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How to Prove It: A Structured Approach
Daniel J. Velleman
Publisher: Cambridge University Press (2006)
Details: 384 pages, Paperback
Topics: Proofs and Logic, Transition to Advanced Mathematics
MAA Review[Reviewed by Michael Berg, on 07/19/2006]
Here are the reasons I’m not using this book in my course on how to do proofs in the Fall semester of this year:
Perhaps, as time goes by, and it’s again my turn to teach this course on “baby proofs,” I’ll just give in and do the sensible thing and opt for Velleman’s How To Prove It. (Even its title evinces good taste: how many of us don’t have fond memories of Polya’s classic by a similar name?).
Some details, then: Velleman’s book is divided into seven chapters (Sentential Logic, Quantificational Logic, Proofs, Relations, Functions, Mathematical Induction, and Infinite Sets), covering over 300 pages. The prose is clear and cogent (and even suited to self-study for the rare lone wolf), the exercises are plentiful and are pitched at the right level (and many of them have solutions in the back of the book), and the paperback version of the book comes in at a penny shy of $30.00 Incredible!
I recommend this book very highly!
Michael Berg is Professor of Mathematics at Loyola Marymount University in California.