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Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions)

4.7 out of 5 stars 7 customer reviews
ISBN-13: 978-0883853337
ISBN-10: 0883853337
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Editorial Reviews

Review

'This book is written in an engaging, conversational style, and this reviewer found it enjoyable to read through (besides learning a few new things). Along the way, there are a few surprises, like the 'world's fastest proof by induction' and a magic trick. As a resource for teaching, and a handy basic reference, it will be a great addition to the library of anyone who uses combinatorial identities in their work.' Society for Industrial and Applied Mathematics Review

Book Description

Award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns can be understood by simple counting arguments. Numerous hints and references are given for all exercises and the extensive appendix of identities will be a valuable resource. Ideal for readers from high school students to professional mathematicians.
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Product Details

  • Series: Dolciani Mathematical Expositions (Book 27)
  • Hardcover: 208 pages
  • Publisher: The Mathematical Association of America (August 1, 2003)
  • Language: English
  • ISBN-10: 0883853337
  • ISBN-13: 978-0883853337
  • Product Dimensions: 10 x 0.7 x 7 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #658,478 in Books (See Top 100 in Books)

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Top Customer Reviews

Format: Hardcover
I was introduced to this book by a talk that one of the authors (Arthur Benjamin) gave at the MAA Mathfest in Albuquerque in August of 2005. The talk was one of the very best mathematics talks that I've ever attended. Everyone in the audience could follow what was going on, and we all left with an understanding of the basic approach to combinatorial identities used in this book. The authors' approach is to prove combinatorial identities by defining a quantity and then obtaining different formulas for that quantity. One formula becomes the left hand side of an identity while another formula becomes the right hand side.

When I read the book I found that it was just as clearly written, with lots of beautiful examples.
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Format: Hardcover
The proofs in this book are easy enough for a bright high schooler or even an exceptional middle schooler to understand, while still making use of insightful tricks that keep the solutions far from being obvious.
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Format: Hardcover Verified Purchase
"Thoroughly engaging... Accessible to a very broad audience... While the theorems covered may not be new to research mathematicians, I would wager that very few of us have seen them proven in quite this way." -- American Mathematical Monthly [[...]

I am not a mathematician and I learn something cool and useful from this book every few paragraphs. Highly recommended.
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By Abhinav on December 18, 2010
Format: Hardcover
This book is a pleasure to read and find new combinatorial gems. I'd say its accessible to anyone who's done basic counting - either in high school or a first discrete math course. I found it a bit odd that it starts with the fiibonacci numbers instead of simpler identities like Pascal, Chairperson, etc but the proofs are fairly illustrative though not the very through (the authors seem to believe that the student is already familiar with the ideas of disjoint sets and unions). Overall though, if you know a few counting identities and know the basic idea behind counting in two ways, this book is a wonderful extension!

It also makes for really good casual reading because unlike most math, reading a combinatorial proof doesn't usually require rewriting with pen and paper to understand well and have that "Aha!" moment.
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