Cover of: How to prove it by Daniel J. Velleman
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December 11, 2020 | History
An edition of How to prove it (1994)

How to prove it

a structured approach

2nd ed.
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This edition was published in 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 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 '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.

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Edition Availability
Cover of: How to Prove It
How to Prove It: A Structured Approach
2019, Cambridge University Press
in English
Cover of: How to Prove It
How to Prove It: A Structured Approach
2019, Cambridge University Press
in English
Cover of: How to prove it
How to prove it: a structured approach
2006, Cambridge University Press
in English - 2nd ed.
Cover of: How to Prove It
How to Prove It
2002, Cambridge University Press
eBook in English
Cover of: How to prove it
How to prove it: a structured approach
1994, Cambridge University
in English

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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 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 '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

2nd ed.

This edition was published in 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 One-to-one 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

Dewey Decimal Class
511.3
Library of Congress
QA9 .V38 2006, QA9.V38 2006

The Physical Object

Pagination
p. cm.

ID Numbers

Open Library
OL3413317M
Internet Archive
howtoproveitstru00vell_901
ISBN 10
0521861241, 0521675995
ISBN 13
9780521861243, 9780521675994
LC Control Number
2005029447
Library Thing
360379
Goodreads
3357126
739735

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