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How to prove it
a structured approach
by Daniel J. Velleman
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This edition was published in 2006 by Cambridge University Press in New York.
Written in English
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.
Previews available in: English
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1
How to Prove It: A Structured Approach
2019, Cambridge University Press
in English
1108439535 9781108439534

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How to Prove It: A Structured Approach
2019, Cambridge University Press
in English
110842418X 9781108424189

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3
How to prove it: a structured approach
2006, Cambridge University Press
in English
 2nd ed.
0521861241 9780521861243

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4 
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5
How to prove it: a structured approach
1994, Cambridge University
in English
0521441161 9780521441162

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How to prove it
First published in 1994
Work Description
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.
How to prove it
a structured approach
This edition was published in 2006 by Cambridge University Press in New York.
Table of Contents
Introduction  
Sentential logic  
1.1 Deductive reasoning and logical connectives  
1.2 truth tables  
1.3 variables and sets  
1.4 operations on sets  
1.5 The conditional and biconditional connectives  
Quantificational logic  
2.1 Quantifiers  
2.2 Equivalences involving quantifiers  
2.3 More operations on sets  
Proofs  
3.1 proof strategies  
3.2 proofs involving negations and conditionals  
3.3 Proofs involving quantifiers  
3.4 Proofs involving conjunctions and biconditionals  
3.5 Proofs involving disjunctions  
3.6 Existence and uniqueness proofs  
3.7 More examples of proofs  
Relations  
4.1 Ordered pairs and cartesian products  
4.2 Relations  
4.3 More about relations  
4.4 Ordering relations  
4.5 Closures  
4.6 Equivalence relations  
Functions  
5.1 Functions  
5.2 Onetoone and onto  
5.3 Inverses of functions  
5.4 Images and inverse images: a research project  
Mathematical induction  
6.1 Proof by mathematical induction  
6.2 More examples  
6.3 Recursion  
6.4 Strong induction  
6.5 Closures again  
Infinite sets  
7.1 Equinumerous sets  
7.2 Countable and uncountable sets  
7.3 The cantor  
Schroder  
Bernstein theorem  
Appendix 1: Solutions to selected exercises  
Appendix 2: Proof designer  
Suggestions for further reading  
Summary for proof techniques  
Index. 
Edition Notes
Includes bibliographical references and index.
Classifications
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History
 Created April 1, 2008
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