Proofs that Really Count: The Art of Combinatorial Proof

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Mathematical Association of America, Nov 13, 2003 - Mathematics - 194 pages
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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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Review: Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions)

User Review  - Jeff Yoak - Goodreads

This is one of my favorite math books ever, but it is hard enough that I can't make it through in the small bites I have time for. I plan on revisiting when I have time to spend hours at a time focused on it. Read full review

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About the author (2003)

Athur Benjamin received his PhD in from Johns Hopkins University. He currently teaches mathematics at Harvey Mudd COllege. He is a Fellow the Institute for Combinatorics and its Applications. With Jennifer Quinn , he is the editor of "Math Horizons," a student magazine published by the Mathematical Association of America.

Jennifer Quinn received her PhD in Combinatorics from the University of Wisconsin. She currently teaches at Occidental College. With Arthur Benjamin she the editor of "Math Horizons," a student magazine published by the Mathematical Association of America.

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