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How to Prove It: A Structured Approach / Edition 2

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Overview

Many students have trouble the first time they take a mathematics course in which proofs play a sigficant role. This book will prepare students for such courses by teaching them techniques for writing and reading proofs. No background beyond high school mathematics is assumed. The book begins with logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. This understanding of the language of mathematics serves as the basis for a detailed discussion of the most important techniques used in proofs, when and how to use them, and how they are combined to produce comples proofs. Material on the natural numbers, relations, functions, and infinite sets provides practice in writing and reading proofs, as well as supplying background that will be valuable in most theoretical mathematics courses.
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Editorial Reviews

From the Publisher
"The prose is clear and cogent ... the exercises are plentiful and are pitched at the right level.... I recommend this book very highly!"
MAA Reviews

"The book provides a valuable introduction to the nuts and bolts of mathematical proofs in general."
SIAM Review

"This is a good book, and an exceptionally good mathematics book. Thorough and clear explanations, examples, and (especially) exercised with complete solutions all contribute to make this an excellent choice for teaching yourself, or a class, about writing proofs."
Brent Smith, SIGACT News

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Product Details

  • ISBN-13: 9780521675994
  • Publisher: Cambridge University Press
  • Publication date: 1/16/2006
  • Edition description: Revised Edition
  • Edition number: 2
  • Pages: 398
  • Sales rank: 185,752
  • Product dimensions: 5.98 (w) x 8.98 (h) x 0.87 (d)

Meet the Author

Daniel J. Velleman received his B.A. at Dartmouth College in 1976 summa cum laude, the highest distinction in mathematics. He received his Ph.D. from the University of Wisconsin-Madison in 1980 and was an instructor at the University of Texas-Austin, 1980–1983. His other books include Which Way Did the Bicycle Go? (with Stan Wagon and Joe Konhauser), 1996; Philosophies of Mathematics (with Alexander George), 2002. Among his awards and distinctions are the Lester R. Ford Award for the paper Versatile Coins (with Istvan Szalkai), 1994, the Carl B. Allendoerfer Award for the paper 'Permutations and Combination Locks' (with Greg Call), 1996. He's been a member of the editorial board for American Mathematical Monthly from 1997 to today and was Editor of Dolciani Mathematical Expositions from 1999-2004. He published papers in Journal of Symbolic Logic, Annals of Pure and Applied Logic, Transactions of the American Mathematical Society, Proceedings of the American Mathematical Society, American Mathematical Monthly, Mathematics Magazine, Mathematical Intelligencer, Philosophical Review, American Journal of Physics.

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Table of Contents

1. Sentential logic; 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction; 7. Infinite sets.

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