Proofs That Really Count

Proofs That Really Count

The Art of Combinatorial Proof

eBook - 2003
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While combinatorial mathematical proofs are not necessarily the simplest approach, Benjamin (Harvey Mudd College) and Quinn (Occidental College) believe them to bring concrete understandings to many mathematical problems. They select identities that frequently arise in mathematics and offer combinatorial (or "counting") proofs for them. Identities covered include Fibonacci numbers, Lucas identities, linear recurrences, continued fractions, binomial identities, and Stirling numbers. Annotation (c) Book News, Inc., Portland, OR (

Cambridge Univ Pr
Demonstration of the use of simple counting arguments to describe number patterns; numerous hints and references.
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.

Publisher: [Washington, D.C.] : Mathematical Association of America, ©2003
ISBN: 9780883853337
Characteristics: 1 online resource (xiv, 194 pages) : illustrations
Additional Contributors: Quinn, Jennifer J.


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