Proofs That Really Count The Art of Combinatorialproof

Brand new. We distribute directly for the publisher. Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones usi [more]

Brand new. We distribute directly for the publisher. 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 w[less]

Brand new. We distribute directly for the publisher. Mathematics is the science of patterns, and mathematicians attempt to understand these patterns and discover new ones usi [more]

Brand new. We distribute directly for the publisher. 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.[less]

BRAND NEW BOOK! Shipped within 24-48 hours. Normal delivery time is 5-12 days. Please note some orders may be shipped from UK with same delivery timeframe, ***NO EXPEDITED OR [more]

BRAND NEW BOOK! Shipped within 24-48 hours. Normal delivery time is 5-12 days. Please note some orders may be shipped from UK with same delivery timeframe, ***NO EXPEDITED ORDERS***[less]