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Proofs that really count : the art of combinatorial proof / Arthur T. Benjamin and Jennifer J. Quinn.
- Format:
- Book
- Author/Creator:
- Benjamin, Arthur, author.
- Quinn, Jennifer J., author.
- Series:
- Dolciani Mathematical Expositions
- Dolciani Mathematical Expositions ; v.42
- Language:
- English
- Subjects (All):
- Combinatorial enumeration problems.
- Physical Description:
- 1 online resource (xiv, 194 pages) : digital, PDF file(s).
- Edition:
- 1st ed.
- Place of Publication:
- Washington : Mathematical Association of America, 2003.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- 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.
- Notes:
- Title from publisher's bibliographic system (viewed on 02 Oct 2015).
- Includes bibliographical references (p. 187-190) and index.
- Description based on print version record.
- ISBN:
- 1-61444-208-8
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