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



Pub. Date:
John Wiley & Sons Inc

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What version or edition is this?
This is the 6th edition with a publication date of 7/22/2013.
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Solow, How to Read and Do Proofs, provides a systematic approach for teaching students how to read, think about, understand, and create proofs. It develops a method for communicating proofs, categorizing, identifying, and explaining (at the student’s level) the various techniques that are used repeatedly in virtually all proofs. These clear, concise explanations promote understanding of the theoretical mathematics behind abstract mathematics and give students a greater opportunity to succeed in advanced courses. Along with the addition of three new chapters, a “Part 2” is added to the Sixth Edition, which focuses on the mathematical thought processes associated with proofs. The teaching of this foregoing thinking processes reduces the time needed for readers to learn advanced mathematics courses while simultaneously increasing their depth of understanding so as to enable them to use mathematics more effectively as a problem-solving tool in their personal and professional lives.

Table of Contents

Foreword xi

Preface to the Student xiii

Preface to the Instructor xv

Acknowledgments xviii

Part I Proofs

1 Chapter 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 53

6 Quantifiers III: Specialization 69

7 Quantifiers IV: Nested Quantifiers 81

8 Nots of Nots Lead to Knots 93

9 The Contradiction Method 101

10 The Contrapositive Method 115

11 The Uniqueness Methods 125

12 Induction 133

13 The Either/Or Methods 145

14 The Max/Min Methods 155

15 Summary 163

Part II Other Mathematical Thinking Processes

16 Generalization 179

17 Creating Mathematical Definitions 197

18 Axiomatic Systems 219

Appendix A Examples of Proofs from Discrete Mathematics 237

Appendix B Examples of Proofs from Linear Algebra 251

Appendix C Examples of Proofs from Modern Algebra 269

Appendix D Examples of Proofs from Real Analysis 287

Solutions to Selected Exercises 305

Glossary 357

References 367

Index 369 

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