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

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When engineers, computer scientists, and economists need to learn how to read, think about, and create proofs, they turn to Solow. In order to make the material more relevant, the exercises in each chapter have been revised and expanded. New and more complete discussions are included on how to use a previously-proved proposition in both the forward and backward processes. The fifth edition also presents new, self-contained chapters on uniqueness, induction, either/or, and max/min methods. Several final examples of how to read and do proofs are included in the final chapter to reinforce the reader's knowledge of the various proof techniques.

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Editorial Reviews

From the Publisher
"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)

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Product Details

  • ISBN-13: 9780470392164
  • Publisher: Wiley
  • Publication date: 12/8/2009
  • Edition number: 5
  • Pages: 320
  • Sales rank: 1,352,062
  • Product dimensions: 5.90 (w) x 8.90 (h) x 0.50 (d)

Table of Contents

1 The truth of it all 1
2 The forward-backward method 9
3 On definitions and mathematical terminology 23
4 Quantifiers I : the construction method 35
5 Quantifiers II : the choose method 45
6 Quantifiers III : specialization 59
7 Quantifiers IV : nested quantifiers 69
8 Nots of nots lead to knots 79
9 The contradiction method 87
10 The contrapositive method 99
11 Uniqueness methods and induction 107
12 Either/or and max/min methods 123
13 Summary 135
App. A Examples of proofs from discrete mathematics 143
App. B Examples of proofs from linear algebra 157
App. C Examples of proofs from modern algebra 175
App. D Examples of proofs from real analysis 193
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