How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
"In this book, Houston has created a primer on the fundamental abstract ideas of mathematics; the primary emphasis is on demonstrating the many principles and tactics used in proofs. The material is explained in ways that are comprehensible, which will be a great help for people who seem to hit the wall regarding what to do when confronted with the creation of a proof... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof."Charles Ashbacher, Journal of Recreational Mathematics"The author provides concise, crisp explanations, including definitions, examples, tips, remarks, warnings, and idea-reinforcing questions. Houston expresses thoughts clearly and concisely, and includes succinct remarks to make points, clarify arguments, and reveal subleties."W.R. Lee, Choice Magazine