How to Read and Do Proofs: An Introduction to Mathematical Thought Processes / Edition 4

How to Read and Do Proofs: An Introduction to Mathematical Thought Processes / Edition 4

by Daniel Solow
     
 

ISBN-10: 0471680583

ISBN-13: 9780471680581

Pub. Date: 10/28/2004

Publisher: Wiley

Learn how to read, understand, and do proofs!

Daniel Solow’s new Fourth 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

Overview

Learn how to read, understand, and do proofs!

Daniel Solow’s new Fourth 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 actually do proofs. You’ll learn when each technique is likely to be successful, based on the form of the theorem.

This Fourth Edition features quick reference summaries of the proof techniques on the front and back covers, a new forward uniqueness method, a new section on counterexamples, and four new appendices in discrete mathematics, linear algebra, modern algebra, and real analysis that illustrate how the various proof techniques from the body of the text arise in doing actual mathematics.

Critical acclaim

“I think that Solow has written an excellent text that I will highly recommend as a supplementary text for several upper division mathematics courses including abstract algebra and mathematical analysis.”––Phillip Bean, Mercer University

“His already fine book becomes more usable by having the four subject-targeted appendices.”––Richard Delaware, UMKC

“The book covers all the basic proof techniques in a very readable, concise way without overwhelming the student. The organization is great. I like the short chapters highlighting only one concept at a time.”––Josephine Hamer, Western Connecticut State University

“Very clear, rigorous, extremely thorough, almost unique in what it tries to do, reaches out to weaker students.”––Michael Thaddeus, Columbia University

Product Details

ISBN-13:
9780471680581
Publisher:
Wiley
Publication date:
10/28/2004
Edition description:
Older Edition
Pages:
288
Product dimensions:
6.24(w) x 9.37(h) x 0.38(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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