by Arthur Benjamin and Jennifer Quinn
is now available in the MAA eBooks Store!
Purchase your copy today for only $22.50.
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.
Read the MAA Review written by Darren Glass, an associate professor at Gettysburg College, below.
"Several years ago I attended a conference at which Arthur Benjamin, one of the authors of the book under review, gave a talk about Fibonacci Numbers. In particular, he gave the following interpretation. Let fn count the number of ways to tile an n-by-1 board with 1-by-1 square tiles and 2-by-1 domino tiles. One can show that fn = Fn+1, where Fn is the standard nth Fibonacci number defined by F0 = 0, F1 = 1, and the recursion relation Fn = Fn-1 + Fn-2. He proceeded to show how this definition could be used to give a combinatorial proof of many of the Fibonacci Number identities that we are familiar with, such as Fm+n=Fm+1Fn + FmFn-1..."
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