Daniel Solow - How to Read and Do Proofs (6e) torrent

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

by Daniel Solow


# ISBN-13: 9781118164020
# Publisher: Wiley
# Publication year: 2013
# Edition number: 6
# Pages: 336


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.

Contents
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Part I: Proofs

1 The Truth of It All
2 The Forward-Backward Method
3 On Definitions and Mathematical Terminology
4 Quantifiers I: The Construction Method
5 Quantifiers II: The Choose Method
6 Quantifiers III: Specialization
7 Quantifiers IV: Nested Quantifiers
8 Nots of Nots Lead to Knots
9 The Contradiction Method
10 The Contrapositive Method
11 The Uniqueness Methods
12 Induction
13 The Either/Or Methods
14 The Max/Min Methods
15 Summary

Part II: Other Mathematical Thinking Processes

16 Generalization
17 Creating Mathematical Definitions
18 Axiomatic Systems

Appendix A Examples of Proofs from Discrete Mathematics
Appendix B Examples of Proofs from Linear Algebra
Appendix C Examples of Proofs from Modern Algebra
Appendix D Examples of Proofs from Real Analysis
Solutions to Selected Exercises

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