Proofs That Really Count
Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2006! Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones using a variety of tools. 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.