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Proofs that Really Count. The Art of Combinatorial Proof Dolciani Mathematical Expositions

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Manufacturer: The Mathematical Association of America
Author: Arthur T. Benjamin
Binding: Hardcover
Publication Date: 2003-08-01
Publisher: The Mathematical Association of America
Label: The Mathematical Association of America
Number Of Pages: 208

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Editorial Review
Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. In Proofs That Really Count, award-winning math professors Arthur Benjamin and Jennifer Quinn demonstrate that many number patterns, even very complex ones, can be understood by simple counting arguments. The book emphasizes numbers that are often not thought of as numbers that count: Fibonacci Numbers, Lucas Numbers, Continued Fractions, and Harmonic Numbers, to name a few. Numerous hints and references are given for all chapter exercises and many chapters end with a list of identities in need of combinatorial proof. The extensive appendix of identities will be a valuable resource. This book should appeal to readers of all levels, from high school math students to professional mathematicians.
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Customer Reviews

great

2008-02-13
This is just a fantastic book on combinatorics. Although not as long as most combinatorics texts it packs in a great deal of information. Very well-written with a lively style. Probably, the best thing about it for me is how clear the exposition is. I really learned a lot from this book.

easy to understand and full of insights

2007-01-09
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.

Winner of the 2006 Mathematical Association of America Beckenbach Book Prize

2006-04-01
"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 [http://www.maa.org/reviews/reallycount.html]

I am not a mathematician and I learn something cool and useful from this book every few paragraphs. Highly recommended.

Outstanding exposition

2006-01-07
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.

Lovely author

2005-05-26
I haven't read this book yet, but I have a signed copy after seeing Jenny Quinn speak at the 2005 meeting of the Northwest chapter of the Mathmatics Association of America. If her written work is anything like her speaking, then this should be a great book. Her combinatorial proofs are an interesting approach to old equations, and she presents them in a very clear manner. A most enthusiastic lady.