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Book of Proof

4.48  ·  Rating details ·  170 ratings  ·  15 reviews
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Alth ...more
Paperback, 306 pages
Published December 1st 2009 by Virginia Commonwealth University Mathematics (first published 2009)
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David Sarkies
Jun 23, 2018 rated it really liked it  ·  review of another edition
Shelves: science
Playing with Numbers
22 June 2018 - Sydney

Well, what do you know, a university textbook that doesn’t actually break the bank. In fact a University text book that actually costs you absolutely nothing. I’m definitely going to give this book some good marks for that. Yeah, I remember the last time I was at Uni and the most expensive aspect of it was the books (well, yes, the fees, but the government technically pays for that). In fact when I did Law you could be assured that the yearly book bill w
David Molnar
Feb 06, 2016 rated it it was amazing  ·  review of another edition
Outstanding. I have used this as a supplemental text in a few courses, and would totally consider adopting it as the primary text for the right course. There is certainly enough here for a full semester's work. And, it's open source, which means it is not only free (the author's website is a google away) but also remixable - meaning, you are free to create and distribute your own version of the text under a creative commons license ( as long as you do so ...more
Brian Albrecht
Mar 25, 2015 rated it it was amazing  ·  review of another edition
Shelves: grad-prep
I feel weird giving 5 stars to a book about proofs. It's not a great book in the sense that The Great Gatsby is. Getting over that, I'm assuming anyone who would look at this book would know what to expect from it.

It has a specific job, to teach basic proofs. At that job, it is the best book available. You can get the PDF for free on Prof. Hammack's website, but I bought the physical copy. So before you start your Real Analysis course with Baby Rudin or your graduate economics courses with proof
Sung Yoon
Oct 17, 2016 rated it really liked it
Don't try to use this book to win an argument against your wife.
Aug 28, 2017 rated it it was amazing  ·  review of another edition
Hammacks's Book of Proof is a wonderful introduction to the world of upper division mathematics. I think that this book would be perfect to read before starting with LA/DEs and I wish I had read it before taking those classes. Hammack gently leads the reader through many important mathematic concepts that are taken as understood by the reader in many upper division classes. This books is a must read for anyone going into upper division math, regardless of major!
Michael Chan
Jul 28, 2018 rated it it was amazing  ·  review of another edition
Shelves: math, owned
It introduces the fundamental concepts of Discrete Mathematics and Proofs. You will learn the basic syntax languages used by Mathematicians.

The theories are explained with Proofs, described in a clear and concise way, with sufficient exercises at the end. I went thru the exercises, and took me awhile to finish, but it was enjoyable.

Topics include: Sets, Logic, Counting, Relations, Functions, Set Cardinality
Proof methods include: Direct, Contrapositive, Contradiction, Induction, etc.
Dhiraj Kumar
Oct 21, 2019 rated it it was amazing  ·  review of another edition
Shelves: mathematics
There are certain ways to write a mathematical proof. We all know that but the unfortunate thing is we are rarely taught that. This book provides the foundation which enables one to be confident about their proofs and write more rigorous proofs.
I will come back to this book again and again.
Really great.
I was looking for an introductory (really introductory) book on proof and I found it.
Mar 25, 2020 rated it it was amazing  ·  review of another edition
Great book on the processes and methodologies of formal rigorous mathematical proofs. A must for a mathematics student(s).
Alexander Snitsarenko
A masterpiece on proofs. Focus on a set theory and logic. Amazing selection of exercises. Doing all exercises is a must
Helena Zhu
Aug 26, 2019 rated it it was amazing  ·  review of another edition
A comprehensive and excellent introduction to proofs, includes answers to odd-number exercises.
Mar 08, 2015 rated it it was amazing  ·  review of another edition
Delightful and challenging. More succinct than Velleman's How to Prove It.
Hb20007 (Hanna)
Dec 26, 2015 rated it it was amazing  ·  review of another edition
One of the best math textbooks that I have read in college, also happens to be the one which didn't cost me a single buck
May 28, 2014 marked it as to-read  ·  review of another edition
Thus far, the most accessible illustration of the implication operation's logic table......
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“Mathematics is filled with such instances where it is important to regard one set as a subset of another.” 1 likes
“Sets are fundamental because every mathematical structure,
object or entity can be described as a set. Logic is fundamental because it
allows us to understand the meanings of statements, to deduce information
about mathematical structures and to uncover further structures.”
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