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

by Arthur T. Benjamin (Author), Jennifer Quinn (Author)
4.7 out of 5 stars 7 customer reviews
ISBN-13: 978-0883853337
ISBN-10: 0883853337
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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: #637,349 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

32 of 35 people found the following review helpful
Outstanding exposition
By Brian Borchers on January 7, 2006
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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16 of 17 people found the following review helpful
easy to understand and full of insights
By Bennett Haselton on January 9, 2007
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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19 of 22 people found the following review helpful
Winner of the 2006 Mathematical Association of America Beckenbach Book Prize
By Joshua Jordan on April 1, 2006
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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1 of 1 people found the following review helpful
Delightful!
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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