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

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'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

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.

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.

About the Author

Arthur T. Benjamin received his PhD in Mathematical Sciences from John Hopkins University. He is currently Professor and Chair of the Mathematics Department at Harvey Mudd College.

Jennifer J. Quinn received here PhD in Combinatorics from the University of Wisconsin, Madison. She is currently Associate Professor and Chair of the Mathematics Department at Occidental College.

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