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

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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.

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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: 9780471680581
  • Publisher: Wiley, John & Sons, Incorporated
  • Publication date: 10/28/2004
  • Edition description: Older Edition
  • Edition number: 4
  • Pages: 288
  • Product dimensions: 6.24 (w) x 9.37 (h) x 0.38 (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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