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.
About Daniel J. Velleman
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 WisconsinMadison in 1980 and was an instructor at the University of TexasAustin, 19801983. 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 19992004. 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.Details Book
Author  :  Daniel J. Velleman 
Publisher  :  Cambridge University Press 
Data Published  :  16 January 2006 
ISBN  :  0521861241 
EAN  :  9780521861243 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  400 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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