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How to Prove It: A Structured Approach
by Daniel J. Velleman2nd
9780521675994
0521675995
Paperback
1/16/2006
Cambridge University Press
Questions About This Book?
What version or edition is this?
This is the 2nd edition with a publication date of 1/16/2006.
What is included with this book?
 The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
Summary
Many students have trouble the first time they take a mathematics course in which proofs play a significant role. This new edition of Velleman's successful text will prepare students to make the transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a stepbystep breakdown of the most important techniques used in constructing proofs. The author shows how complex proofs are built up from these smaller steps, using detailed 'scratch work' sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. To give students the opportunity to construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. This book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and of course mathematicians.
Table of Contents
Preface to the Second Edition  ix  
Preface  xi  
Introduction  1  (7)  
1 Sentential Logic  8  (47)  

8  (6)  

14  (12)  

26  (8)  

34  (9)  

43  (12)  
2 Quantificational Logic  55  (29)  

55  (9)  

64  (9)  

73  (11)  
3 Proofs  84  (79)  

84  (11)  

95  (13)  

108  (16)  

124  (12)  

136  (10)  

146  (9)  

155  (8)  
4 Relations  163  (63)  

163  (8)  

171  (9)  

180  (9)  

189  (13)  

202  (11)  

213  (13)  
5 Functions  226  (34)  

226  (10)  

236  (9)  

245  (10)  

255  (5)  
6 Mathematical Induction  260  (46)  

260  (7)  

267  (12)  

279  (9)  

288  (12)  

300  (6)  
7 Infinite Sets  306  (23)  

306  (9)  

315  (7)  

322  (7)  
Appendix 1: Solutions to Selected Exercises  329  (44)  
Appendix 2: Proof Designer  373  (2)  
Suggestions for Further Reading  375  (1)  
Summary of Proof Techniques  376  (5)  
Index  381 