Richard Hammack

• Sophomore level text for an introduction to proofs course
• Third edition (copyright 2018) in print and PDF. The third edition is a slightly expanded version of the second edition, but the two editions are otherwise compatible (exercises have not been renumbered, etc.).
• Widely used (more than 20,000 printed copies sold) with an extensive course adoption list available from the book’s home page
• Softcover version (380 pages) from Amazon or Barnes and Noble for about $21
• Comprehensive review in the MAA Digital Library linked from the book’s home page
• For more information and to download

From the author’s preface:

This text is an expansion and refinement of lecture notes I developed while teaching proofs courses over the past ten years. It is written for an audience of mathematics majors at Virginia Commonwealth University, a large state university….However, I am mindful of a larger audience. I believe this book is suitable for almost any undergraduate mathematics program.

Designed for the typical bridge course that follows calculus and introduces the students to the language and style of more theoretical mathematics, Book of Proof has 13 chapters grouped into four sections: (I) Fundamentals, (II) How to Prove Conditional Statements, (III) More on Proof, (IV) Relations, Functions, and Cardinality. One math professor who has used the book writes:

Hammack’s book is great. I’ve used the book twice now, will use it again, and have recommended it to other instructors. I have used it in a discrete math course which serves as a “transition” course for our majors.