Two weeks ago, I finished reading Book of Proof (link goes to Amazon) by Professor Richard Hammack, and so far, it was the best book that I have read about introduction to mathematical proofs. I recommend this book to high school students who are interested in pursuing a mathematics degree, to college students who are math majors, and to teachers who will teach or who are teaching an introductory course on mathematical proofs. Here are some of the reasons why I really like this book.
The explanations of concepts in this book are very clear and the concepts are well-connected. Maybe this is because the author’s long experience in teaching this course (or maybe he is just a very good teacher). This book is a product of the author’s lecture notes on teaching mathematical proofs for the past 14 years. Easy Examples and Exercises
You will understand a math book better if you read the text and do the exercises. The highlight of this book is to understand the structure of proofs and not to prove hard problems. Since this book has relatively easier examples and exercises compared to others (at least compared to those I’ve read), you will finish the book in a shorter period of time and would be able to focus on understanding the techniques in proving without being stuck at some of the problems.
Connection to Truth Tables
The author always connects the discussion of the proof structure to truth tables and logical connectives. For instance, the author always comes back to the truth tables to introduce proof structures such as direct proof, proof by contradiction, and proof by contrapositive.
This book has complete solutions to all exercises even on exercises on proofs.
If you are interested in purchasing a hard copy of the book, you can buy it here, but there’s a free PDF copy at Professor Richard Hammack’s website.