This book is an introduction to the standard methods of proving mathematical theorems. It has been approved by the American Institute of Mathematics' Open Textbook Initiative . Also see the Mathematical Association of America Math DL review (of the 1st edition) and the Amazon reviews . An adoptions list is here On July 24, 2020 I issued edition 3.2 in print and PDF (ISBN's unchanged). This slight revision corrects a handful of typos found by readers. Also, after living with the red cover for two years, I switched to a more contemplative blue. All orders printed after July 24 will have the blue cover.

You can order a copy through Barnes & Noble or Amazon. You can also download aversion HERE . (The contents links below will take you to specific chapters in this file.)

13.1 The Triangle Inequality 13.2 Definition of a Limit 13.3 Limits That Do Not Exist 13.4 Limit Laws 13.5 Continuity and Derivatives 13.6 Limits at Infinity 13.7 Sequences 13.8 Series

11.1 Relations 11.2 Properties of Relations 11.3 Equivalence Relations 11.4 Equivalence Classes and Partitions 11.5 The Integers Modulo n 11.6 Relations Between Sets

10.1 Proof by Induction 10.2 Proof by Strong Induction 10.3 Proof by Smallest Counterexample 10.4 Examples: The Fundamental Theorem of Arithmetic 10.5 Fibonacci Numbers

8.1 How to Prove a is an element of A 8.2 How to Prove A is a subset of B 8.3 How to Prove A = B 8.4 Examples: Perfect Numbers

6.1 Proving Statements with Contradiction 6.2 Proving Conditional Statements with Contradiction 6.3 Combining Techniques 6.4 Some Words of Advice

3.1 Lists 3.2 The Multiplication Principle 3.3 The Addition and Subtraction Principles 3.4 Factorials and Permutations 3.5 Counting Subsets 3.6 Pascal's Triangle and the Binomial Theorem 3.7 The Inclusion-Exclusion Principle 3.8 Counting Multisets 3.9 The Division and Pigeonhole Principles 3.10 Combinatorial Proof

2.1 Statements 2.2 And, Or, Not 2.3 Conditional Statements 2.4 Biconditional Statements 2.5 Truth Tables for Statements 2.6 Logical Equivalence 2.7 Quantifiers 2.8 More on Conditional Statements 2.9 Translating English to Symbolic Logic 2.10 Negating Statements 2.11 Logical Inference 2.12 An Important Note

1.1 Introduction to Sets 1.2 The Cartesian Product 1.3 Subsets 1.4 Power Sets 1.5 Union, Intersection, Difference 1.6 Complement 1.7 Venn Diagrams 1.8 Indexed Sets 1.9 Sets That Are Number Systems 1.10 Russel's Paradox

(Hover on the chapter title to see the subsections.)

Thanks to the readers who wrote to report mistakes and typos! I incorporate reader feedback in periodic revisions. Please contact me at rhammack@vcu.edu if you find any additional mistakes, no matter how minor.





Instructors and Readers: I'd like to post sample tests and additional exercises for Book of Proof on this page. Contributions are welcome! For more information, click on the link for ancillary material below.

