02521nam a22002897a 4500 20220623131244.0 220623b |||||||| |||| 00| 0 eng d 9789393330116 :Donated from NBHM 511.62 BEN Benjamin, Arthur Proofs that Really Count : the art of combinatorial proof / Arthur Benjamin [Washington, : Mathematical Association of America, @2003 xiv, 194p 24cm. Donated Dolciani mathematical expositions, no. 27. 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. 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 Mathematics General principles of mathematics Mathematics -- Combinatorics. Mathematics -- Discrete Mathematics. Kombinatorische Analysis Benjamin, Arthur Quinn, Jennifer J. MDL 59429 59429 0 0 ddc 0 0 MDL MDL 2022-06-23 Donated from NBHM 0 511.62 BEN M384 2022-06-23 00:00:00 2022-06-23 MDL