Proofs that Really Count: The Art of Combinatorial Proof

Title

Proofs that Really Count: The Art of Combinatorial Proof

Files

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Description

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.

ISBN

0883853337

Publication Date

8-2003

Publisher

Mathematical Association of America

City

Washington D.C.

Keywords

combinatorics, mathematics, problem solving, proof theory

Disciplines

Discrete Mathematics and Combinatorics | Mathematics | Physical Sciences and Mathematics