How to Read and Do Proofs: An Introduction to Mathematical Thought Processes / Edition 5

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes / Edition 5

by Daniel Solow
     
 

ISBN-10: 0470392169

ISBN-13: 9780470392164

Pub. Date: 12/08/2009

Publisher: Wiley

Danieli solow's new fifth edition of How to Read and Do Proofs will help you master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once you have a firm grasp of the techniques, you'll be better equipped to read understand and actuary do proofs. You'll learn when each technique is likely to

Overview

Danieli solow's new fifth edition of How to Read and Do Proofs will help you master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once you have a firm grasp of the techniques, you'll be better equipped to read understand and actuary do proofs. You'll learn when each technique is likely to be successful, based on keywords that appear in the theorem.

This Fifth Edition features a complete revision and expansion of the exercises in the main body of the text. Other changes include replacing the previous Chapters 11 and 12 with new Chapters 11-14 new discussions in Chapters 1, 3 and 5 expanding on previous content and covering new material; and the inclusion of several, unitying examples at the conclusion of the text.

Product Details

ISBN-13:
9780470392164
Publisher:
Wiley
Publication date:
12/08/2009
Pages:
320
Product dimensions:
5.90(w) x 8.90(h) x 0.50(d)

Table of Contents

Foreword ix

Preface to the Student xi

Preface to the Instructor xiii

Acknowledgments xvi

1 The Truth of It All 1

2 The Forward-Backward Method 9

3 On Definitions and Mathematical Terminology 25

4 Quantifiers I: The Construction Method 41

5 Quantifiers II: The Choose Method 51

6 Quantifiers III: Specialization 67

7 Quantifiers IV: Nested Quantifiers 79

8 Nots of Nots Lead to Knots 91

9 The Contradiction Method 99

10 The Contrapositive Method 113

11 The Uniqueness Methods 123

12 Induction 131

13 The Either/Or Methods 143

14 The Max/Min Methods 153

15 Summary 161

Appendix A Examples of Proofs from Discrete Mathematics 175

Appendix B Examples of Proofs from Linear Algebra 189

Appendix C Examples of Proofs from Modern Algebra 207

Appendix D Examples of Proofs from Real Analysis 225

Solutions to Selected Exercises 243

Glossary 289

References 297

Index 299

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