology and limits in metric spaces, continuity, uniform continuity, compact and connected sets, differentiation, Riemann-Stieltjes integrals, and the Weierstrass-approximation theorem. Prerequisite: MTH 202. Alternate years: fall semester, odd years and spring semester, even years, respectively.
321
History of Mathematics
2
A course designed to develop an understanding of the historical and current relationships of mathematics to society and the sciences. Junior status.
322
Multivariable Calculus
3
A study of the calculus of real-valued functions of several variables, vector calculus, solid analytical geometry, and differential equations. The TI-89 graphing calculator is required. Prerequisite: MTH 301. Alternate years: spring semester, even years.
An introduction to geometry theories from a modern axiomatic viewpoint. Basically concerned with Euclidean geometry with an introduction to non-Euclidean geometry. Alternate years: fall semester, even years.
402
Point Set Topology
3
An introduction to point-set topology. Topics include general theory, connected and compact spaces, the separation axioms, and properties which remain invariant under certain mappings. On demand.
403
Probability and Statistics
3
A study of the theory of probability and statistics based on a knowledge of calculus. Topics include combinatorial analysis, the axioms of probability, expectation, moment generating functions, random variables, sampling, parameter estimation, hypothesis testing, and regression. Alternate years: fall semester, odd years.
405
Set Theory
3
An introduction to the theory of sets. Topics include the algebra of sets, relations, Peano axioms, order and well ordering, axiom of choice, Zorn's lemma, ordinal and cardinal numbers with their respective arithmetics, Schroder-Bernstein theorem, and the continuum hypothesis. On demand.
432
Ordinary Differential Equations
3
An introduction to ordinary differential equations, and the associated methods, theory, and applications. Topics include first-order equations, second- and higher-order linear equations, and systems of first-order linear equations. Prerequisite: MTH 301. Spring semester, even years.
441
Senior Project
3
A primary emphasis of this course is to provide an opportunity for seniors to demonstrate their knowledge of and abilities in mathematics or a mathematics-related area by completing a senior project. In particular, students will demonstrate that they can: communicate in writingclearly and effectively, deal effectively with basic concepts, deal effectively with theoretical concepts as they arise, and apply their mathematical knowledge to develop and understand concepts outside their normal course of study. Prerequisite: Senior Status. Offered fall semester. |
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Overview
Elementary geometry in n-dimensional Euclidean space is a subject that, under the stimulus of computational geometry, is regaining its former position. This is the first textbook that addresses some fundamental problems of Euclidean geometry that have been solved over the last half-century. The authors, who have made significant contributions to the subject, have taken pains to keep the exposition elementary, making the relationship between it and combinatorics transparent. It should be required reading of anyone in mathematics or computer science who deals with the visual display of information.
Editorial Reviews
From the Publisher
"Elementary methods and exceptionally clear exposition bring a once seemingly advanced subject within the ken of a wide audience of mathematics students. Highly recommended for upper-division undergraduate and graduate students." Choice
"The exposition is marvellous: clear and precise... The powerful theory of valuations, intrinsic volumes and invariant measures built by Hadwiger, Groemer, McMullen and others is an impressive development. The beautiful exposition would make this volume worthwhile even if Klain and Rota hadn't 'something new' to say." Bulletin of the AMS
"The text is very elegant...This book is a very tantalizing one in that there is a definite sense that much of the subject is mature, even the combinatorial analogies |
Essentials of College Algebra with Modeling and VisualizationToday's algebra students want to know thewhybehind what they are learning and it is this that motivates them to succeed in the course. By focusing on algebra in a real-world context, Gary Rockswold gracefully and succinctly answers this need. As many topics taught in today's college algebra course aren't as crucial to students as they once were, Gary has developed this streamlined text, covering linear, quadratic, nonlinear, exponential, and logarithmic functions and systems of equations and inequalities, to get to the heart of what students need from this course. By answering thewhyand streamlining thehow, Rockswold has created a text to serve today's students and help them to truly succeed. |
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This handbook includes illustrated, concise explanations of the most common terms used in general math classes, categorized by subjects that include measurement, algebra, geometry, fractions and decimals, statistics and probability, and problem solving. This newly updated edition also discusses how students can use manipulatives and basic math tools to improve their understanding and includes handy measurement conversion tables.
Each term has a concise definition and an example or illustration. This is a guide that needs to be in every child's desk.
Editorial Reviews
School Library Journal
Gr 4–8—Solid, clearly written definitions of commonly used terms are the mainstay of this revision. "Organized to reflect the different areas of mathematics taught in elementary and junior high schools," entries are arranged alphabetically within chapters such as "Whole Numbers and Operations," "Algebraic Ideas," and "Problem Solving." Students will have to use the index in order to find information. The examples are reasonably complicated and provide good learning reinforcement. Some strategies, such as the windowpane method of multiplying, may require adult assistance. Many entries include one or more examples; for instance, students researching "Division Strategies" will find advice on using a multiples table, repeated subtraction, and manipulatives tangible aids such as paper squares. There are numerous references to manipulatives in the definitions, and the book includes a 40-page chapter on learning with their assistance, which is new to this edition, as are many additional terms and helpful conversion tables. Also new is full color, which is pleasing to the eye, and is complemented by a simple layout with ample white space. This title is worth purchasing even for libraries that own a previous edition, and is a worthy addition to classroom shelves as well as it gives teachers another tool for teaching these sometimes elusive concepts.—Stephanie Farnlacher, Trace Crossings School, Hoover, AL
Related Subjects
Meet the Author
Theresa R. Fitzgerald has been a fourth-grade teacher with the Linden Community Schools since 1992. Theresa's love of math and interest in helping children understand its concepts led to the development of the best-selling Math Dictionary for Kids |
Essentials of Using and Understanding Mathematics A Quantitative Reasoning Approach
9780201793871
0201793873
Summary: 1. Thinking Critically. Recognizing Fallacies. Propositions and Truth Values. Sets and Venn Diagrams. Critical Thinking in Everyday Life. 2. Approaches to Problem Solving. The Problem Solving Power of Units. Standardization Units: More Problem Solving Power. Problem Solving Guidelines and Hints. 3. Numbers in the Real World. Uses and Abuses of Percentages. Putting Numbers in Perspective. Dealing with Uncertainty. How... Numbers Deceive: Polygraphs, Mammograms, and More. 4. Financial Management. The Power of Compounding. Savings Plans. Loan Payments, Credit Cards, and Mortgages. 5. Statistical Reasoning. Fundamentals of Statistics. Should You Believe a Statistical Study? Statistical Tables and Graphs. Graphics in the Media. Correlation and Causality. Characterizing a Data Distribution. 6. Probability: Living with the Odds. Fundamentals of Probability. Combining Probabilities. The Law of Large Numbers. Counting and Probability. 7. Exponential Astonishment. Growth: Linear vs. Exponential. Doubling Time and Half-Life. Exponential Modeling. 8. Mathematics and the Arts. Mathematics and Music. Perspective and Symmetry. Proportions and the Golden Ratio. 9. Mathematics and Politics. Voting: Does the Majority Always Rule? Apportionment: The House of Representatives and Beyond.
Bennett, Jeffrey O. is the author of Essentials of Using and Understanding Mathematics A Quantitative Reasoning Approach, published 2002 under ISBN 9780201793871 and 0201793873. Seventy three Essentials of Using and Understanding Mathematics A Quantitative Reasoning Approach textbooks are available for sale on ValoreBooks.com, seventy used from the cheapest price of $0.25, or buy new starting at $165 |
Tristan Needham offers intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style. This text will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones.
These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
This text will show you the field of complex analysis in a way you almost certainly have not seen before. Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing us attractive pictures at every step of the way. If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses.
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Although aimed at the complete beginner, professional mathematicians and physicists may also enjoy the fresh insights afforded by this unusual approach. The book contains new geometric arguments that yield a more intuitive and elementary approach than the conventional.
There are over 500 diagrams to illuminate the geometric reasoning, no advanced prerequisites, unusually wide-ranging exercises that investigate important and interesting facts on penetrating (yet elementary) treatments of such important topics. |
Mathematical Analysis for Business, Economics, and the Life and Social Sciences
This book is ideal for one- or two-semester or two- or three-quarter courses covering topics in college algebra, finite mathematics, and calculus for ...Show synopsisThis book is ideal for one- or two-semester or two- or three-quarter courses covering topics in college algebra, finite mathematics, and calculus for students in business, economics, and the life and social sciences. Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for students manageability for teachers and learning for students. The table of contents covers a wide range of topics efficiently, enabling instructors to tailor their courses to meet student needs stain, writing or reminder marks. The binding is straight and tight. The book itself is very nice. Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for readers learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding164371643728 |
Practice Makes Perfect: Trigonometry is a comprehensive guide and workbook that covers all the basics of trigonometry that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples, so you can learn at your own pace and really absorb the information. You get to apply your knowledge and practice what you've learned through a variety of exercises, with an answer key for instant feedback. Offering a winning solution for getting a handle on math right away, Practice Makes Perfect: Trigonometry is your ultimate resource for building a solid understanding of trigonometry fundamentals.
Gain a solid understanding of the principles of trigonometry and how these concepts apply to real life with McKeague/Turner's TRIGONOMETRY. This book's proven approach presents contemporary concepts in brief, manageable sections using current, detailed examples and interesting 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 ...
Teach Yourself Trigonometry, now fully revised and updated to take account of recent trends in mathematics, is suitable for beginners and those needing to brush up their skills. It covers the basics in depth, then goes on to give comprehensive coverage of more advanced trigonometry. Each chapter contains a number of worked examples and many carefully graded exercises. Full demonstrations of trigonometric proofs are given in the answers.
Does the Pythagorean Theorem sound like greek to you? Confusing sine with astrological sign? The Standard Deviants are more fun than a textbook and cheaper than hiring a tutor! This trigonometry tutorial will guide you through the twisted world of the Pythagorean Theorem, sines, cosines, tangents, amplitude, curves, double-angle formulas, sum-to-product-formulas and identities, and more! Includes Trigonometry Parts 1&2 at a 15% discount.
Mathematics Describing the Real World Precalculus and Trigonometry-Bruce H. Edwards AVI, XviD, 640x480, 29.97 fps | English, MP3@128 kbps , 2 Ch | ~36x30 mins | 10.82 GB The Teaching Company | 2011 | Course no. 1005 Trad... Filesonic, Fileserve, Uploading, Wupload, Uploadstation Links Engoy all members !!!...
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About Mathematica
Some of the pioneering work in the 1970s on artificial intelligence yielded what we now recognize today as computer algebra systems. Though they are no longer associated with this realm of AI science, computer algebra systems are much used by research mathematicians, scientists, and engineers in creating the everyday vocabulary for research and discovery. In short, a computer algebra system, or CAS, is essentially a type of software that lets users work in symbolic mathematics.Users are able to use a CAS to manipulate mathematical expressions including polynomials in multiple variables, as well as derivatives, integrals, sums, and products of expressions, among many other expressions. One of the most popular CAS programs currently in use is Mathematica from Wolfram Research. It also serves as a programming language, giving users a powerful new tool.Mathematica is perhaps aptly named since Sir Isaac Newton's seminal work was titled Philosophiae Naturalis Principia Mathematica. In it, he revealed his extensive work in physics including the laws of motion and the law of universal gravitation, all based in part on his own invention of 'the calculus.' The modern-day Mathematica program itself works on a variety of platforms and is even made in a student version. Researchers as well as students can find both brand-new and used versions of Mathematica available at auction. It's possible to bid on the PC or Mac versions of the program and many copies are unopened. Expand your work and your knowledge of computer algeba systems with the help of Mathematica. |
This web page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those...
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This web page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies. I am tired of seeing these same old errors over and over again. (I would rather see new, original errors!) I caution my undergraduate students about these errors at the beginning of each semester. Outline of this web page:ERRORS IN COMMUNICATION, including teacher hostility or arrogance, student shyness, unclear wording, bad handwriting, not reading directions, loss of invisible parentheses, terms lost inside an ellipsis ALGEBRA ERRORS, including sign errors, everything is additive, everything is commutative, undistributed cancellations, dimensional errors CONFUSION ABOUT NOTATION, including idiosyncratic inverses, square roots, order of operations, ambiguously written fractions, stream-of-consciousness notations. ERRORS IN REASONING, including going over your work, overlooking irreversibility, not checking for extraneous roots, confusing a statement with its converse, working backward, difficulties with quantifiers, erroneous methods that work, unquestioning faith in calculators. UNWARRANTED GENERALIZATIONS, including Euler's square root error, xx. OTHER COMMON CALCULUS ERRORS, including jumping to conclusions about infinity, loss or misuse of constants of integration, loss of differentials.
A large resource for physics teachers, especiallly at the high school level. Includes news, articles,projects, and a forum. ...
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A large resource for physics teachers, especiallly at the high school level. Includes news, articles,projects, and a forum. From the authors: "The Science House works in partnership with K-12 teachers to emphasize the use of hands-on learning activities in mathematics and science. Through school demonstration programs, student science camps, teacher workshops and innovative laboratory training and support projects, The Science House annually reaches over 2000 teachers and 20,000 students in 60 North Carolina counties. The activities of The Science House bring the science, mathematics and technology expertise of NC State University to enhance teacher effectiveness and to help students visualize careers in these disciplines." In addition to high school physics, site contains a large collection ofhands on activities for physics/astronomy, chemistry (especially Countertop Chemistry), and environmental/earth science.
A collection of webMathematica scripts on a variety of topics in mathematics including calculus, number theory and abstract...
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A collection of webMathematica scripts on a variety of topics in mathematics including calculus, number theory and abstract algebra. In each script, html form input is processed by a remote version of Mathematica and output is returned. No Mathematica expertise is required other than familiarity with some notation (e. g. Pi for pi ).
The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States middle and high...
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The USA Mathematical Talent Search (USAMTS) is a free mathematics competition open to all United States middle and high school students. The USAMTS is primarily funded by the National Security Agency, which has funded the program since 1992
Educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general. Topics...
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Educational and entertaining items pertaining to physics, to the mathematical sciences, and to mathematics in general. Topics include mechanics, waves, light, and mathematics in support of science learning. |
This course presents the mathematical foundations of linear algebra, which includes a review of basic matrix algebra and linear systems of equations as well as basics of linear transformations in Euclidean spaces, determinants, and the Gauss-Jordan Algorithm. The more substantial part of the course begins with abstract vector spaces and the study of linear independence and bases. Further topics may include orthogonality, change of basis, general theory of linear transformations, and eigenvalues and eigenvectors. Other topics may include applications to least-squares approximations and Fourier transforms, differential equations, and computer graphics. |
Welcome to Math Learning Center MLC
Welcome to Math Learning Center (MLC)
In order to adapt to the varied and diverse needs of Cerritos College students, the Math Learning Center (MLC) offers semi-independent courses in six different levels of mathematics: Prealgebra, elementary algebra, intermediate algebra, college algebra, and trigonometry. The format of these courses offers maximum flexibility for students with time constraints, or students who wish to progress more rapidly than normal lecture classes.
Mathematics classes in LC-111 are SEMI-INDEPENDENT classes. These classes cover the same content as other Mathematics courses, but use an entirely different method of instruction. Instead of attending regular lectures, students read and learn the material on their own. Tutorial assistance is provided Mondays and Wednesdays 10:00 a.m. - 8:00 p.m., Tuesdays and Thursdays 9:00 a.m - 9:00 p.m and Fridays 10:00 a.m. - 3:00 p.m. Students take exams according to the schedule given on their class syllabus. These classes are recommended ONLY for students with a strong background in Mathematics who are independent learners. For students who experience Math anxiety or whose background in Mathematics is not strong, we recommend enrolling in a traditional lecture class. |
This site provides collections of applets categorized as lessons and references, plotters and calculators, interactive...
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This site provides collections of applets categorized as lessons and references, plotters and calculators, interactive exercises, mathematical recreations, virtual classes and miscellaneous. Several applets from this site have been reviewed separately.
Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math...
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Thousands of FREE, short, online videos that are focused on explaining and modeling the learning of specific topics in math (basic arithmetic and math to calculus), statistics, biology, physics, chemistry, finance, and other topics. The topics cover K-12 levels and higher education. The simple and clear presented information enables learners to see and review the topics and how to solve the problems at their pace with as much practice as they wish. In particular there are over a thousand videos just for mathematics. The site also contains a handful of interactive mathematics learning objects that are of the drill and practice type.
This teaching tool is designed to help students see the importance of math in their everyday life. On the site, students...
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This teaching tool is designed to help students see the importance of math in their everyday life. On the site, students watch videos, play games and activities, watch "how to" videos, and get help if needed. After participating, students discuss how they solved their problems and how they feel about the work they completed on a classroom blog.
MathAid is a commercially available collection of learning objects incorporating lecture notes, interactive java applets, and...
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MathAid is a commercially available collection of learning objects incorporating lecture notes, interactive java applets, and drill and practice. Entire courses (Intermediate Algebra, Algebra II, Precalculus, Trigonometry, College Algebra, and College Algebra and Trigonometry) are avialable for purchase. Smaller learning objects such as linear regression, conic sections, and matrices are available free online or can be purchased for download. |
Geometry of War - Ivars Peterson (MathTrek)
Leonardo da Vinci was not alone in his fascination with military technology. The University of Oxford's Museum of the History of Science is now featuring a fascinating online exhibition called The Geometry of War, 1500-1750. The 81 illustrations, accompanied
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The Geometry Pages - Cathi Sanders
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geometry-pre-college - Math Forum
A discussion group accessible as a Web-based discussion, a mailing list, or a Usenet newsgroup, for discussions concerning school geometry curricula, teaching geometry, new software and texts, problems for students, and supplementary materials such as
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geometry-puzzles - Math Forum
A discussion group accessible as a Web-based discussion, a mailing list, or a Usenet newsgroup, for interesting problems and conundrums that require only a knowledge of elementary geometry, and discussions of solutions. Read and search archived messages;
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geometrywiz - Teresa Ryan
Blog subtitled "learning about learning and teaching mathematics." Posts, which date back to November, 2013, have included "Reflecting on Learning Objectives," "Reflections and Inquiry," "What Started as Tough, Becomes Good," "Refresh, Reflect, and Reinvent,"
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Getsmarter.org - Council on Competitiveness
A free web site designed to help improve math and science education. Interactive quizzes, games, and tutorials allow students to learn more about specific topics and improve their skills. MSTV, a series of interactive modules, shows how math and scienceGraphing Calculator - Pacific Tech
Graphing Calculator is a tool for quickly visualizing math: type an equation and it is drawn for you without complicated dialog boxes or commands. Graphing Calculator 2.2, a commercial release, features symbolic and numeric methods for visualizing twoGrowth Creature Lab - Mike Riedy
This lab ties the growth of creatures into the Fundamental Theorem of Similarity and extends it to logistic growth. The lab shows students how to collect data from the growing creatures and how the data apply to geometry. Sections of the lesson include:
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handsonmath.com - Charles Gronberg
Hands-on geometry model building materials to purchase, tested and test marketed by the American Association for the Advancement of Science in the late 1990s with the intention of targeting at-risk middle-school students (minorities and girls). The
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HegartyMaths - Colin Hegarty
Hundreds of narrated screencasts covering the UK's Key Stage 3, GCSE and A-Level curriculums, along with many past paper solution walkthroughs. Instructional videos — most for students; some for teachers — also available from the HegartyMaths
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Hey Math!
Animated lessons on a wide range of topics, plus a repository of questions indexed by concept and grade. Many more lessons are available for purchase. Started in Chennai, India, by Nirmala Sankaran and Harsh Rajan, Hey Math is a partnership with the Millennium
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Decatur, GA AlgebraThey will trace the historical development of the modern atomic theory and explain the current quantum mechanical model of the atom. The periodic table will be defined and explained using the modern atomic theory. The properties of atoms will be explored. |
Connections
lesson from Illuminations asks students to look at different classes of polynomial functions by exploring the graphs of the functions. Students should already have a grasp of linear functions, quadratic functions, and what is meant by a polynomial function. The lesson is intended for grades 9-12 and should take three class periods to complete.Wed, 19 Jan 2011 03:00:03 -0600Polynomial Puzzler
algebra lesson helps students explore polynomials by solving puzzles. The activity explains the relationship between expanding and factoring polynomials, as well as factoring trinomials, and multiplying monomials and binomials. The lesson includes an activity sheet, downloadable in PDF format. The material is appropriate for grades 9-12 and should require 1 class period to complete.Fri, 31 Dec 2010 03:00:03 -0600Problem Solving Seminar
Wed, 22 Dec 2010 03:00:02 -0600Taylor Polynomials I
by Lang Moore and David Smith for the Connected Curriculum Project, this is a module using differentiation to find coefficients of polynomial approximations to functions that are not polynomials. This is one of a much larger set of learning modules hosted by Duke University.Tue, 15 Jun 2010 03:00:01 -0500Taylor Polynomials II
by Lang Moore and David Smith of the Connected Curriculum Project, this module continues the study of polynomial approximations to functions, concentrating on the region of convergence. This is one within a much larger set of learning modules hosted by Duke University.Wed, 19 May 2010 03:00:02 -0500Function Institute
(x,y) functions: linear (slope-intercept, point-slope, and general forms), polynomial (definition, roots, graphs), and exponential (definition, exponential growth, radioactive decay, money matters - simple, compound, and continuous interest, effective annual rate, ordinary annuity, and loans). From the Mathematics area of Zona Land: Education in Physics and Mathematics.Fri, 19 Sep 2008 03:00:05 -0500Elementary Algebra
by HippoCampus, a project of the Monterey Institute for Technology and Education, this free online course "is a study of the basic skills and concepts of elementary algebra, including language and operations on sets, operations on signed numbers, simple linear equations and inequalities in one variable, operations on polynomials (including beginning techniques of factoring), integer exponents, brief introduction to radicals, introduction to graphing, and applications." The course has seven chapters: Basic algebra principles; Linear equations and set theory; Inequalities & absolute values; Graphs of linear equations; Exponents, monomials, and polynomials; Factoring polynomials and solving quadratic equations; and Rational and radical expressions and equations. Each is broken into two or three lessons containing objectives, readings, multimedia components, and sample problems. The Topic View section of the site provides the concepts taught in the course in either alphabetical or sequential order for educators looking for more specific and targeted supporting materials for an introductory algebra classroom.Thu, 17 Jul 2008 03:00:02 -0500Introductory Algebra: Algebra 1B
by HippoCampus, a project of the Monterey Institute for Technology and Education, this free online course follows up on a previous course, Algebra 1A, which "develops algebraic fluency by providing students with the skills needed to solve equations and perform important manipulations with numbers, variables, equations, and inequalities. In addition, the course develops proficiency with operations involving monomial and polynomial expressions." Along with providing a syllabus, the Course View section of the site is broken into three units: Exponents, monomials, and polynomials; Relations, functions, & quadratic equations; and Rational & radical expressions & equations. Each unit has five lessons, and each lesson has objectives, readings, multimedia components, assessments, and answers. Also, for instructors looking for more targeted teaching tools, the Topic View of the course presents both a sequential and alphabetical list of individual concepts covered in the course.Wed, 16 Jul 2008 03:00:03 -0500Art and Algebra
by artist Cynthia Wilson at Spokane Falls Community College, this lesson combines art, geometry, and algebra to create two-dimensional models for abstract paintings. On this page, visitors will find a very brief description, along with materials for creating an in-class project complete with objectives, materials, procedures, and a handout for students. In it, students are asked to analyze the use of geometric shapes in the works of Piet Mondrian and Frank Lloyd Wright and create their own compositions by tiling. It is an excellent resource, which allows educators to illustrate to students the importance of mathematics in other disciplines.Wed, 23 Apr 2008 03:00:02 -0500Derivatives
Bourne developed the Interactive Mathematics site while working as a mathematics lecturer at Ngee Ann Polytechnic in Singapore. The site contains numerous mathematics tutorials and resources for students and teachers alike. This specific page is focused on differentiation, or finding derivatives. Bourne walks users through an introduction to differentiation and limits, and then moves on to more specific applications like rate of change, derivatives of polynomials, and differentiating powers of a function. Each topic includes graphs and interactive materials designed to aid users in understanding the presented concepts. The information here is presented in a clear, straightforward manner that is appropriate for introductory and advanced calculus students alike.Tue, 22 Apr 2008 03:00:03 -0500Algebra Review in Ten Lessons
University of Akron has created these excellent algebra tutorials that review some of the main topics in the discipline. There are ten lessons, which focus on topics like radicals and exponents, basic algebra, expansion, polynomials, functions, and trig curves. Each lesson has a table of contents and interactive resources like quizzes, in-line examples, and exercises. Words that appear in green or brown are hyperlinks; click on them to learn more about that topic. Tutorials are viewed as a PDF file, and users must have Acrobat Reader 3.0 or greater to access them. This is a perfect resource for anyone who needs to refresh their knowledge of basic algebra concepts, and is also great for those who are just learning about the subject.Wed, 9 Apr 2008 03:00:02 -0500Mathematics with Alice
with Alice to a wonderland of math! This website utilizes Lewis Carroll's bright universe and most-recognizable character in order to teach mathematical concepts. Many students may feel as though they have stepped through the looking glass when attempting to learn math, but here Alice can help them find their way back again by explaining unfamiliar mathematical terms and concepts in a clear, demonstrative fashion. Despite the use of a children's book as the organizing theme, this website remains true to the historical Carroll and is designed with community college students in mind. Instructors will also find Alice's assistance helpful either as an assignment or inspiration for their classes.Fri, 4 Apr 2008 03:00:02 -0500Polynomials, Rational Functions
page reserved for the analytic study of polynomial functions studied in calculus classes. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; selected topics; other web sites with this focus.Fri, 21 Dec 2007 03:00:02 -0600Maths: Algebra (Constants and Equations Pages)
algebra, "a branch of maths where symbols are used to represent numbers," defining and describing the field and highlighting keywords used. All of the most common algebraic identities: Addition/Subtraction; Multiplication/Division; Polynomials; Powers; Logarithms; Surds; and Complex Numbers.Fri, 7 Dec 2007 03:00:02 -0600Polynomial Functions and Mathematical Modeling
this Real World Learning Object, students will use data collected from the Global Sun – Temperature Telecollaborative project to learn how "linear functions, quadratic functions and other high-order polynomials can be used to model relationships." Over the course of the exercises included in the present learning object, "students will examine and evaluate a number of models created using archived data collected in this project and [t]hey will decide which model best fits the data based on a variety of criteria." This is a useful resource for math and science teachers attempting to teach introductory mathematical modeling techniques.Thu, 22 Nov 2007 03:00:02 -0600 |
't speak for Science but in Engineering there isn't really a big step up from the LC. The first half in first year just goes over differentiation and integration, adding a few bits here and there. Then there is stuff on series expansions which is just a step further than where the LC took it. The second half is much different. Your looking at solving matrices (larger than 2x2) and differential equations, but the concepts aren't hard to grasp. It's more the amount of material rather than the difficulty that I remember from doing first year engineering maths. |
Support Curriculum
A key component of pathways is providing students with support services, which include the supplemental instruction and materials necessary to excel in a rigorous academic program. The unfortunate reality is that some students enter high school lacking fundamental mathematics and literacy skills, making it difficult for them to keep up with high school level work. To address this issue, supplemental instruction must move beyond a reiteration of the original material and offer new ways for students to master these subjects.
For example, ConnectEd has designed an engaging curriculum to help prepare students for success in college-preparatory high school mathematics. The project-based curriculum aims to increase students' motivation to learn and their retention of mathematics skills and concepts through activities such as designing a wind turbine or building a combination lock. Through their hands-on math lessons students learn basic skills, as well as problem solving and communication skills.
View Pre-Algebra Support Curriculum Unit Descriptions (PDF, 198 KB)
View Algebra I Support Curriculum Unit Descriptions(PDF, 257 KB)
To receive a complete set of ConnectEd's math support curriculum, attend one of our professional development sessions. The trainings provide a hands-on experience of our project-based mathematics curriculum, implementation strategies, and a chance to work with other like-minded math educators. |
Math Resources
Math Links and Resources appear below. The links open new windows to the referenced Web sites.
The Khan Academy is an excellent resource that offers over 1,400 video tutorials for all levels of math.
WolframMathworld claims to be "the web's most extensive mathematics resource." Mercer University is a Mathematica campus; access math tools through the Mercer network from the home page of WolframResearch.
The Math Forum @ Drexel offers an index to many good math resources. Ask Dr. Math maintains an extensive archive of commonly-asked questions and answers your individual questions as well.
Read the article Coping with Math Anxiety and you will find useful strategies for working math problems and taking exams. The parent web site Platonic Realms presents mathematical content in an unusual and appealing format.
These sites are not part of the Academic Resource Center or the Mercer University Web server. Therefore, Mercer University is not responsible for their content. If you have any problems or questions, please email the Academic Resource Center at arc@mercer.edu. |
Repetition is another way of figuring out difficult concepts and problems resolved. If repetition is what works best for you I can work on going over repeatedly and giving you as many example problems as you need. Expressions, Equations, and Functions
Properties of Real Numbers
Solving Line |
Dupont, WAPre-algebra gives students the basic building blocks for algebra. Single variable equations and ratios are the biggest focus for pre-algebra students. Weaknesses in fractions and division cause the majority of problems for students in Pre-Algebra. |
ALEX Lesson Plans
Title: Penny Drop That Thang!
Description:
This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College- and Career-Ready Standards showcase lesson plan 17: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. [A-REI3] [MA2013] AL1 (9-12) 20: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. [A-REI6
Subject: Mathematics (8 - 12) Title: Penny Drop That Thang! Description: This lesson is designed to introduce and extend students' knowledge on slope and linear equations. Students will be able to differentiate finding the slope to creating a linear equation.
This is a College- and Career-Ready Standards showcase lesson plan.
Title: Exploring Slope
Description:
The Exploring Slope Description: The
Title: Incline Plane and the Crashing Marble
Description:
StudentsStandard(s): [S1] (8) 1: Identify steps within the scientific process. [S1] (8) 8: Identify Newton's three laws of motion. [S1] (8) 9: Describe how mechanical advantages of simple machines reduce the amount of force needed for work. [S1] (8) 10: Differentiate between potential and kinetic energy 3: Use proportional relationships to solve multistep ratio and percent problems. [7-RP36 - 8), or Science (8) Title: Incline Plane and the Crashing Marble Description: Students
Title: Graphing Stations
Description:
ThisStandard(s): from Graphing Stations Description: This
Title: Human slope
Description:
StudentsStandard(s): 7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [8-EE5
Subject: Mathematics (6 - 12) Title: Human slope Description: Students
Title: Investigating School Safety and Slope
Description:
Using Investigating School Safety and Slope Description: Using
Title: We Love to Graph!
Description:
TheStandard(s): [TC2] CA2 (9-12) 11: Critique digital content for validity, accuracy, bias, currency, and relevance.8), or Technology Education (9 - 12) Title: We Love to Graph! Description: The
Title: Heads Up!
Description:
TheStandard(s):7 - 8) Title: Heads Up! Description: The
Title: What is the slope of the stairs in front of the school?
Description:
The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally GEO (9-12) 31: Prove the slope criteria for parallel and perpendicular lines, and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). [G-GPE5]
Subject: Mathematics (8 - 12) Title: What is the slope of the stairs in front of the school? Description: The purpose of this lesson is to help students apply the mathematical definition of slope to a concrete example. The students will learn to make the appropriate measurements and apply the formula to calculate the slope of the stairs experimentally., Supreme Court Handshake
Description:
In Title: Supreme Court Handshake Description: In Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Beyond Handshakes
Description:
In this lesson, one of a multi-part unit from Illuminations, students explore triangular numbers. This exploration enhances students ability to generalize a pattern with variables.
Standard(s): Title: Beyond Handshakes Description: In this lesson, one of a multi-part unit from Illuminations, students explore triangular numbers. This exploration enhances students ability to generalize a pattern with variables. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
Title: Building Bridges
Description:
In investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [8-SP1
Subject: Mathematics,Professional Development Title: Building Bridges Description: In Create Graphing What
Description:
This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphs.
Standard(s): 13: Interpret the equation y = mx + b as defining a linear function Graphing What Description: This reproducible activity sheet, from an Illuminations lesson, is used by students to record independent and dependent variables as well as the function and symbolic function rule for a set of graphsimate other and whereALEX Learning Assets
Title: What's the Function?
Digital Tool:
Answer Garden, an online brain-storming tool Web Address URL:
Standard(s):
[Title:What's the Function? Digital Tool: Answer Garden, an online brain-storming tool |
Description:
This paper examines why it is necessary to learn algebra. It shows its everyday uses and importance. It uses some basic examples such as calculating the miles per gallon of a car, and solving a calendar riddle.
From the paper:
"Algebra is simply the branch of mathematics in which the operations and procedures of addition and multiplication are applied to variables rather than specific numbers. It is also probably the subject about which schoolchildren are most likely to ask the question: What good will this ever do me when I get out of school. This paper puts forth three different answers to that eternal question of what good will algebra do me?"
Cite this Argumentative Essay:
APA Format
Why is Algebra so Important? (2002, May 05)
Retrieved April 19, 2014, from
Comments
The following paper will look at the struggling US economy and will outline why the economy is slowing down, what the government has done to address the issue (and whether this has been enough) and what the outlook appears to be. Specifically, the ... |
Algebra
Algebra is the foundation of modern mathematics. In this course we draw from materials by the amazing Salman Khan, of Khan Academy, to show you how to work with variables to write expressions, equations, inequalities, and functions.
The course provides an introduction to the mathematical analysis and linear algebra. The course starts with the real numbers and the related one-variable real functions by studying limits, and continuity.
This course begins your journey into the "Real World Math" series. These courses are intended not just to help you learn basic algebra and geometry topics, but also to show you how these topics are used in everyday life.
This introductory mathematics course is for you if you have a solid foundation in arithmetic (that is, you know how to perform operations with real numbers, including negative numbers, fractions, and decimals). Numbers and basic arithmetic are used often in everyday life in both simple situations, like estimating how much change you will get when making a purchase in a store, as well as in more complicated ones, like figuring out how much time it would take to pay off a loan under interest.
Linear algebra is the study of vector spaces and linear mappings between them. In this course, we will begin by reviewing topics you learned in Linear Algebra I, starting with linear equations, followed by a review of vectors and matrices in the context of linear equations.
Numerical analysis is the study of the methods used to solve problems involving continuous variables. It is a highly applied branch of mathematics and computer science, wherein abstract ideas and theories become the quantities describing things we can actually touch and see.
Statistics is about extracting meaning from data. In this class, we will introduce techniques for visualizing relationships in data and systematic techniques for understanding the relationships using mathematics.
The main purpose of this course is to bridge the gap between introductory mathematics courses in algebra, linear algebra, and calculus on one hand and advanced courses like mathematical analysis and abstract algebra, on the other hand, which typically require students to provide proofs of propositions and theorems. |
Functions and Change: A Modeling Approach to College Algebra and Trigonometry by Bruce Crauder, Benny Evans and Alan Noell
English | 2007 | ISBN: 0618858040 | 657 pages | PDF | 9.42 MB
Intended for precalculus courses requiring a graphing calculator, Functions and Change emphasizes the application of mathematics to real problems students encounter each day. Applications from a variety of disciplines, including Astronomy, Biology, and the Social Sciences, make concepts interesting for students who have difficulty with more theoretical coverage of mathematics. In addition to these meaningful applications, the authors' easy-to-read writing style allows students to see mathematics as a descriptive problem-solving tool. An extended version of the successful Functions and Change: A Modeling Approach to College Algebra, this text includes three chapters of trigonometry |
4th and 5th grade students.
This book is an introduction to the field of Cryptology. It uses the Gaia Theory by James Lovelock and Unconscious Collective Theory proposed by Carl Jung regarding teleology. It uses analogies with current technology to show how Earth functions like a Super Computer using Symbolic Systems. Earth would be a planet-sized single cell organism with an electromagnetic field shell membrane.
Beyond All Reasonable Doubt is the story of the greatest puzzle of all time – whether there is, or is not, a Creative Force that many call God. Here, the author shows why mathematics, quantum theory, cosmology, genetics and other forms of science can neither prove nor disprove the reality of God. They all raise further open-ended questions...
Volume 8 focuses on news passing through the Associated Press Feed in early January 2013. It uses more of Forensic Cryptology applied to Olivia Munn taking Taylor Swift's Award, the Seattle Seahawks vs. the Atlanta Falcons on 1/13 of 2013, Katherine Webb vs. the Alabama Crimson Tide, and the 2013 Golden Globe Awards. It discusses the symbolism of the Omega 13 Device in "Galaxy Quest."
This volume shows how the map of the United States can be grafted onto the Space Battleship Yamato (Argo) in the 1970s cartoon "Star Blazers." It discusses how the cartoon was laced with symbols and metaphors that apply to the current state of world affairs. The journey that the Argo makes to Queen Starsha in Iscandar is the journey people must make within themselves to save Mother Earth.
We include an extensive selection of questions.
This eBook introduces the subject of circle and circle geometry, introduces the equation of a circle, explores circle geometry, examines tangential lines to circles and their properties and equations, as well as exploring arc-length and sector area of circles where angles are represented in radians. Further, we include some elementary questions for the student to enjoy.
This eBook introduces the subject of differentiation, across this wide-ranging subject, starting with definitions and first principles to developing an understanding and appreciation of the first and second order differentials of the equation y = xn through a development of the equations of the gradient and normal to a curve at a particular point as well as a thorough review of maximum, minimum .. |
books.google.com - "What can I do with a degree in math?" You... Jobs for Math Majors, Second Ed.
You guide covers the basics of a job search and provides detailed profiles of careers in math. From the worlds of finance and science to manufacturing and education, you'll explore a variety of job options for math majors and determine the best fit for your personal, professional, and practical needs.
Do you want to be an actuary? Work in the banking industry? Program computers? In this updated edition, you'll find:
Job-search basics such as crafting résumés and writing cover letters
Self-assessment exercises to help determine your professional fit
Investigative tools to help you find the perfect job
Networking tips to get your foot in the door before your résumé is even sent
True tales from practicing professionals about everyday life on the job
Current statistics on earnings, advancement, and the future of the profession
Resources for further information, including journals, professional associations, and online resources
Microsoft powerpoint - mathcareers career paths as given in the very readable book. career paths as given in the very readable book. Great Jobs for Math Majors. by Stephen Lambert. and Ruth ... ~dingram/ MAA/ MathCareers.pdf
GREAT JOBS FOR MATH MAJORS-买好书 But it provides you with valuable skills and training that can be applied to a wide range of careers. Great Jobs for Math Majors helps you explore these ... book/ 493853.htm |
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Fundamentals of Mathematical Analysis
Publisher:
American Mathematical Society
Number of Pages:
362
Price:
74.00
ISBN:
9780821891414
This undergraduate textbook builds on Sally's Tools of the Trade: Introduction to Advanced Mathematics and requires a solid background in calculus and linear algebra. Two detailed appendices, covering nearly thirty pages, are references for the prerequisite number theory and linear algebra. This is a dense work, light on illustrations and with little in the way of flavoring asides. Exercises are sprinkled throughout the chapters, rather than gathered at the end. No solutions are provided, which is fine for a work that is not intended as a self-sufficient resource for independent readers. This also makes it an efficient reference or adjunct work to any assigned text. I would have been glad to have had it myself when I first encountered this material.
The handful of "Challenge Problems" leading off each chapter should serve as a focusing, if bracing, introduction to each chapter. Preceding this is often a paragraph-length introduction to the subject at hand. Typically, this is from a related important work by authors such as Banach and Toeplitz. Following are the expected definitions, theorems, and proofs seasoned with the aforementioned exercises. The chapters conclude with "Independent Projects." These comprise aligned and select material that unifies and applies the theory. This supplemental content, designed to expand the reader's understanding, separates this text from others that may be considered. Examples of these projects include an exploration of spectral theory for compact self-adjoint operators on a Hilbert space and differentiability of a monotone function.
Sally begins by constructing the real and complex numbers, then explores metric theory, normed linear spaces, and differentiation in separate chapters. The chapter on integration follows Lebesgue, not Riemann, and the seven-chapter work concludes with Fourier analysis. Terms and notation are helpfully indexed separately. The elegant, complete, and rigorous presentation makes this an idea work for capable undergraduate and graduate students interested in learning and even teaching real analysis.
Tom Schulte teaches mathematics at Oakland Community College in Michigan. |
st an…
art Calculator a polar graph is generated if the expressions include only 2 variables and at least one is Greek letter α, β, γ or θ. The input pad of Smart Calculator includes a θ button to assist user to input polar expressions;* Add input function to input values from command line while program is running;* Support multiple SD cards. User is able to select the storage to place app's data and SCP for JAVA;* Fun…
cientific Calculator Plus is a powerful mathematical tool to do mathematical analysis and evaluate complicated mathematical expressions similar to Matlab. More than Matlab, it has a mathematical equation(s) solver which helps user to solve mathematical problems. It supports complex number, matrix, (higher level) integration, 2D, polar and 3D chart, string, programming (using a easy-to-use language called MFP) and unit conversion. It can run in bo |
Practical Problems in Mathematics: For Welders
Book Description: Practical Problems in Mathematics for Welders, 5E, takes the same straightforward and practical approach to mathematics that made previous editions so highly effective, and combines it with the latest procedures and practices in the welding industry. With this applications oriented book, readers will learn how to solve the types of math problems faced regularly by welders. Each unit begins with a review of the basic mathematical procedures used in standard operations and progresses to more advanced formulas. With real-world welding examples and clear, uncomplicated explanations, this book will provide readers with the mathematical tools needed to be successful in their welding careers |
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). |
Math Level L: Logarithms, Calculus
Level L marks the beginning of calculus. Students begin by studying logarithmic functions, followed by basic differentiation and definite and indefinite integration. The level concludes with an analysis of applications of integration, including areas, volumes, velocity and distance. |
Summary: One of the authors' stated goals for this publication is to ''modernize'' the course through the integration of Mathematica. Besides introducing students to the multivariable uses of Mathematica, and instructing them on how to use it as a tool in simplifying calculations, they also present intoductions to geometry, mathematical physics, and kinematics, topics of particular interest to engineering and physical science students. In using Mathematica as a tool, the authors take pains no...show moret to use it simply to define things as a whole bunch of new ''gadgets'' streamlined to the taste of the authors, but rather they exploit the tremendous resources built into the program. They also make it clear that Mathematica is not algorithms. At the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The problem sets give students an opportunity to practice their newly learned skills, covering simple calculations with Mathematica, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numberical integration. They also cover the practice of incorporating text and headings into a Mathematica notebook. A DOS-formatted diskette accompanies the printed work, containing both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students. This supplementary work can be used with any standard multivariable calculus textbook. It is assumed that in most cases students will also have access to an introductory primer for Mathematic |
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Math Resources
Students looking for help with mathematics or statistics have resources other than the ULC - math/stats help available to them. These include:
the Math Readiness Course - this non-credit course is a review of high school mathematics concepts that are used in calculus. It is offered as a two-week summer course, as an evening course during fall and winter sessions, and as an online course. Please visit the Math Readiness page for more information.
the Exercises in Math Readiness website - this is a local collection of notes and exercises on high school math topics is a web-based sampling of the exercises from the University of Saskatchewan Math Readiness course.
books - the University Bookstore stocks some books on refresher mathematics (e.g. "College Algebra," "Forgotten Trigonometry") in the U of S bookstore (they might be in the math textbook section or in the general reference section). There are also review "sheets" in the mathematics textbook section of the bookstore. Interested students may want to look for books on refresher mathematics in the University Library. Some students have found borrowing high school textbooks from the Education Library helpful in reviewing math concepts.
Suggestions for Students Who Like Mathematics or Statistics
Do you enjoy your mathematics or statistics courses? If you are interested in pursuing a mathematics or statistics program of study, contact the Department of Mathematics and Statistics (email: math@math.usask.ca). Additionally, you might enjoy touching base with other students who have similar interests. E-mail Holly Fraser at holly.fraser@usask.ca and she'll put you in touch with other people who share your interest in and enthusiasm for mathematics and statistics. |
Description:
The traditional approach to engineering mathematics education begins with one year of freshman calculus as a prerequisite to subsequent core engineering courses. However, the inability of incoming students to successfully advance through the traditional freshman calculus sequence is a primary cause of attrition in engineering programs across the country. As a result, the WSU model seeks to redefine the way in which engineering mathematics is taught, with the goal of increasing student retention, motivation and success in engineering.
The WSU approach begins with the development of a novel freshman-level engineering mathematics course, EGR 101 Introductory Mathematics for Engineering Applications. Taught by engineering faculty, the course includes lecture, laboratory and recitation components. Using an application-oriented, hands-on approach, the course addresses only the salient math topics actually used in core engineering courses. These include the traditional physics, engineering mechanics, electric circuits and computer programming sequences. The EGR 101 course replaces traditional math prerequisite requirements for the above core courses, so that students can advance in the engineering curriculum without having completed a traditional freshman calculus sequence. This has enabled a significant restructuring of the engineering curriculum, including the placement of formerly sophomore-level engineering courses within the freshman year. The WSU model concludes with the development of a revised engineering math sequence, taught by the math department later in the curriculum, in concert with College and ABET requirements. The result has shifted the traditional emphasis on math prerequisite requirements to an emphasis on engineering motivation for math, with a "just-in-time" structuring of the new math sequence.
MERC Reviewers comments: The instructor has spent considerable amount of time and effort to develop this course. I really commend the instructor for the innovativeness in using MATLAB for solving problems and relating to practical applications. I very highly recommend that this course be offered to bring about the role of mathematics in engineering education. |
Polynomial regression models are often used in economics such as utility function, forecasting, cost and befit analysis, etc....
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Polynomial regression models are often used in economics such as utility function, forecasting, cost and befit analysis, etc. This JavaScript provides polynomial regression up to fourth degrees. This site also presents a JavaScript implementation of the Newton's root finding method.
This course is designed to introduce you to quantitative analysis (QA), or the application of statistics in the workplace. ...
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This course is designed to introduce you to quantitative analysis (QA), or the application of statistics in the workplace. The student will learn how to apply statistical tools to analyze data, draw conclusions, and make predictions of the future. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Business Administration 204) |
Mathematics: Applications and Concepts is a three-text Middle School series intended to bridge the gap from Elementary Mathematics to High School Mathematics. The program is designed to motivate middle school students, enable
Sweet Sue's adventures explain to the beginning reader all the traits and habits of an unusually interesting animal. Whether Sweet Sue is catching food (including live bees) or training her frisky young,
SMP Interact: Framework Edition supports a teacher-led, discussion-based approach as the revised Framework promotes. With three differentiated tiers providing coherance and clear progression it has been extensively trialled to ensure effectiveness and
Imagine killer nannies patrolling the streets of New York, their baby carriages bristling with automatic weapons, even as prowling, infertile parent-wannabes make desperate grabs at the carriages' precious cargo.... This is the
Classic Chemistry Demonstrations is an essential, much-used resource book for all chemistry teachers. It is a collection of chemistry experiments, many well-known others less so, for demonstration in front of a class
This book fits the Business Mathematics course in high schools. It is structured around a three-pronged approach: Basic math review, personal finance and business mathematics. Build and strengthens students' basic skills in |
More About
This Textbook
Overview
This introduction to recent developments in algebraic combinatorics illustrates how research in mathematics actually progresses. The author recounts the dramatic search for and discovery of a proof of a counting formula conjectured in the late 1970s: the number of n x n alternating sign matrices, objects that generalize permutation matrices. While it was apparent that the conjecture must be true, the proof was elusive. As a result, researchers became drawn to this problem and made connections to aspects of the invariant theory of Jacobi, Sylvester, Cayley, MacMahon, Schur, and Young; to partitions and plane partitions; to symmetric functions; to hypergeometric and basic hypergeometric series; and, finally, to the six-vertex model of statistical mechanics. This volume is accessible to anyone with a knowledge of linear algebra, and it includes extensive exercises and Mathematica programs to help facilitate personal exploration. Students will learn what mathematicians actually do in an interesting and new area of mathematics, and even researchers in combinatorics will find something unique within Proofs and Confirmations.
Editorial Reviews
From the Publisher
"Bressoud has created a beautiful new genre of mathematical exposition. It is neither popular mathematics, nor textbook, nor research monograph, nor problem book. It is all these and much more: a historical novel, a detective story and, implicitly, a philosophical manifesto. Yet the mathematics is deep, and all the proofs are complete...Proofs and Confirmations is destined to be a classic." American Mathematical Monthly has done a very nice job of presenting us with a readable book which delivers a self-contained look at some current mathematics. And he's done a wonderful job at exposing the flavor of research mathematics. Take a look." MAA Online
"the book will appeal to anyone who likes algebra and combinatorics, and is curious as to what is currently going on at intersection of these two disciplines." William Gasarch |
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Math instructors promoting calculator usage in college classrooms may want to rethink their teaching strategies, says Samuel King, postdoctoral student in the University of Pittsburgh's Learning Research & Development Center. King has proposed the need for further research regarding calculators' role in the classroom after conducting a limited study with undergraduate engineering students published in the British Journal of Educational Technology.
"We really can't assume that calculators are helping students," said King. "The goal is to understand the core concepts during the lecture. What we found is that use of calculators isn't necessarily helping in that regard."
Together with Carol Robinson, coauthor and director of the Mathematics Education Centre at Loughborough University in England, King examined whether the inherent characteristics of the mathematics questions presented to students facilitated a deep or surface approach to learning. Using a limited sample size, they interviewed 10 second-year undergraduate students enrolled in a competitive engineering program. The students were given a number of mathematical questions related to sine waves—a mathematical function that describes a smooth repetitive oscillation—and were allowed to use calculators to answer them. More than half of the students adopted the option of using the calculators to solve the problem.
"Instead of being able to accurately represent or visualize a sine wave, these students adopted a trial-and-error method by entering values into a calculator to determine which of the four answers provided was correct," said King. "It was apparent that the students who adopted this approach had limited understanding of the concept, as none of them attempted to sketch the sine wave after they worked out one or two values."
After completing the problems, the students were interviewed about their process. A student who had used a calculator noted that she struggled with the answer because she couldn't remember the "rules" regarding sine and it was "easier" to use a calculator. In contrast, a student who did not use a calculator was asked why someone might have a problem answering this question. The student said he didn't see a reason for a problem. However, he noted that one may have trouble visualizing a sine wave if he/she is told not to use a calculator.
"The limited evidence we collected about the largely procedural use of calculators as a substitute for the mathematical thinking presented indicates that there might be a need to rethink how and when calculators may be used in classes—especially at the undergraduate level," said King. "Are these tools really helping to prepare students or are the students using the tools as a way to bypass information that is difficult to understand? Our evidence suggests the latter, and we encourage more research be done in this area."
King also suggests that relevant research should be done investigating the correlation between how and why students use calculators to evaluate the types of learning approaches that students adopt toward problem solving in mathematics |
ical Analysis in Engineering: How to Use the Basic Tools
This user-friendly text shows how to use mathematics to formulate, solve and analyse physical problems. Rather than follow the traditional approach ...Show synopsisThis user-friendly text shows how to use mathematics to formulate, solve and analyse physical problems. Rather than follow the traditional approach of stating mathematical principles and then citing some physical examples for illustration, the book puts applications at centre stage; that is, it starts with the problem, finds the mathematics that suits it and ends with a mathematical analysis of the physics. Physical examples are selected primarily from applied mechanics. Among topics included are Fourier series, separation of variables, Bessel functions, Fourier and Laplace transforms, Green's functions and complex function theories. Also covered are advanced topics such as Riemann-Hilbert techniques, perturbation methods, and practical topics such as symbolic computation. Engineering students, who often feel more awe than confidence and enthusiasm toward applied mathematics, will find this approach to mathematics goes a long way toward a sharper understanding of the physical |
The book is a wonderful presentation of the essential concepts, ideas and results of Euclidean Geometry useful in solving olympiad problems of various level of difficulties. The theoretical part is excellently illustrated by challenging olympiad problems. The complete solutions to these problems are carefully presented, most of them together with several interesting comments and remarks.
MSC main category:
51 Geometry
MSC category:
51-01
Review:
Geometry is one of the most important and active fields in Mathematics with a substantial and large variety of applications in several disciplines, and with a very high impact in all levels of mathematical education.
This book deals with the essential results in plane Euclidean Geometry that are useful in solving difficult olympiad problems. The reader will become acquainted with well - known theorems such as Menelaus theorem, Ceva theorem, Ptolemy theorem, Stewart theorem, Euler nine point circle and the Euler line, etc., in the context of some complex geometric problems.
This book provides a very synthetic presentation of concepts and ideas in Euclidean Geometry, most of them without proof since its main goal is to illustrate by nonstandard problems how these ideas can be used. The book clearly demonstrates how instrumental it is to use various tools for the formulation of basic geometrical questions in order to find the simplest and the most intuitive arguments to solve a variety of problems. The book under review fully fits this purpose. In several situations and from different points of view the book presents the power of some natural geometric ideas. Most of the material is really suitable for advanced high-school classes and the book itself could offer a great service of attracting bright students to Mathematics.
The textbook is organized into six chapters. The first four chapters present some theoretical results including suggestive examples on the following aspects : Euclid's Elements, logic, methods of proof, fundamentals on geometric transformations and some important theoretical results in solving problems. Chapter 5 contains carefully selected Olympiad - caliber problems and it is organized into three sections : geometric problems with basic theory, geometric problems with more advanced theory, geometric inequalities.
The book concludes with a useful and relevant bibliography containing 99 references. It also contains an index of symbols and a subject index.
I would like to conclude this review with the statement of appreciation of the Fields Medalist Michael H. Freedman who wrote the foreword of the book :
`"........Young people need such texts, grounded in our shared intellectual history and challenging them to excel and create a continuity with the past. Geometry has seemed destined to give way in our modern computerized world to algebra. As with Michael Th. Rassias' previous homonymous book on number theory, it is a pleasure to see the mental discipline of the ancient Greeks so well represented to a youthful audience ".
All in all the text is a highly recommendable choice for any olympiad training program, and fills some gaps in the existing literature in Euclidean Geometry. The book is a very useful source of models and ideas for students, teachers, heads of national teams and authors of problems, as well as for people who are interested in mathematics and solving difficult problems.
This volume belongs to a three-volume edition devoted to reprint classical papers on algebraic and differential topology published in the 1950s-1960s. This is a collection of carefully chosen classical papers who have had a big impact in the development of algebraic topology during the XX century.
MSC main category:
55 Algebraic topology
Review:
This volume belongs to a three-volume edition devoted to reprint classical papers on algebraic and differential topology published in the 1950s-1960s. Some of these papers may be difficult to find, and several of them have been translated (by V.P. Golubyatnikov) into English for this volume.
The first volume was dedicated to Cobordism theory, the second one to Smooth structures on manifolds. The present volume is devoted, as the title says, to Spectral sequences in topology. The papers appearing in the volume are the following:
This is a collection of carefully chosen classical papers who have had a big impact in the development of algebraic topology during the XX century. The papers that were published in other languages have been translated into English. All the papers are accompanied by useful comments about further developments or related publications.
This is a nice volume that should not be missing in any Mathematics Library.
This is a collection of problems and solutions of miscellaneous mathematical problems at an advanced undergraduate level. They are selected from the notes of Jim Totten (1947-2008) after he passed away unexpectedly. Jim Totten was problem editor and later editor in chief of Crux Mathematicorum of the Canadian Mathematical Society.
URL for publisher, author, or book:
MSC main category:
00 General
MSC category:
00A07
Review:
Jim Totten was problem editor and later editor in chief of the journal Crux Mathematicorum of the Canadian Mathematical Society. In 1986 he collected 80 of his problems under the title Problems of the Week as volume 7 of the ATOM (A Taste of Mathematics) series published by the CMS. The origin of the title is that when he started teaching in 1976, he posted a weekly problem to challenge his students. The response to these was so positive that it tempted him to continue the idea for about 30 more years.
The present book contains 406 problems and solutions that were collected from Totten's notes that he left after his unexpected death in 2008. Although, to solve the problems, the required mathematics are at an undergraduate level, covering many different topics such as logic, geometry, functions, number theory, statistics, etc., the problems are often quite challenging. Even for professional mathematicians they are not at all trivial. They are often formulated as brain teasing puzzles with an underlying recreational flavour. Whatever the formulation is, the solution always requires some sound mathematical reasoning. The witty solutions are included and often require more than just the application of standard class room recipes. Not that they are terribly complicated, once you know the trick, but it may take a pencil and possibly several pages of trial an error to arrive at the key that will set you on the rails to find the solution. Since Fermat's margin note, we know that a problem with a simple formulation can take a highly advanced body of mathematics to solve a seemingly simple problem. Not in the case of these problems. All what is needed stays well within the package that an undergraduate student should be able to deal with. Just a clear and agile mind that is sensitive for this type of puzzles suffices.
The kind of problems can best be illustrated by giving two examples that I selected just because they are short to formulate. Here is one from number theory: "How old is the captain, how many children has he, and how long is his boat, given the product 32118 of the three desired integers? The length of his boat is given in feet (several feet), the captain has both sons and daughters, he has more years than children, but he is not yet one hundred years old." And here is one from plane geometry: "Three circles or radius r each pass through the centers of the other two. What is the area of their common intersection?".
Solving all of the problems will provide many hours and days of puzzling pass-time. There is however the temptation to read the answer prematurely because the proposed solution immediately follows the problem formulation, enticing the reader to read it before he or she even tried to work it out him- or herself. If the purpose is that the reader should indeed find the solutions, then it might have been a better idea to give all the problems in the first part and all the solutions in a second part. However, if the reader is looking for problems to give to others and at the same time estimate the level of difficulty, then the present format is of course the better one. It is technically also the simpler solution because many of the geometric problems require drawings, which should then be repeated for problem and answer to avoid an annoying flipping back and forth to match the text with the figure.
There are of course many other popular puzzler books on the market that also have a lot of brain teasers and logical recreations, but these are usually requiring less mathematics and less computation. Martin Gardner's mathematical puzzles come close, but there the emphasis is often on the recreational aspect, rather than on the mathematical side. In Totten's problems the scales tip much more to the mathematical side.
The book studies different analysis perturbation of operators , including Moore-Penrose inverse, and Drazin inverse of operaors .Several miscellaneous applications are also included.
MSC main category:
46 Functional analysis
Review:
This book concerns with the theory of stable perturbations of operators in
Banach spaces . Thus the perturbation analysis for generalized inverses, the
Moore-Penrose inverse and Drazin inverse of operators under stable pertur-
bation. After a preliminary chapter including several basic results in Func-
tional Analysis ( Hilbert spaces, operators and C + algebras ) the book studies
carefully the relationships among the densely-defined operators with closed
range and the reduced minimum modulus of densely defined operators . The
Moore-Penrose inverse and its stable perturbations in Hilbert spaces and in
C ∗ -algebras is also presented . Several results of the K-theory in C + algebras
are also included. The last chapters of the book contain some miscellaneous
applications and related topics to the perturbation theory, like the approxi-
mate polar decomposition in C ∗ -algebras, and some applications of Moore-
Penrose inverses in frame theory.The list of references in the Bibliography is
quite extensive. |
understanding of Algebra 1 will make all the subsequent math classes make more sense. Algebra 2 covers a wide variety of topics that can be confusing to the new Algebra 2 learner. If one explanation for solving a problem doesn't work, I try to find an explanation that will work for the student in terms the student can understand |
The Math Zone
The Math Zone is located in the new, state-of-the-art Math Learning Center in North Hall, directly adjacent to Echlin Hall.
An Innovation in Learning Mathematics
The Math Zone provides a non-traditional education experience in mathematics that is targeted to each student's unique learning style. The Math Zone is located in the new, state-of-the-art Math Learning Center in North Hall, directly adjacent to Echlin Hall, and is a part of the Department of Mathematics.
Math at your own pace.
The Math Zone uses "adaptive technology" to create an individualized educational experience where students learn at their own pace with the support of math instructors and tutors. The learning platform quickly understands (or adapts to) areas where students demonstrate mastery of topics and moves on to deliver precise instruction and support to subjects where a student is having difficulty.
Our goal is student success.
The faculty are there not only to answer the math questions students have, but to monitor student progress and to guide them in the mathematics learning process. Students have an opportunity to complete up to three courses in mathematics in a single semester, or move more slowly if they need the time to absorb new ideas.
The Math Zone is an innovation in mathematics education, merging e-learning technology with traditional teaching methods to enhance student success.
Important Details for Students to Know
If you are taking a math class run through the Math Zone, and have any questions regarding your class, please contact the Math Zone Coordinator.
A brief explanation of the learning environment you will encounter in the Math Zone can be found by navigating through our online documents: |
Edward Delafuente's Recommendations
It is a hard subject- don't expect a handout but this professor takes the time to explain the concepts in simpler terms and will review anything the students request. He also gives websites you can go to for practice and is generous with curves |
"Bryon here helps people prepare for tests of advanced numerical skills that are used extensively to weed out candidates for management and graduate jobs and for places in postgraduate courses. The main tests are the ABLE Financial Appraisal, GMAT, SHL Graduate Battery, and McKinsey Problem Solving, but they are similar enough that he takes them as a group rather than distinguishing between them. The nine sample tests cover accounting and business comprehension, geometry and further quantitative operations, advanced numeracy, and data interpretation. He pres answers and explanations, and a key for interpreting scores." -- Book News
There is an increasing need for numeracy skills in all aspects of life and What Teachers Need to Know About Numeracy explores the issues that are emerging regarding the teaching of these skills, beginning with preschool and the early years of primary school through to adults with poor numeracy skills. It draws on research and relevant literature from several different countries to provide a comprehensive overview of the subject and contains many links to other sources of information and additional resources.
Numerical reasoning and data interpretation tests are routinely used in recruitment procedures. These tests represent a considerable challenge for many candidates, and the prospect of facing them can be daunting. How to Pass Numerical Reasoning Tests is a valuable resource for anyone who needs to brush up on their math skills. An overview of the basics is followed by a step-by-step guide to numerical tests, including fractions and decimals, rates, percentages and ratios, and proportions. This revised edition is full of useful tips to help the reader understand and answer questions without using a calculator.
There are many approaches to researching the difficulties in learning that students experience in the key areas of literacy and numeracy. This book seeks to advance understanding of these difficulties and the interventions that have been used to improve outcomes. The book addresses the sometimes complementary and sometimes contradictory results, and generates new approaches to understanding and serving students with difficulties in literacy and numeracy
With Big Brys BBQ You Will Learn Everything You Need To Know About Western style Barbeque. Big Bry Is A True Cowboy: An Ex-professional Bull Rider, Hunter And All American Guy. Hes Kind, Informative And Even A Little Silly At Times. Titles And Recipes Accompany His Guidance, So Anyone Can Follow Along. Big Brys Western style BBQ Teaches The Average Person Professional Santa Maria Barbequing Techniques
Written in a superb jargon-free style, this book offers important insights into the often confusing world of numeracy. By looking at learning difficulties in maths from several perspectives, including the language of mathematics, thinking styles and the demands of individual topics, Steve Chinn delivers a comprehensive yet succinct text which will become an essential classroom companion to anyone who uses it.
For Math Aficionados From All Walks of Life THE LITTLE GREEN MATH BOOK is based on a simple but powerful observation: Individuals who develop outstanding math and numeracy skills do so primarily by mastering a limited number of the most important math principles and problem solving techniques, which they use over and over again. What are these recurring principles and techniques? The answer to this question is the basis of this book. |
The West Point Bridge Design Contest Web site has a number of educational resources for middle and high school students. The main feature is the bridge design software, which allows the user to "model, test, and...
This Website from the University of Tennessee, Knoxville's Mathematics Department provides tutorials, drills, and computer programs that aid in understanding pre-calculus and calculus. The well-organized materials...
From abelian group to zero divisor (definitions), and from Artin-Wedderburn theorem to Wedderburn's theorem, this site provides concise explanations of complex concepts in abstract algebra. Provided by Professor John A....
This online tutorial is intended for college students taking an early course in mathematical optimization or linear differential equations. Although it is written by a professor of economics, little economic theory is...
The Agency for Toxic Substances and Disease Registry, an agency of the US Department of Health and Human Services, seeks "to serve the public by using the best science, taking responsive public health actions, and... |
In this module, students draw on their foundation of the analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students identify and make connections between zeros of polynomials and solutions of polynomial equations. The role of factoring, as both an aid to the algebra and to the graphing of polynomials, is explored. Students continue to build upon the reasoning process of solving equations as they solve polynomial, rational, and radical equations, as well as linear and non-linear systems of equations. An additional theme of this module is that the arithmetic of rational expressions is governed by the same rules as the arithmetic of rational numbers. |
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Find a Shrewsbury, MA CalThe topics studied in Algebra 2 include equations and inequalities, quadratic functions, powers and polynomials. Students who study Algebra 2 work to solve equations using matrices. The course also sees the introduction of concepts such as exponential and logarithmic functions |
Wednesday, October 24, 2012
Symbolab - A Scientific Equation Search Engine
Symbolab is a new search engine designed for mathematicians and scientists. The search engine is a semantic search engine which means that rather than just searching the text of your query Symabolab attempts to interpret and search for the meaning of your query. What this means is that when you type in an equation you will get results as links and get results as graphs when appropriate. Think of it Symbolab as a cross between Google and Wolfram Alpha.
Applications for Education
Symbolab could be a useful search engine for mathematics students. The search results can be sorted to find explanations of how to solve an equation, what an equation is used for, as well as videos and examples of an equation in use.
Math teachers, have you used Symbolab? How might you use it in your classroom? |
Practicing Math in the Classroom
As many of you know, I instruct courses in mathematics. I recognize that
1) most of you hate math here, so you are the perfect audience to ask
2) most who hate math don't get much practice in it.
So I focus my instruction on practicing problem solving in math after providing a key formula. As the hipsters you are that despise math, I'll sum my questions up as succinctly as possible.
1) You exist as you are. You find yourself in a math course, and you struggle to solve problems. What is something you would like to see from an instructor (in a problem solving session) that will help you to solve it? Do you prefer it if the instructor solves everything out mechanistically and then asks you to help him solve the next similar problem? Or do you prefer he start from scratch on the first one, and encourage participation on each step of the process?
2) You're too shy to ask a question you're struggling with. As someone who doesn't read minds, we cannot anticipate your difficulties. How would you like your instructor to approach the problem, assuming he did anticipate your difficulties?
3) Do you prefer seeing alternative ways to solving a problem, or would you rather see one method used universally to every problem you see (I strongly advise against the latter).
These are the core questions, and feel free to bring up anything you would like to see or not see as well if you were in this scenario. All suggestions are welcome.
Note: I ask not because I struggle to teach—I ask because many of my students share your disdain toward math and are too shy to speak out toward their difficulties and what they want to see. I also instruct the derivations in lectures—this is a separate class which supplements the material taught. My presentation skills are already fine—this topic is poised in such a way to ask what you, in particular, seek when you struggle.
Of course, I won't do exactly everything you say since Math needs to teach critical thinking, which many of you lack (waah waaah). So it stands to reason that some of your suggestions will not fall into line with what math teaches.
Is it notation that bothers you that you want to learn? Is it the inability to see step 1 to step 2? Of course everyone has different difficulties, but share your difficulties and what you think may help.
Format: First, address your difficulty in as much detail as you can, and then suggest any number of ways you feel this difficulty may be alleviated by a problem solving session and what your instructor can do to help.
I think this will benefit us all, since you will tackle your math phobia head on (if you actually care to provide a legitimate reply) and will help me to produce people that don't cower in the fetus position when they hear fields of math.
Nota Bene: This is college level mathematics; try to seclude your answers to the realm of college. You may include others as I think many methods carry over, but not all will. If you can provide insight for calculus that would be lovely.
Wow, you have a major superiority complex, your post is pretty much toxic with the condescending attitude. I worry that you are a teacher, and I think I may see why you have a problem with getting through to your students. You claim it is maths your students disdain, but I have read one post by you and disdain you as the writer rather than your subject matter. As for your student's being 'too shy' to speak out about difficulties, can you blame them? If you talk to them the way you speak to us then I wouldn't approach you for anything.
I myself have never really had trouble in math, but I'll drop my two cents. Many of my friends on high school had some trouble, and I can convey many of the things that they described.
1) I (and many of my friends) have found it extremely helpful for the teacher/instructor to show how a problem is done first, so that I can see what technique we are actually trying to learn. If the teacher simply writes up the initial problem and asks "What now?" when the problem revolves around an entirely new concept that we have not yet learned, it seems to end up being a big waste of time. Think about it like this: If someone were to write a sentence in a foreign language, one that you have not learned, and they ask you to fill in the words one by one, how much are you actually going to learn?
2) I like it very much if the teacher simply approaches and asks something along the lines of "How are you doing?" or "How's it going?" – This makes it very easy to just say "It's going alright, but there's this one problem…"
3) This one varies strongly from individual to individual. For someone with a naturally high capacity for math, it might be easier and more beneficial for them to learn a few different ways to do each variation, and they can sort of adopt one as their own based on what they are more comfortable with. However, I know that some people, regardless of how hard they try, how long they study, or how much they practice, continue to have a difficult time when a new concept needs to be learned. It's just the way their brain functions be it due to a learning disability or simply due to genetics. For these people it may be beneficial to teach them a method that is more easily adapted to different concepts. Personally, I see no harm in learning a broader and more efficient, universal method, but I'll trust that you have valid reasons for advising against it.
I do think that you should clean up your post in a couple of places, though. Namely the second sentence in the 'hipster' paragraph and the entirety of the 'critical thinking' paragraph – it is completely unnecessary and uncalled-for. You can leave the "I'll sum my questions up as succinctly as possible" part of the prior, but the rest is condescending and superfluous. You won't get helpful feedback from people if feel they are being degraded by the asker.
Personally I don't hate math I've just never been good at it. It seems that I needed things explained to me a bit more than the average candidate. Unfortunately it seems that teachers misread this as meaning I have a low level IQ and need to be in a lower level class set. I'm sure this has probably been similar for others. But I'm actually quite fascinated by maths and wish I didn't need things explained to me so much during secondary/high school, because now I find myself interested in most of the compulsory subjects I struggled learning back then but, I have very little foundation to build upon.
However, I did notice a dramatic shift of perspective and understanding when I had things explained to me one on one. When it was getting close to my final Maths exams, I would pay a visit to my Maths teacher's classroom at the end of the school day to get things directly explained to me. Maths seemed a lot easier than I had originally thought when I took this approach, my only problem now was memorizing formulas and methods to solving equations. I didn't do great in my exams as I only got to get these things explained to me a few times but I believe I did much better than I would have without taking this approach.
1) So personally I would advise to spend short one to one periods (when possible) with the students that appear less able in the class. To find out whether they really are less able or are just struggling to understand your phonetic explanation of the mathematical formula to given problems.
2) Also I think it may be very beneficial to emphasize the importance to the class that they understand what you just explained or taught, before moving on with a lesson. And then like you said with your second question – if you anticipate or suspect particular students are not quite getting it, ask them directly if they got it or not. If you get the vibe that they're getting it, I guess it's all good. If not, you could always try a different approach to explaining a particular equation or something.
I hate meth, its addictive and harmful.
Oh, you mean math?
1- I would like my instructor to do a math problem in front of me explaining each step in the way, then I do the similar problems following his steps.
2- I would tell him that I would like him to explain the point that is causing the problem.
3- If there are hundered ways to solve a problem, I want learn atleast fifty.
4- I usually understand a problem in first try unless if I am not payinf attention.
My usual approach is trying to find alternatives while watching the instructor attempt to solve a problem. It also brings in at least some fun to try and solve each problem without using the methode you are supposed to use (today we had to prove whatever or not Σ((-1)^n*n/(1+n^2))) was convergent. While you can try to look at this using Leibniz you can also try it using it's simulairy to (-1)^n*n/n^2=(-1)^n*1/n which is conditionally convergent.
I love math. I learn best when I am given the basic blocks, and then given a more advanced problem. I am currently taking calculus, and we are addressing rectangular approximation. I am currently trying to figure out the "better way" to estimate that sort of area, using calculus. I have a feeling it will be something along the lines of linear regression, but I am having difficulty proving it. You might scoff at me missing something that probably seems obvious in retrospect, but this is fun for me.
Well, while we are helping you with your teaching skills, let me help with your asking for help skills.
Here's some comments that I dont like from your post and reasons for them.
1) Math teaches you critical thinking, which many of you lack (waah waaah) DID WE JUSTBECOMEBABIES?!? If you are gonna make me into a baby, just dont even bother asking me a question; cuz apparently you think I'm too stupid to know.
2) tackle your math phobia head on (if you actually care to provide a legitimate reason)
This, first of all, assumes that we all have math phobias. I myself, love math. Then again, if I had you as a teacher, I might DEVELOP A PHOBIA. But I digress. Second, if you assume that we have a large capacity to give you bad reasons, WHYASK US AT ALL? Try not making us sound like trollish idiots.
3) (i strongly advise against the latter)
If you are asking for a whole hearted opinion, dont craft the responses before they respond to you. Let them answer their own way. If you dont like their answers, there's no point in asking.
4) Most of you hate math here
Again, thank you for assuming! Jeez, thats like saying that most of us are trolls, or most of us are teenagers. You got no proof buddy. LEARN TO BE NICE TO THEPEOPLEYOUAREASKINGFORADVICE!
5)hipsters you are that dispise math
a) asumptions. b) the word hipster is very outdated. Also, thanks for labeling us.
6) As someone who doesnt read minds
You now assume that we expect you to know our problems. This is really an unnessecary comment.
Obviously, you have ALOT of problems with teenagers. This scares me, especially since you are a "teacher". If this is how you talk when you need something, then I would hate to talk to you when you feel you have an advantage; which when you are a teacher, must happen alot. Learn to repect others and people will actually tell you their troubles in math. Then you wont have to go on forums and demonstrate to us why you have a hard time connecting with students.
Don't assume a student is stupid if they don't get it, some just need it taught a different way. I know I did, but I got left in the dust all through my junior high and high school math classes. I needed very personal instruction that was slow where every little detail of the problem is explained.I needed a teacher that had enough patience not to get angry when I made simple mistakes or when I asked questions that you would think everyone should know.
From my experience as both a student and a teacher, if the students are afraid to come up to you privately to ask for your help, then there's something wrong with your classroom environment. A lot of times it isn't the fact that a student is shy so they won't ask a question, it's that they're afraid of being ridiculed. Your demeanor in the post speaks volumes about how you might treat your students, both publicly and privately, in the classroom. Before you can really expect to see any kind of change and acceptance of what you're teaching, students have to accept who is teaching it and feel a comfortable enough relationship to trust the person who is teaching them. Without that in your classroom, you can't expect students to take anything you say seriously, or believe you care enough about them to truly want to help.
If you knew your students well enough, they should feel comfortable around you, and you should already know and understand their needs in the classroom environment, without them having to explicitly tell you.
I assume where you say college level you mean further education, most likely degree level. That means that your student's chose to do maths, and are likely paying for their studies. You also say your students disdain maths…Though I am guessing from the lack of replies the OP has retired back under his bridge like a good troll, either that or you cannot take criticism, but then why ask? Though you did try to set up your post in such a way to only get the answers you wanted to hear which sadly, for you, we have not obliged in.Many colleges (in the US at least, not sure about other countries) have required classes that the student must take in order to graduate. So you may have gone to college to learn Chemistry and you ma be only interested in Chemistry, but o still have to pass a math class and an English class before you can graduate (for example). Different colleges have different required classes, some don't have any at all, but the point is they can be in a college math class without liking math if only so they can get the required credit.
Rather belated, but I certainly couldn't imagine directly engaging an instructor when struggling with a topic. I would simply look into the matter with available materials at hand. But ultimately it boils down to what sort of personal relationship we have, and my confidence in their ability as an instructor, beyond their familiar with the subject.
But, I've never done any college level math courses. Last math I chewed on was the Monty Hall problem, which balked me at first but seems obvious in retrospect. Can't say I ever felt math phobic, but never felt a need for greater math in my life. It became little more then a game, idle speculation.
1. Teach your pupils how to use Math books. Good Math books generally start with a index, then alternate a formula section with a practice section, and include solutions and vocabulary/definitions at the end.
Its generally very important for those struggling to be able to look up Formulas they are struggling with.
Sadly most formula sections are only written in one version with the explanations being a combination of math example and Math language written explanation. Neither of which many students can fully understand. That makes it quite important to teach math language as well as just the formulas. Having students keep a note book for Math vocabulary and testing on it regularly can be helpful as can presenting alternate versions of the formula sections(that use a different style of speech/vocabulary).
2. As with the vocabulary, tests are commonly the best way to find out what problems a Student has. Here its important to not just grade the test but put in some effort to understand and keep track of which mistakes which students make.
Is it just careless slip/mistake or a repeated mistake.
Quite often students struggling with a new Formula are doing so because they lack understanding in a old formula thats used in the new one. For example a new formula using percentages or fractions that are already supposed to be known. Some never really understood the old formula and some have just forgotten, either way they often need help understanding the old one before they can master the new.
Now, where are you going to get the time to do all this stuff, especially what has to be done with students during class? With the common class sizes caring individually for each student is commonly near impossible. And setting the pace for the class can be very hard. Too fast and the slower students get left behind and too slow and the faster students get bored and held back. Here you can commonly hit a hare and turtle with one stone, by having the class break in groups of 4-8 (ideal number is commonly 6) with 2 of the better students teaching the other 2-6. The better students get the benefit of repetition and an added insight one can only gain when one has reprocess the know data in a way that other slower students can understand. While the slower students get their individual education.
Homework is also important since math is in much parts about perfect form. Knowing how to do it and actually doing it right are quite often not the same. Generally only repeatedly solving Problems in perfect form can help here. Time in school is generally not enough. So homework is practically necessary. Do not use grades as primary punishment for not doing homework. Most students have no idea how valuable grades can be. Its generally not a now and here punishment that will change their behavior, but instead a 2-4 times a year kick in the Ass(when the parents notice the bad grades).
after reading your post, I can conclude that your students don't hate maths.. they hated you. If I'm one of your students, I will not be interested to learn the subject you're teaching because you are arrogant and yeah, scary.
Anyway, I'm a maths student and I teach maths too. First thing I do before teaching is learning the students' characteristics. And well, every person in that class has different ways of learning. Some might learn really fast, some might learn a bit slower, some might need to play games to understand/adapt the formula and more.yeh. my teacher just read everything in the book and then gave us exercises to do. woulda bee nice to thoroughly work through it all and explain everything.
but doing the same lessons every year multiple times proly made the teachers very tired and lazy.
I sometimes wonder whether you and Janton are having a private competition to be the most curmudgeonly bastard on the forum.
Now this may be going off at a bit of a pointless tangent, but then again it could be relevant. When I was at school I could do maths, but had little to no interest in it. Then I joined the school's cadet corps and learned gunnery. When I found out that quadratic equations were used in the compliation of the aiming tables we used, they suddenly became a lot more interesting, and I was keen to learn more. For me, pure theory was deadly dull, but a practical and (at the time) relevant application made it important for me to learn the subject properly |
...References available on request.Algebra is a subject which is critical that a student do well in. The ability to master this subject will greatly affect the students performance in all subsequent math classes. The concepts in this course build upon one another Algebra 2 delves deeper into the concepts and skills introduced in Algebra 1 as well as introducing analytical geometry. |
Algebra: Form and Function
9780471707080
ISBN:
0471707082
Edition: 1 Pub Date: 2009 Publisher: Wiley
Summary: This text offers a fresh approach to algebra that focuses on teaching readers how to truly understand the principles, rather than viewing them merely as tools for other forms of mathematics. It relies on a storyline to form the backbone of the chapters and make the material more engaging.
Connally, Eric is the author of Algebra: Form and Function, published 2009 under ISBN 9780471707080 and 0471707082. Five ...hundred seventy two Algebra: Form and Function textbooks are available for sale on ValoreBooks.com, one hundred sixty five used from the cheapest price of $30.33, or buy new starting at $153 |
Algebra for College Students - Text - 8th edition
Summary: Kaufmann and Schwitters have built this text's reputation on clear and concise exposition, numerous examples, and plentiful problem sets. This traditional text consistently reinforces the following common thread: learn a skill; use the skill to help solve equations; and then apply what you have learned to solve application problems. This simple, straightforward approach has helped many students grasp and apply fundamental problem solving skills necessary for future mathematics course...show mores in an easy-to-read format. The new Eighth Edition of ALGEBRA FOR COLLEGE STUDENTS includes new and updated problems, revised content based on reviewer feedback and a new function in iLrn. This enhanced iLrn homework functionality was designed specifically for Kaufmann/Schwitters' users. Textbook-specific practice problems have been added to iLrn to provide additional, algorithmically-generated practice problems, along with useful support and assistance to solve the problems for students11 |
Intermediate Algebra for College Students: Instructor's4-color hardback text w/complete text-specific instructor and student print/enhanced media supplement package AMATYC/NCTM Standards of content and Pedagogy integrated in current, researched, real-world Applications, Discover For Yourself Boxes and extensively revised Exercise Sets. Graphing calculator content is featured in Technology Boxes, applications and exercises Early introduction and heavy emphasis on modeling demonstrates and utilizes the concepts of introductory algebra to help students solve problems as well as develop critical thinking skills One-page Chapter Projects (which may be assigned as collaborative projects or extended applications) conclude each chapter and include references to related Web sites for further student exploration The influence of mathematics in fine art and their relationships are explored in applications and chapter openers to help students visualize mathematical concepts and recognize the beauty in math
Preface
ix
To the Student
xxiii
Algebra and Problem Solving
1
(128)
The Real Numbers and the Number Line
2
(15)
Operations with the Real Numbers and Algebraic Expressions
17
(12)
Graphing Equations
29
(15)
Properties of Integral Exponents
44
(13)
Scientific Notation
57
(8)
Soving Linear Equations
65
(12)
Mathematical Models
77
(12)
Strategies for Soving Problems
89
(40)
Chapter Project
113
(2)
Summary
115
(2)
Review Problems
117
(8)
Chapter Test
125
(4)
Functions, Linear Functions, and Inequalities
129
(94)
Introduction to Functions
130
(15)
Linear Functions and Slope
145
(19)
The Point-Slope Equation of a Line
164
(11)
Solving Linear Inequalities
175
(9)
Compound Inequalities
184
(11)
Equations and Inequalities Involving Absolute Value
195
(8)
Linear Inequalities Containing Two Variables
203
(20)
Chapter Project
210
(2)
Summary
212
(2)
Review Problems
214
(5)
Chapter Test
219
(4)
Systems of Linear Equations and Inequalities
223
(92)
Linear Systems of Equations in Two Variables
224
(16)
Problem Solving and Modeling Using Systems of Equations
240
(15)
Linear Systems of Equations in Three Variables
255
(14)
Matrix Solutions to Linear Systems
269
(12)
Solving Linear Systems of Equations Using Determinants and Cramer's Rule |
Solving Algebra
Pitsco Education's Algebra Academy uses real-world, hands-on learning activities to provide students with meaningful context to the abstract nature of algebra. It combines engaging student-directed content with individual prescribed lessons that give students of all learning styles and abilities a meaningful learning experience they need to succeed in "the gateway course." |
text encompasses the most important aspects of plane and spherical trigonometry in a question-and-answer format. Its 913 specially selected questions appear with detailed answers that help readers refresh their trigonometry skills or clear up difficulties in particular areas. Questions and answers in the first part discuss plane trigonometry, proceeding to examinations of special problems in navigation, surveying, elasticity, architecture, and various fields of engineering. The final section explores spherical trigonometry and the solution of spherical triangles, with applications to terrestrial and astronomical problems. Readers can test their progress with 1,738 problems, many of which feature solutions. 1946 edition. 494 figures. |
Franklin, MA PrecalPre-calculus is a big amorphous field that varies a lot from school to school. In most places, it includes trigonometry, analytical geometry, and an introduction to limits, although limits are strictly speaking part of calculus. It's not unusual for some courses to include solid geometry and advanced algebra, such as synthetic division, sequences, and series. |
Geogebra Workshop Workshop run by Priscilla Allan To structure our learning, and to make learning visible, I have an "I can do" Checklist for you
Activities with Geogebra in a preservice program Andreas Philippou and Costantinos Christou University of Cyprus Abstract ... lessons with GeoGebra improved not only teachers' mathematical content knowledge
The GeoGebralessons in the laboratory guide focus on promoting the understand-ing of concepts and procedures. Figures 1 and 2 provide an example of a student ac-tivity sheet and accompanying GeoGebra sketch from the
lessons with GeoGebra Reflections and group discussions on open lessons with GeoGebra 11:30 - 12:15 Lunch 12:15 - 13:45 Workshop Talk and workshop Talk Learn how to use GeoGebra's programming features to create self-correcting exercises. Troels ...
The GeoGebra Circle you have on your computer is a "Unit Circle". What makes it so special? The radius is equal to one, so the circumference is 2 . An angle has been created that lies in standard position (vertex at origin, one vector on the x-axis oriented
Geogebra, a useful tool for achieving school progress Adriana Bînzar ... These lessons in Geogebra have raised the interest of many students as evidenced by their active participation in the lessons, the highest scores obtained, their ...
First participants learned basic commands about GeoGebra. During lessons pre service teachers of mathematics used dynamic worksheets. Data were collected by participants' works and opinions on dynamic mathematics software.
GeoGebra: Another way of looking at Mathematics ... GeoGebra, lessons becoming more attractive for the audience. Also it should be mentioned that such lessons allow the presentation and explanation of a larger number of particular cases. By this ...
Effectiveness of Using Geogebra on Students' Understanding in Learning Circles Praveen SHADAAN[1] ... Such information is crucial in planning lessons for large classes and where learners are of varied abilities. The study ...
experience in designing lessons plans with GeoGebra, and this experience positively influenced prospective teachers' perspectives about the use of technology in the teaching and learning of mathematics. However, some prospective teachers, ...
GeoGebra, "who is dynamic mathematics software for all levels of education that joins arithmetic, geometry, algebra and calculus. ... avoided, such as: the students low interest and the very theoretical character of the lessons. References
Integrating GeoGebra into IWB-equipped teaching environments: preliminary results ... lessons by participating teachers are currently being video-recorded and further interviews are to be conducted with teachers and students to better understand the
range of materials that could be useful to teachers in preparing GeoGebralessons. There are two GeoGebra institutes in Serbia and they offer different activities in order to increase GeoGebra use in classrooms". A teacher from seminar in Novi Sad:
lessons are an excellent tool for learning and teaching mathematics. •In this presentation, we propose the use of GeoGebra ... The GeoGebra`s facilities allow the teacher to: • give high quality, attractive presentations linking to real
GeoGebra is free algebra, geometry and calculus software [1], [2], [3] developed in the University of ... and online lessons are available in these languages [2]. GeoGebra NA2010 July 27-28 2010 Ithaca College, Ithaca, NY, USA
GeoGebra as e-Learning Resource for Teaching and Learning Statistical Concepts Dijana Capeska Bogatinoska1, Aleksandar Karadimce1, ... The probability and statistics lessons should provide to the students the ability to collect, organize and analyze numerical data, ...
Lessons 1. physics 1. visualizing projectile motion and its dependence on all variables ... Use GeoGebra's built-in vector math to find the net force. Does your answer always make sense? If not, how is what we've built in GeoGebra wrong?
organize the work during lessons but also the use of GeoGebra together with other modern instructional equipments, e.g. other computer programs, SmartBoards, course management systems etc. The Institute will publish information and news of its work as well as GeoGebra worksheets in
(GeoGebra) in their math lessons and some don't. (See project description.) About myself: I am a textbook writer and math teacher at an upper secondary school in Maaloy, at the west coast of Norway. Last year I got a scholarship from the Norwegian University of
GeoGebra in the Context of the IT Surrounding Environment and Curriculum, 2010 ... GeoGebra software in lessons. We agree a new level of competences, teacher trainer for GeoGebra which have expertise in pedagogy, psychology and didactic science.
Classical geometry with GeoGebra ... In my lessons I use computer software for visualization, for the proving of geometric problems in the plane and in the space or for the demonstration of the application of geometry in practice.
Calculus Animations with GeoGebraGeoGebra is a free, web-based software that does dynamic geometry and graphing. ... lessons, questioning strategies, and activities and watching clips of the lessons, I will lead the participants in a discussion about ways in which
Use Geogebra's "Exterior Segments in Circles". (example on the left) Using explicit instruction, have students practice calculating the missing segment length. Repeat the exercise in Geogebra with several different measurements.
For these lessons offered, GeoGebra can be considered as an important choice. GeoGe-176 MUHARREM AKTUMEN AND MEHMET BULUT bra provides important opportunities in the classroom, with its interface that has been trans-lated into 48 languages, its help menu, its alge-
Integrating technology into Math lessons is a complex issue that has to be addressed from a holistic viewpoint that takes into account different interrelated components. In ... GeoGebra software is lower than the motivation for the use of technology.
This unit is comprised of lessons in which students will be given various information and data to use to investigate different parent functions. ... Students can create a GeoGebra file to graph their equations from
Also open source software GeoGebra is used for teaching geometry and algebra concepts. Through this paper I would highlight my explorations, experiments and ... (Moodle, eXe), Photo story lessons, using GeoGebra for teaching geometry and algebra.
GeoGebra for planning lessons is summed up by Amanda Ladbury's comment that "I wish GeoGebra had been around when I was at school". Further ideas An opportunity arose a couple of weeks after our introduction to the software to share GeoGebra
Geogebra, a Tool for Mediating Knowledge in the Teaching and Learning of Transformation of Functions in Mathematics by RAZACK SHERIFF UDDIN DISSERTATION ... in subsequent lessons, that the learner could not recall it or talk about it.
All lessons are discussed in the context of a real world application. VIII. REFERENCE/RESOURCE MATERIALS: Graphing calculators will be required. Student Exploration Worksheets and Exit Slip Assessments will be needed for all three lessons. Computers to access GeoGebra would |
Educational Use
Browse Materials (266)
Book description: This is a text on elementary trigonometry, designed for students ...
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Book description: This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.
There are 495 exercises in the book, with answers and hints to selected exercises.
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Dr. Stitz and Dr. Zeager co-wrote this college algebra textbook with the ...
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Dr. Stitz and Dr. Zeager co-wrote this college algebra textbook with the vision of creating a high-quality, open-source textbook that is within reach and accessible to the average college student. In recognition of their work, both authors received the prestigious Faculty Innovator Award from the University System of Ohio in 2010.
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CK-12's Texas Instruments Trigonometry Student Edition Flexbook is a helpful companion to a trigonometry course, providing students with more ways to understand basic trigonometric concepts through supplementary exercises and explanations.
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CK-12's Texas Instruments Trigonometry Teacher's Edition Flexbook is a helpful companion to a trigonometry course, providing students with more ways to understand basic trigonometric concepts through supplementary exercises and explanations.
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This textbook covers topics such as Trigonometry and Right Angles, Circular Functions, ...
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This textbook covers topics such as Trigonometry and Right Angles, Circular Functions, Trigonometric Identities, Inverse Functions, Trigonometric Equations, Triangles and Vectors, as well as Polar Equations and Complex Numbers. It can also be used in conjunction with other directed courses in Mathematical Analysis or Linear Algebra as a full course in Precalculus. This digital textbook was reviewed for its alignment with California content standards.
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Study and Difficulties of Mathematics
One of the twentieth century's most eminent mathematical writers, Augustus De Morgan enriched his expositions with insights from history and ...Show synopsisOne of the twentieth century's most eminent mathematical writers, Augustus De Morgan enriched his expositions with insights from history and psychology. On the Study and Difficulties of Mathematics represents some of his best work, containing points usually overlooked by elementary treatises, and written in a fresh and natural tone that provides a refreshing contrast to the mechanical character of common textbooks. Presuming only a knowledge of the rules of algebra and Euclidean theorems, De Morgan begins with some introductory remarks on the nature and objects of mathematics. He discusses the concept of arithmetical notion and its elementary rules, including arithmetical reactions and decimal fractions. Moving on to algebra, he reviews the elementary principles, examines equations of the first and second degree, and surveys roots and logarithms. De Morgan's book concludes with an exploration of geometrical reasoning that encompasses the formulation and use of axioms, the role of proportion, and the application of algebra to the measurement of lines, angles, the proportion of figures, and surfaces.Hide synopsis
1.
Softcover,
Pranava Books,
2013
Description:New. 302 pages. Reprinted from 1910 edition. New 2013 edition...New. 302 pages. Reprinted from 1910 308 pages. Reprinted from 1902 edition. New 2013 edition...New. 308 pages. Reprinted from 1902Hardcover,
Pranava Books,
2013
Description:New. 302 pages. Reprinted from 1910 edition. Smyth/Section Sewn...New. 3024.
Hardcover,
Pranava Books,
2013
Description:New. 308 pages. Reprinted from 1910 edition. Smyth/Section Sewn...New. 308 312 pages. ReInk Books reprint from the 1910 edition. This...New. 312 pages. ReInk Books reprint from the 1910: The Open Court Publishing Company; [etc, etc. ])
Description:New. Hardcover reprint of the original 1910 edition-beautifully...New. Hard The Study And Difficulties Of Mathematics. De Morgan, Augustus. Indiana: Repressed Publishing LLC, 2012. Original Publishing: On The Study And Difficulties Of Mathematics. De Morgan, Augustus. Chicago: The Open Court Publishing Company: Etc, Etc., 1910. Subject: Mathematics, Study and teaching |
Synopses & Reviews
Publisher Comments:
Study faster, learn better-and get top grades with Schaum's Outlines
Millions of students trust Schaum's Outlines
Use Schaum's Outlines to:
Brush up before tests
Find answers fast
Study quickly and more effectively
Get the big picture without spending hours poring over lengthy textbooks
Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!
This Schaum's Outline gives you:
A concise guide to the standard college course in statistics
486 fully worked problems of varying difficulty
660 additional practice problems
Synopsis:
About the Author
Murray Speigel, Ph.D., was Former Professor and Chairman of the Mathematics Department at Rensselaer Polytechnic Institute, Hartford Graduate Center.Larry Stephens, Ph.D., (Omaha, NE) is Professor of Mathematics at the University of Nebraska and is also the author of several books.
"Synopsis"
by McGraw, |
In this section:
About This Product
Description
For courses in Elementary Number Theory for math majors, for mathematics education students, and for Computer Science students.
This introductory undergraduate text is designed to entice a wide variety of majors into learning some mathematics, while teaching them to think mathematically at the same time. Starting with nothing more than basic high school algebra, the reader is gradually led from basic algebra to the point of actively performing mathematical research while getting a glimpse of current mathematical frontiers. The writing style is informal and includes many numerical examples, which are analyzed for patterns and used to make conjectures. Emphasis is on the methods used for proving theorems rather than on specific results.
Features
• A low-key introduction to Number Theory – Enables students to explore an area of math different from standard calculus sequences.
– Encourages students to make mathematical discovers on their own through use of open-ended problems. Ex.___
• RSA cryptosystem, elliptic curves, and Fermat's Last Theorem are featured, enabling students to see real-life applications of mathematics.
• Proof of Fermat's Last theorem by Andrew Wiles – Provides overview, introducing students to one of the most significant mathematical achievements of the 20th century.
New To This Edition
• A new chapter that introduces the theory of continued fractions – Includes the recursion formula for convergents and the difference of successive convergents (Ch. 39, "The Topsy-Turvy World of Continued Fractions")
• New chapter on big-Oh notation and how it is used to describe the growth rate of number theoretic functions and to describe the complexity of algorithms (Ch. 38, "Oh, What a Beautiful Function").
• A new chapter on "Continued Fractions, Square Roots and Pell's Equation" (Ch. 40) – A continuation of the previous chapter, inlcuding a discussion of periodicity of continued fractions for quadratic irrationalities and the relationship between such continued fraction and solutions to Pell's equation |
Soal Soal Un Matematika Smp Kelas 9 |
SCHAUM'S OUTLINE OFThe Schaum's Outline of LinearAlgebra contains 1. useful summaries of the most important material and a large number of solved problems covering a wide range of topics. Consequently, it is an excellent tool for reviewing and practicing course material.
Unlike the Schaum's outline of linearalgebra, which is more about the physical interpretation of matrices as vectors, this Schaum's outline is good for learning techniques of solutions that were meant for large matrices.
Schaum'sOutlineofLinearAlgebra, fourth edition, by Lipschutz and Lipson, McGraw-Hill. Prerequisites: Calculus 1 and 2 with a grade of C or higher. ... to linearalgebra, an introduction to ordinary differential equations, and the application of
† From LinearAlgebra and Vector Calculus at Texas A&M: { Sections 1.1{1.2 † From Schaum's Outline of Beginning LinearAlgebra: { Sections 2.1{2.9 Required problems. Turn in a solution for each of the following problems. 1. Find all solutions to the following system of linear equations:
Schaum's Outlines, McGraw-Hill, 2009 ... linearalgebra, the course reading and homework will not be assigned in the order of presentation given in the textbook. 6 Assumed Programming Skills ! It is assumed that students know Matlab or an equivalent
Lipschutz Beginning LinearAlgebraSchaum's Outlines, 1997. Format: There will be one three-hour lecture per week. Assigned problems from the text will be collected and graded every two weeks. See the pdf file "Homework Assignments
SCHAUM'S SOLVED PROBLEMS SERIES l 3000 SOLVED PROBLEMS IN PRECALCULUS Philip Schmidt, Ph.D. State University of New York at New Paltz ... of a Function / 3.4 Step Functions and Continuity / 3.5 Linear Functions / 3.6 The Algebra of Functions
Texts: LinearAlgebra with Applications by Steven J. Leon and LinearAlgebra (Schaum's Outline Series) by Seymour Lipschutz. The Schaum's book has many, many worked-out examples that students should study, and many problems with solutions. |
Principles of NumericalComputer science rests upon the building blocks of numerical analysis. This concise treatment by an expert covers the essentials of the solution of finite systems of linear and nonlinear equations as well as the approximate representation of functions. A final section provides 54 problems, subdivided according to chapter. 1953 edition. |
Comprehensive, stimulating blackline master activities to develop spatial knowledge and concepts. Included
in the book are templates for a variety of 3-D shapes that can be constructed to
support the activities. more...
Blackline master book designed
to complement a remedial Math program for small groups of students.
Explains
the basic concepts of number, exploring in detail the processes of addition,
subtraction, multiplication and division.
Decimals are investigated in detail as
well as their relationship with percentages. The activities are sequenced in
line... more...
Statistics for the Utterly Confused, Second Edition
When it comes to understanding statistics, even good students can be confused. Perfect for students in any introductory non-calculus-based statistics course, and equally useful to professionals working in the world, Statistics for the Utterly Confused is your ticket to success. Statistical... more...
A self-teaching guide to basic arithmetic, covering whole numbers, fractions, percentages, ratio and proportion, basic algebra, basic geometry, basic statistics and probability You'll be able to learn more in less time, evaluate your areas of strength and weakness and reinforce your knowledge and confidence. more...
This is a topic that becomes increasingly important every year as the digital age extends and grows more encompassing in every facet of life Discrete mathematics, the study of finite systems has become more important as the computer age has advanced, as computer arithmetic, logic, and combinatorics have become standard topics in the discipline.... more...
Your complete guide to a higher score on the CSET: Mathematics. Features information about certification requirements, an overview of the test - with a scoring scale, description of the test structure and format and proven test-taking strategies Approaches for answering the three types of questions: multiple-choice... more... |
This book introduces the mathematics that supports advanced computer programming and the analysis of algorithms. The primary aim of its well-known authors is to provide a solid and relevant base of mathematical skills - the skills needed to solve complex problems, to evaluate horrendous sums, and to discover subtle patterns in data. It is an indispensable text and reference not only for computer scientists - the authors themselves rely heavily on it! - but for serious users of mathematics in virtually every discipline. Concrete Mathematics is a blending of CONtinuous and disCRETE mathematics. "More concretely," the authors explain, "it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems." The subject matter is primarily an expansion of the Mathematical Preliminaries section in Knuth's classic Art of Computer Programming, but the style of presentation is more leisurely, and individual topics are covered more deeply. Several new topics have been added, and the most significant ideas have been traced to their historical roots. The book includes more than 500 exercises, divided into six categories.Complete answers are provided for all exercises, except research problems, making the book particularly valuable for self-study. Major topics include: *Sums *Recurrences *Integer functions *Elementary number theory *Binomial coefficients *Generating functions *Discrete probability *Asymptotic methods This second edition includes important new material about mechanical summation. In response to the widespread use of the first edition as a reference book, the bibliography and index have also been expanded, and additional nontrivial improvements can be found on almost every page. Readers will appreciate the informal style of Concrete Mathematics. Particularly enjoyable are the marginal graffiti contributed by students who have taken courses based on this material. The authors want to convey not only the importance of the techniques presented, but some of the fun in learning and using them. 0201558025B04062001 [via]
More editions of Concrete Mathematics: A Foundation for Computer Science:
This book is a tribute to Paul Erdos, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch or problem posers". It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptations of money and position, Erdos never had a home and never held a job. His "home" was a bag or two containing all his belongings and a record of the collective activities of the mathematical community. His "job" was one at which he excelled: identifying a fundamental roadblock in some particular line of approach and capturing it in a well-chosen, often innocent-looking problem, whose solution would likewise provide insight into the underlying theory. By cataloguing the unsolved problems of Erdos in a comprehensive and well-documented volume, the authors hope to continue the work of an unusual and special man who fundamentally influenced the field of mathematics. [via]
Discrete mathematics, the study of finite structures, is one of the fastest-growing areas in mathematics. The wide applicability of its evolving techniques points to the rapidity with which the field is moving from its beginnings to its maturity, and reflects the ever-increasing interaction between discrete mathematics and computer science. This Series provides broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, and the analysis of algorithms. The Wiley-Interscience Series in Discrete Mathematics and Optimization will be a substantial part of the record of the extraordinary development of this field. A complete listing of the titles in the Series appears on the inside front cover of this book.
"[Integer and Combinatorial Optimization] is a major contribution to the literature of discrete programming. This text should be required reading for anybody who intends to research this area or even just to keep abreast of developments." --Times Higher Education Supplement, London
Introduction to the Theory of Error-Correcting Codes Second Edition Vera Pless For mathematicians, engineers, and computer scientists, here is an introduction to the theory of error-correcting codes, focusing on linear block codes. The book considers such codes as Hamming and Golay codes, correction of double errors, use of finite fields, cyclic codes, B.C.H. codes, weight distributions, and design of codes. In a second edition of the book, Pless offers thoroughly expanded coverage of nonbinary and cyclic codes. Some proofs have been simplified, and there are many more examples and problems. 1989 (0 471-61884-5) 224 pp. [via] |
Elementary Differential Geometry presents the main results in the differential geometry of curves and surfaces suitable for a first course on the subject. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct and straightforward approach is used throughout.
New features of this revised and expanded second edition include:
a chapter on non-Euclidean geometry, a subject that is of great importance in the history of mathematics and crucial in many modern developments. The main results can be reached easily and quickly by making use of the results and techniques developed earlier in the book.
Coverage of topics such as: parallel transport and its applications; map colouring; holonomy and Gaussian curvature.
Around 200 additional exercises, and a full solutions manual for instructors, available via
Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields.
The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view.
Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.
, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results.
It covers differential geometry far beyond what general relativists perceive they need to know. And it introduces readers to other areas of mathematics that are of interest to physicists and mathematicians, but are largely overlooked. Among these is Clifford Algebra and its uses in conjunction with differential forms and moving frames. It opens new research vistas that expand the subject matter.
In an appendix on the classical theory of curves and surfaces, the author slashes not only the main proofs of the traditional approach, which uses vector calculus, but even existing treatments that also use differential forms for the same purpose.
Readership: Physicists and mathematicians working on differential geometry.
This unique monograph by a noted UCLA professor examines in detail the mathematics of Kerr black holes, which possess the properties of mass and angular momentum but carry no electrical charge. Suitable for advanced undergraduates and graduate students of mathematics, physics, and astronomy as well as professional physicists, the self-contained treatment constitutes an introduction to modern techniques in differential geometry. The text begins with a substantial chapter offering background on the mathematics needed for the rest of the book. Subsequent chapters emphasize physical interpretations of geometric properties such as curvature, geodesics, isometries, totally geodesic submanifolds, and topological structure. Further investigations cover relativistic concepts such as causality, Petrov types, optical scalars, and the Goldberg-Sachs theorem. Four helpful appendixes supplement the text.
Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces généralisés" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.
Both classical geometry and modern differential geometry have been active subjects of research throughout the 20th century and lie at the heart of many recent advances in mathematics and physics. The underlying motivating concept for the present book is that it offers readers the elements of a modern geometric culture by means of a whole series of visually appealing unsolved (or recently solved) problems that require the creation of concepts and tools of varying abstraction. Starting with such natural, classical objects as lines, planes, circles, spheres, polygons, polyhedra, curves, surfaces, convex sets, etc., crucial ideas and above all abstract concepts needed for attaining the results are elucidated. These are conceptual notions, each built "above" the preceding and permitting an increase in abstraction, represented metaphorically by Jacob's ladder with its rungs: the 'ladder' in the Old Testament, that angels ascended and descended...
In all this, the aim of the book is to demonstrate to readers the unceasingly renewed spirit of geometry and that even so-called "elementary" geometry is very much alive and at the very heart of the work of numerous contemporary mathematicians. It is also shown that there are innumerable paths yet to be explored and concepts to be created. The book is visually rich and inviting, so that readers may open it at random places and find much pleasure throughout according their own intuitions and inclinations.
Marcel Berger is the author of numerous successful books on geometry, this book once again is addressed to all students and teachers of mathematics with an affinity for geometry.
This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.
Differential geometry arguably offers the smoothest transition from the standard university mathematics sequence of the first four semesters in calculus, linear algebra, and differential equations to the higher levels of abstraction and proof encountered at the upper division by mathematics majors. Today it is possible to describe differential geometry as "the study of structures on the tangent space," and this text develops this point of view.
This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin. The main goal of this book is to bring the undergraduate student who already has a solid foundation in the standard mathematics curriculum into contact with the beauty of higher mathematics. In particular, the presentation here emphasizes the consequences of a definition and the careful use of examples and constructions in order to explore those consequences. |
+ By Study Edge
Algebra Nation is a FREE algebra and Algebra End-of-Course Exam (EOC) resource for students, teachers, and parents in Florida. Algebra Nation's resources include aligned videos, study guides, an online practice tool, and an interactive Algebra Wall where you can get answers to all your algebra questions from teachers and Study Experts (our expert algebra tutors).
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(62 stars)
by Lennysha Blackstock on 16/04/2014
Helps me with my math. And it increase my skills
(62 stars)
by Dhroov Patel on 15/04/2014
The videos will not go full screen. This would really be helpful.
(62 stars)
by viena andino on 11/04/2014
Frozen
(62 stars)
by Noah L on 08/04/2014
It helps out with algebra 1, but the scrolling is horrible for my tablet
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Love it
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by nikki renaee on 01/04/2014
It has a workbook that it follows. Each video is a different page of the book. Do not download without the book. |
TH432 Advanced Calculus
Course Description
A look at sets, functions and the real numbers. Topics include the Completeness axiom, cardinality and Cantor's Theorem, LimSup and LimInf; the topology of R1 and R2, open sets, limit points, compactness and the Heine-Borel Theorem, continuous functions properties, uniform continuity, the Mean-Value theorem; the Riemann integral and the Lebesgue Measure.
Learning Outcomes
Demonstrate proficiency in correct formulation and proving theorems covered in the class.
Be able to show different ways to disprove incorrect mathematical statements on concrete examples.
Have clear understanding and strong awareness of mathematical concepts covered in this course and be able to solve problems formulated in terms of these concepts. |
The TI-89 incorporates graphical and numerical features with a powerful computer algebra system that has the potential to dramatically alter how and what our students should learn. By incorporating th... More: lessons, discussions, ratings, reviews,...
Advanced Placement Statistics with the TI-89 book is intended to facilitate the use of the TI-89 graphing calculator with most introductory statistics texts. It includes the activities for the topics ... More: lessons, discussions, ratings, reviews,...
This tool is a customized spreadsheet that is preloaded so that the user can numerically investigate affine recurrence relations. By using the File menu the user can also create a new spreadsheet. It ... More: lessons, discussions, ratings, reviews,...
Students investigate the models by which fractal patterns aggregate. Several questions are posed and different activities are suggested to go along with the Diffusion-Limited Aggregation applet.Activity simulates the planning of an airstrike mission on a facility defended by surface-to-air missiles (SAM's). Students are asked to determine the minimum number of aircraft needed to destroy the... More: lessons, discussions, ratings, reviews,...
This mathlet allows you to solve simple linear equations through the use of a balance beam. Unit blocks (representing 1s) and X-boxes (for the unknown, X), are placed on the pans of a balance beam. More: lessons, discussions, ratings, reviews,...
Algebra Concepts is a tool for introducing many of the difficult concepts that are necessary for success in higher level math courses. This program includes a special feature, the Algebra Tool Kit, wh... More: lessons, discussions, ratings, reviews,...
Algebra Concepts is an interactive learning system designed to provide instruction in mathematics at the 7th grade enrichment through adult levels. The instructional goals for Algebra Concepts include... More: lessons, discussions, ratings, reviews,...
The user reviews definitions of important algebra terms. After viewing further explanations and some examples, users can interactively test their understanding of the definitions of important algebra... More: lessons, discussions, ratings, reviews,...
Students play a generalized version of connect four, gaining the chance to place a piece on the board by solving an algebraic equation. Parameters: Level of difficulty of equations to solve and type o... More: lessons, discussions, ratings, reviews,...
A video that focuses on the TI-Nspire graphing calculator in the context of teaching algebra. In this program the TI-Nspire is used to explore the nature of linear functions. Examples ranging from ... More: lessons, discussions, ratings, reviews,...
This tool is designed for those students who best learn by drilling/quizzing. It randomly presents examples of equalities and inequalities (such as "If a=b then ac = bc") and gives you three choices |
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Abstract
This study investigated the achievement of gifted students on mathematics problems that were designed to assess both conceptual and procedural knowledge of polynomial functions, and it attempted to determine the impact of the students ' mathematical belief systems on this achievement. The students were enrolled in a three-week Algebra II course at a summer program for gifted mathematics students. Data sources were belief scales, in-class examinations, and in-depth interviews. Qualitative and quantitative analyses indicated that the students were able to make a variety of connections among concepts related to polynomials and functions, and they easily applied their mathematical knowledge to real world phenomena. The participants suffered, however, from several misconceptions relating to the understanding of the roles of the independent and dependent variables in functions. They also struggled with the concept of symmetry and how it relates to polynomial functions. Statistical analyses suggested that belief systems were correlated with achievement, but the conclusions from this study were ambiguous since the correlations were unexpectedly negative. Through its identification of potential conceptual difficulties that gifted students may encounter in their learning of polynomial functions, this study suggested specific topics that teachers of gifted students should consider when planning their instructional activities. |
Introductory Algebra for College Students -With CD - 5th edition
Summary: KEY BENEFIT: TheBlitzer Algebra Seriescombines mathematical accuracy with an engaging, friendly, and often fun presentation for maximum student appeal. Blitzerrsquo;s E...show morequations and Inequalities in One Variable; Problem Solving; Linear Equations and Inequalities in Two Variables; Systems of Linear Equations and Inequalities; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Roots and Radicals; Quadratic Equations and Introduction to Functions. MARKET: for all readers interested in algebra. ...show less
69 |
Abhijit Dasgupta, "Set Theory: With an Introduction to Real Point Sets"
English | 2014 | ISBN-10: 1461488532 | 442 pages | PDF | 3,8 MB
What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner |
Web Resources
Links
This course develops modern calculus by investigating the
questions, problems, and ideas that motivated its discovery and
practice. We will study the real number system and functions defined
on it, focusing on limits, area and tangent calculations, properties
and applications of the derivative, and the notion of
continuity. Emphasis will be placed on problem-solving and
mathematical thinking.
It has come to my attention that exercise 2.7:4 requires use of implicit differentiation, which we are not covering. So, please disregard 2.7:4; it will not be included in the grading of the assignment.
On our text book's web site, there is a PDF file that reviews topics in algebra and has 160 problems with answers and detailed solutions. You can reach it by clicking on "Textbook Web" on our home page and then clicking "Other Resources" from the textbook web page (it's listed on the left as "Review Algebra", or you can get to the PDF file directly from this post's title.
Just a quick note to let you know that I've updated the schedule to reflect the material we covered today. As the quarter progresses, this will continue to occur. I want the rate of material coverage to be determined by you, not the textbook or me.
I've been using it for such a long time, it didn't occur to me that some people might be unfamiliar with the Greek alphabet. Thank a fellow student for bringing this issue to my attention. And don't be timid about making points like this.
Also, there's no substitute for solving lots of problems if you want to move from "understanding the basic principles" to "being able to work problems easily". One good book you might try for this is Schaum's Outline of Calculus. |
Math You Can Really Use--Every Day skips mind-numbing theory and tiresome drills and gets right down to basic math that helps you do real-world stuff like figuring how much to tip, getting the best deals shopping, computing your gas mileage, and more. This is not your typical, dry math textbook. With a comfortable, easygoing approach, it: |
You are right about the TI-89, it actually has a software built-in. You might opt for TI-84.
Also, there might be another constraint as the main purpose for your consideration, eg you might think what after the buy, it costs pretty high, if you can find some relatives to help you the cost then it'll be fine also for you, won't it ? I think its fine. But you need to clearify why your hesitation all up.
barnaby
#3
Dec30-07, 07:19 AM
P: 17ghost02
#4
Dec31-07, 03:07 PM
P: 47
Graphing Calculator: - TI84 vs Casio CFX9850GC+
I hear Ti's are easy to use. I versatility would more than likely go to the Ti because there are so many programs you can use for it.
Jekertee
#5
Jan1-08, 03:50 AM
P: 44
Quote by barnabySorry I didn't understand ,
easy to use due to familiarity
most calcaultor are made easy for students to use
if the calculators are for complex computation then choose the more functioality since the simple one would completely refuse under whatever circumstances
also it takes TOO long for you to just look and hesitate, if you are not decisive, then ask someone in your class who has more experience to pick one for you.
ghost02
#6
Jan1-08, 11:32 AM
P: 47
Jekertee had the best advice, ask someone in your class.
stewartcs
#7
Jan2-08, 07:57 AM
Sci Advisor
P: 2,283
Quote by barnaby
I'm about to buy a graphing calculator, and I don't know whether to get the Texas Instruments TI-84 (Silver Edition), or the Casio CFX9850GC+ (which has the added frivolity of a colour screen).
I can't get the TI-89, because it has algebra software built in, and so I'm not allowed to use it in an exam...
Your opinions, please?
I personally like the TI-84, but mainly because I'm familiar with using it and not the Casio brands.
The color of the screen to me doesn't matter that much just so long as the calculator is robust and has full functionality.
nanoWatt
#8
Jan7-08, 08:18 AM
P: 89
I just read that about your not being able to have algebra software built in. |
Linear programming is an extremely useful area of applied mathematics and is used on a daily basis by many industries. Most books on linear programming require an in depth knowledge of linear algebra in their exposition, making the subject matter inaccessible to the average reader. This second edition continues the presentation of the subject from a very elementary point of view, using as a foundation just a basic knowledge of high school algebra. The author manages to go into great depth with these minimal prerequisites, and helps the reader understand even some of the most subtle aspects of the subject. This is accomplished by weaving some of the more difficult ideas into informal proofs, with the result that the reader often doesn't even know he or she is reading very difficult material. Some formal proofs are included, and even these are often broken down into small steps to give them clarity. The reader who gets through the whole book will have a strong knowledge of linear programming and also a good basic knowledge of the related areas of game theory, integer programming, goal programming, network analysis, and dynamic programming. This book can be (and has been) used as a primary text for a course in linear programming and related topics. It can also be used for self study by the person who wants to know more about this fascinating and very useful subject. Exercises have been carefully chosen to illustrate a broad range of applications that occur in practice leaving the reader with an appreciation of the wide applicability of this subject to real life problems. Also, solutions to many of the exercises are given, making this an ideal book for the person who is studying this subject independently. A limited number of examination copies are available for instructors who wish to consider this book for adoption. Please contact the author at asultan956@aol.com to receive one. |
Open Calculus is an exportable distance-learning/self-study environment for learning calculus.
Embodied in this open source project is a calculus text, online homework problems, videotapes
of worked examples, and more, which have been organized and linked together in a flexible fashion.
That's Calculus
That's Calculus
A video review of basic calculus concepts, including chemistry applications
such as reaction times and radioactive decay. |
Mathematics Course of Study
The curriculum for mathematics in Mayfield is based on Ohio's New Learning Standards (OLNS).These standards were developed as part of a multi-state effort. The Ohio Achievement Assements measure a student's progress toward achieving these standards in grades 3 through 8. The Ohio Graduation Test measures achievement in grade 10. Passage of the OGT is a graduation requirement. For this reason, instruction in Mathematics is closely aligned to the ONLS. You can access the standards at the link below.
Throughout the curriculum K-12, mathematics content is presented in a way that requires students to construct their own knowledge about math. This approach includes some direct instruction, guided discovery, discussion, and reflection. |
Mathematics For IIT- JEE 2011- 12: Algebra
Mathematics For IIT- JEE 2011- 12: Algebra Book Description
Mathematics for IIT ??? JEE, a Cengage Learning Exam Crack Series, is based on the latest pattern of IIT ??? JEE. A thorough understanding of the basic concepts (in all areas of mathematics) and their application is important for the JEE aspirants. This series of five books covers topics in all the areas of mathematics in a conceptual and coherent manner. The illustrative approach followed in this series is aimed at facilitating mastering of the concepts of mathematics with the help of a variety of solved exercises reflecting the latest pattern of IIT ??? JEE. This series would be highly beneficial for the aspirants in their preparations for the Joint Entrance Examination.
Key Features of the Series.
Enhances the understanding of the concepts of mathematics with a large number of illustrations and examples.
Includes questions and problems from previous years??? IIT ??? JEE papers, which help students understand the pattern of the questions asked in the examination.
Popular Searches
The book Mathematics For IIT- JEE 2011- 12: Algebra by Ghanshyam Tewani, Ghanshyam Tewani
(author) is published or distributed by Cengage Learning India [8131513424, 9788131513422].
This particular edition was published on or around 2010 |
Algebra Word Problem Tutor: Digit Problems review Product Description
Word problems lose some of their mystery with this helpful series geared toward algebra students. Algebra Word Problem Tutor: Digit Problems movie This step-by-step instructional focuses on numeric digits and demonstrates how to glean pertinent information from word problems to form the correct equations. |
A mathematical model is a description of a system using mathematical language. Mathematical models are used not only in the natural sciences and engineering disciplines but they are also used in biology, economics and sociology. Here is a general guideline for how to build a mathematical model.
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Steps
1
Gather the following information: what you already know; sources of relevant data; your assumptions; what you'd like to predict with the model; ways of verifying that the model will be built correctly; and ways to validate the model. Simply, read the problem many times, classify knowns and unknowns and find out what is actually asked in problem.
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2
Make a strategy. After classifying the data, make the strategy how to solve the problem or how to make model. Sketch simple diagrams that outline the elements in the model and how they are connected to each other. As for any complex task, diagram helps.
3
Conduct a thorough literature review. There is no need to re-invent the wheel if somebody else has developed a model that may suit your purposes already. However, you need to fully understand all the assumptions and the applicability of a model before using it.
4
Learn Data Handling.It is important to know what is missing information in the problem. So think carefully about how you are going to handle missing data. If possible, quantify the uncertainties associated with the data. Sometimes, we overlook the missing information,so gain read problem several times and carefully.
5
Begin with a simple model. Make possibilities of different applicable models and then choose the best and simple.According to Occam's Razor principle, among models with similar predictive power, the simplest one is the most desirable.
6
Identify the parameters of the equations and develop a plan how to estimate the parameters from the data. This could be done simply by fitting the equations to the data.
7
Validate your model against a data set that you have not used to build the model.
8
Constantly test your model and update your equations based on new data and |
On Core Mathematics
On Core Mathematics for Grades 6–12 is a complete program for transitioning to the Common Core State Standards with interactive, real-world applications that help students deepen their understanding of crucial math concepts, while addressing the Common Core Curriculum and the Standards for Mathematical Practice. This program allows students to not just "do the math" but also to "understand and explain" their math.
On Core Mathematics helps prepare students for 2014 Assessments by developing their procedural, application and critical thinking skills.
Embedded strategies and lesson background notes for all topics within the Teacher's Editions ensure that you are implementing the Common Core State Standards in the spirit that was intended |
Jun 27, 2008
The National Institute of Standards and Technology (NIST) has released a five-chapter preview of the much-anticipated online Digital Library of Mathematical Functions (DLMF). In development for over a decade, the DLMF is designed to be a modern successor to the 1964 "Handbook of Mathematical Functions," a reference work that is the most widely distributed NIST publication (with over a million copies in print) and one of the most cited works in the mathematical literature (still receiving over 1,600 yearly citations in the research literature). The preview of the new DLMF is a fully functional beta-level release of five of the 36 chapters.
The DLMF is designed to be the definitive reference work on the special functions of applied mathematics. Special functions are "special" because they occur very frequently in mathematical modeling of physical phenomena, from atomic physics to optics and water waves. These functions have also found applications in many other areas; for example, cryptography and signal analysis. The DLMF provides basic information needed to use these functions in practice, such as their precise definitions, alternate ways to represent them mathematically, illustrations of how the functions behave with extreme values and relationships between functions.
The DLMF provides various visual aids to provide qualitative information on the behavior of mathematical functions, including interactive Web-based tools for rotating and zooming in on three-dimensional representations. These 3-D visualizations can be explored with free browsers and plugins designed to work in virtual reality markup language (VRML). Mouse over any mathematical function, and the DLMF provides a description of what it is; click on it, and the DLMF goes to an entire page on the function. The DLMF adheres to a high standard for handbooks by providing references to or hints for the proofs of all mathematical statements. It also provides advice on methods for computing mathematical functions, as well as pointers to available software.
The complete DLMF, with 31 additional chapters providing information on mathematical functions from Airy to Zeta, is expected to be released in early 2009. With over 9,000 equations and more than 500 figures, it will have about twice the amount of technical material of the 1964 Handbook. An approximately 1,000-page print edition that covers all of the mathematical information available online also will be published. The DLMF, which is being compiled and extensively edited at NIST, received initial seed money from the National Science Foundation and resulted from contributions of more than 50 subject-area experts worldwide. The NIST editors for the DLMF are Frank W. J. Olver, Daniel W. Lozier, Ronald F. Boisvert and Charles W. Clark.
Related Stories
The National Institute of Standards and Technology has released the Digital Library of Mathematical Functions (DLMF) and its printed companion, the NIST Handbook of Mathematical Functions, the much-anticipated successors |
Description:
This is an introductory course covering basic concepts in preparation for Algebra I. This course includes adding, subtracting, multiplying, and dividing whole numbers, decimals, fractions, mixed numbers, and integers; manipulating place value and powers of 10; estimating sums, differences, products, and quotients; identifying angles and triangles; and using scientific notation. Note: Due to the nature of the lesson assignments for this course, we are unable to accept assignments submitted via e-mailMID MATH 8A / Online
Schedule Number:
9890
Instructor(s):
Janet Martin
Location:
Dates:
Units:
0.5 Academic Credits
Lessons/Exams:
6 lessons, 1 final exam
Tuition & Mandatory Fees:
6th - 8 |
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