000			02521nam a22002897a 4500
005			20220623131244.0
008			220623b |||||||| |||| 00| 0 eng d
020			_a9789393330116
028			_a:Donated from NBHM
082			_a511.62 BEN
100			_aBenjamin, Arthur
245			_a Proofs that Really Count _b: the art of combinatorial proof _c/ Arthur Benjamin
260			_a[Washington, _b: Mathematical Association of America, _c@2003
300			_axiv, 194p _c24cm.
365			_bDonated
490			_aDolciani mathematical expositions, no. 27.
505			_a Fibonacci identities -- Gibonacci and Lucas identities -- Linear recurrences -- Continued fractions -- Binomial identities -- Alternating sign binomial identities -- Harmonic and stirling number identities -- Number theory -- Advanced Fibonacci & Lucas identities.
520			_a 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
650			_aMathematics
650			_aGeneral principles of mathematics
650			_aMathematics -- Combinatorics.
650			_aMathematics -- Discrete Mathematics.
650			_aKombinatorische Analysis
700			_aBenjamin, Arthur
700			_aQuinn, Jennifer J.
942			_cMDL
999			_c59429 _d59429