# Proofs that Really Count: The Art of Combinatorial Proof

### By Arthur T. Benjamin and Jennifer J. Quinn

Print ISBN: 978-0-88385-333-7
Electronic ISBN: 978-1-61444-208-0
208 pp., Hardbound, 2003
List Price: $58.00 Member Price:$43.50
Series: Dolciani Mathematical Expositions

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 explores more than 200 identities throughout the text and exercises, frequently emphasizing numbers not often 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.

Foreword
1. Fibonacci Identities
2. Gibonacci and Lucas 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 & Lucas Identities
Some Hints and Solutions for Chapter Exercises
Appendix of Combinatorial Theorems
Appendix of Identities
Bibliography
Index