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Mathematical Thinking : Problem Solving and Proofs

by: D'Angelo, John P.; West, Douglas Brent

Mathematical Thinking : Problem Solving and Proofs

by: D'Angelo, John P.; West, Douglas Brent

ISBN 13:
9780132633932
ISBN 10:
0132633930
Edition: 2nd
Format: Hardcover
Copyright: 01/01/2000
Publisher: Addison Wesley
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Summary

This course will differ from other math courses you have taken, because it emphasizes writing and language skills. We do not ask that you memorize formulas, but rather that you learn to express yourself clearly and accurately.

Preface for the Student

Preface for the Instructor

xiv

PART I Elementary Concepts

(74)

Sets and Numbers

(15)

The Quadratic Formula

(2)

Numbers and Problem-Solving

(3)

Sets

(3)

Summary of the Axioms

(3)

Exercises

(4)

Language and Proofs

(18)

Two Theorems about Equations

(2)

Quantifiers and Logical Statements

(4)

Compound Statements and Sets

(3)

Elementary Proof Techniques

(5)

Exercises

(4)

Functions

(21)

Definitions and Examples

(3)

Graphs of Functions

(2)

Bijections

(7)

Composition and Functional Digraphs

(3)

Operators (optional)

(1)

Exercises

(4)

Induction

(19)

The Principle of Induction

(7)

Applications

(5)

Strong Induction

(2)

Exercises

(5)

PART II Properties of Numbers

(60)

Counting and Cardinality

(17)

Representation of Natural Numbers

(3)

Cardinality

(5)

Binomial Coefficients and Counting

(5)

Exercises

(3)

Divisibility

(12)

The Euclidean Algorithm

(3)

Prime Factorization

(1)

The Dart Board Problem

(2)

Exercises

100

(5)

Modular Arithmetic

105

(16)

Equivalence Relations

106

(4)

Applications

110

(2)

Fermat's Little Theorem

112

(2)

Congruence and Groups (optional)

114

(2)

Exercises

116

(5)

The Rational Numbers

121

(14)

Constructing the Rationals

122

(3)

Irrational Numbers

125

(2)

Pythagorean Triples

127

(2)

Fractions and Probability

129

(2)

Further Properties of Rationals (optional)

131

(1)

Exercises

132

(3)

PART III Discrete Mathematics

135

(90)

Combinatorial Reasoning

136

(22)

Amazon no longer offers textbook rentals. We do!

Mathematical Thinking : Problem Solving and Proofs

Mathematical Thinking : Problem Solving and Proofs

9780132633932

0132633930

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Mathematical Thinking : Problem Solving and Proofs

Mathematical Thinking : Problem Solving and Proofs

9780132633932

0132633930

Summary

Table of Contents

Supplemental Materials

Write a Review

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