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How to Prove It: A Structured Approach

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How to Prove It: A Structured Approach Cover

 

Synopses & Reviews

Publisher Comments:

Geared to preparing students to make the transition from solving problems to proving theorems, this text teaches 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. To help students 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. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

Synopsis:

Beginning 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.

Synopsis:

This new edition of Dan Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.

About 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.

Table of Contents

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

Product Details

ISBN:
9780521861243
Author:
Velleman, Daniel J.
Publisher:
Cambridge University Press
Location:
New York
Subject:
Mathematics
Subject:
Logic, symbolic and mathematical
Subject:
Combinatorics
Subject:
Mathematics-Combinatorics
Subject:
Logic
Edition Number:
2
Edition Description:
Revised
Publication Date:
20060331
Binding:
HARDCOVER
Grade Level:
General/trade
Language:
English
Illustrations:
10 tables 536 exercises
Pages:
400
Dimensions:
9.02 x 5.98 x 0.98 in 1.68 lb

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Related Subjects

Humanities » Philosophy » General
Science and Mathematics » Mathematics » Combinatorics
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy
Textbooks » General

How to Prove It: A Structured Approach New Hardcover
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$136.25 In Stock
Product details 400 pages Cambridge University Press - English 9780521861243 Reviews:
"Synopsis" by , Beginning 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.
"Synopsis" by , This new edition of Dan Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
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