How to Prove It: A Structured Approach
BeschreibungBeginning with the basic concepts of logic and set theory, this book teaches the language of mathematics and how it is interpreted. The author uses these concepts as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. He 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.
Inhaltsverzeichnis1. Sentential logic; 2. Quantificational logic; 3. Proofs; 4. Relations; 5. Functions; 6. Mathematical induction; 7. Infinite sets.
PortraitDaniel 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.
Pressestimmen'The book begins with the basic concepts of logic and theory ... These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. No background standard in high scholl mathematics is assumed.' L'enseignement mathematique
Untertitel: A Structured Approach. 10 tables, 536exercises. Sprache: Englisch.
Verlag: Cambridge University Pr.
Erscheinungsdatum: Mai 2006
Seitenanzahl: 336 Seiten