# PROOFS THAT REALLY COUNT

## PROOFS THAT REALLY COUNT

- Item No.
- DOL-27

- Price:
- $55.95

### Product Details

*Proofs That Really Count* by Arthur Benjamin & 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 arguments primarily take one of two forms: - A counting question is posed and answered in two different ways. Since both answers solve the same question they must be equal. -Two different sets are described, counted, and a correspondence found between them. One-to-one correspondences guarantee sets of the same size. Almost one-to-one correspondences take error terms into account. Even many-to-one correspondences are utilized. 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.

*Brand name:*MAA**Authors: Arthur Benjamin and Jennifer Quinn**- ISBN: 9780883853337
- 208 pp.
- Hardbound
- 2003
- Sereis: Dolciani Mathematical Expositions