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Proofs that Really Count by Arthur T. Benjamin, Jennifer Quinn
(The Art of Combinatorial Proof)

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Proofs that Really Count (The Art of Combinatorial Proof) written by Arthur T. Benjamin, Harvey Mudd College and Jennifer Quinn.
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.

Title: Proofs that Really Count (The Art of Combinatorial Proof)
Author(s): Arthur T. Benjamin, Jennifer Quinn
Publisher: Mathematical Association of America
Series: Dolciani mathematical expositions
Year: 2003
Pages: 208
Type: PDF
Language: English
ISBN: 9780883853337,0883853337
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Proofs that Really Count (The Art of Combinatorial Proof) written by Arthur T. Benjamin, Jennifer Quinn cover the following topics.
1.Fibonacci Identities
2.Gibonacci and Locus Identities
3.Linear Recurrences
4.Continued Fractions
5.Binomial Identities
6.Alternating Sign Binomial Identities
7.Harmonic and Stirling Number Identities
8.Number Theory
9.Advanced Fibonacci and Lucas Identities
Some Hints and Solutions for Chapter Exercises
Appendix of Combinatorial Theorems
Appendix of Identities

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