How to Prove It by Daniel J. Velleman
A Structured Approach

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Synopsis

Many mathematics students have trouble the first time they take a course, such as linear algebra, abstract algebra, introductory analysis, or discrete mathematics, in which they are asked to prove various theorems. This textbook 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 step-by-step 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 "scratchwork" sections to expose the machinery of proofs about the natural numbers, relations, functions, and infinite sets. Numerous exercises give students the opportunity to construct their own proofs. 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.
 

About Daniel J. Velleman

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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.
 
Published January 1, 1994 by Cambridge University Press. 309 pages
Genres: Education & Reference, Science & Math. Non-fiction
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