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How to Prove It: A Structured Approach
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Top Customer Reviews
Set Theory is the foundation on which mathematical proofs are based. This book emphasizes set theory.
Velleman uses structured style as a technique. Two columns are prepared. The left column is Givens and right Goal. By restructuring Givens and Goal using relationships and definitions, some parts of Goal statement is moved to Givens, like peeling skins of onion. This process iterates until one finds the proving obvious. The whole process is a "scratch work" and a reader is able to see how the author structures the proof step by step, both from Goal and Givens viewpoints.
In past, there was only a Macintosh proofing program, but now Java version called Proof Designer is out. So Windows and Linux users alike can now enjoy this little program in conjunction with the book. Two disappointments with Proof Designer are that the output is only in the form of a traditional proof style which does not expose "the scratch work" and that the program does not use the two column style used in the book.
There are additional materials such as supplementary exercises, documentation, and a list of proof strategies (which is also available at the end of the book as a good reminder and reference), all available from author's site for free. [search in google like this: velleman "how to prove it" inurl:amherst]
After completion of this book, don't throw it away!Read more ›
However, it could have been better. I bought the book almost 10 years ago. I am a secondary ed. math teacher and when I left college I was quite upset with myself that I had this fancy math degree and couldn't prove anything. I picked up this book and today I'm working on my PhD in mathematics! This book inspired me to that.
First - What's wrong with the book. Not that there really is anything wrong with the book. I have attempted this book 3 times. I admit, the first two times I stalled (1997 - 2001) when I got to page 119. For some reason I couldn't grip those concepts such as intersecting families, etc. The preface of the book says only high school mathematics is required - that is just flat out wrong. This book is more for undergrads and maybe older fossils like me that have delved into mathematics a bit more than average. Also, like all the other reviews, there is too many exercises with no solutions. What really threw me with that is I didn't know if I was setting the written argument up properly. Sure, on the one hand, it's better to NOT have answers so you strive like a mad person to find them. Yet, it's so frustrating to not know if you did something right. The best approach is to do your best I suppose. After the third try (2004 & 2005) I finally completed the book on my own volition and I'm assuming most of my content is correct.
Velleman describes math so well that I honestly admit, I have a full repetoire of tactics to use to solve mathematical proofs. I don't have the confidence to toy with the big boys yet, like correcting a 49 page proof pertaining to the 'Twin Prime Conjecture' ... but it is SO NICE to UNDERSTAND the arguments!Read more ›
Most Recent Customer Reviews
I took my discrete mathematics class with this book. It provides an excellent introduction to proof-writing techniques, sentential logic and discrete math. Read morePublished on November 28, 2010 by Ivane Gamkrelidze
Reading this book will not help you write proofs in the least. How to Prove It, to help you at all, will require lots of time and effort after reading each chapter, actually doing... Read morePublished on June 22, 2008 by Michael P. Quinn
I write this review on the context of having done all the math required for mechanical engineer but never havin to do proofs... as B. Read morePublished on June 17, 2006 by Humberto Mejia
If you're like many math students then there comes a time when you must be prepared to formalise your knowledge and your ability to present this knowledge in a logical and... Read morePublished on September 20, 2005 by Mr. D. Otgaar
After reading this book, proofs have become second nature to me. Before reading this book, I had no idea how to prove anything, I would stare blindly at a problem without knowing... Read morePublished on July 9, 2005 by D. Mota
This is an excellent book for the early undergraduate student. It is actually two books in one. The first half is a careful review of Logic and the essentials of Set Theory with... Read morePublished on February 29, 2004 by Kent S. Kapitan
I bought this book in the hopes that it would help me improve my proof writing skills. Being only a high school graduate (a month ago), I had practically no knowledge of set... Read morePublished on July 24, 2003 by D. Goldman
A basic introduction to understanding math proofs by understanding logic first. It's a good concept for a book, and I think it was executed fairly well. Read morePublished on December 26, 2001 by C. Metcalf
I am a philosophy student with no real mathematics training, though I am very familiar with first order predicate logic. Read morePublished on November 2, 2001 by Theresa