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BOOK OF PROOF

Richard Hammack

This textbook is an introduction to the standard methods of proving mathematical theorems. Click here for a pdf copy of the entire book, or get the chapters individually below.

Contents
Preface

ix

Introduction
x
I: Fundamentals

1. Sets

3

2. Logic

28

3. Counting

57
II: How to Prove Conditional Statements

4. Direct Proof

81

5. Contrapositive Proof

94

6. Proof by Contradiction

103

III: More on Proof

	7. Proving Non-Conditional Statements	113
	8. Proofs Involving Sets	119
	9. Disproof	134
	10. Mathematical Induction	142

IV: Relations, Functions and Cardinality

11. Relations

161

12. Functions

181

13. Cardinality

202

Solutions
216

Index
274

You may download the textbook for free here, or you can order a paperback copy (cover shown on left) from Amazon.com for $12.95.

I welcome comments concerning typographical errors, etc. Thanks to reader feedback, many mistakes have been corrected. The files on this page reflect all updates and corrections as of May 2011; The print version is has also been updated as of June 2011. I will continue to incorporate reader feedback in periodic revisions. My email address is on my home page.

I will continue offering the book for free on my web page, and for the lowest possible price through on-demand publishing.

© 2009 by Richard Hammack; This work is licensed under the Creative Commons Attribution-No Derivative Works 3.0 License; Cover by Eleni Kanakis, used by permission
	ISBN 978-0-9824062-0-5

	4. Direct Proof	81
	5. Contrapositive Proof	94
	6. Proof by Contradiction	103

	1. Sets	3
	2. Logic	28
	3. Counting	57

	11. Relations	161
	12. Functions	181
	13. Cardinality	202

Solutions	216
Index	274