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Full Description
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 emphasizes numbers that are often not 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
1. Fibonacci identities; 2. Lucas identities; 3. Gibonacci identities; 4. Linear recurrences; 5. Continued fractions; 6. Binomial identities; 7. Alternating sign binomial identities; 8. Harmonic numbers and Stirling numbers; 9. Number theory; 10. Advanced Fibonacci and Lucas identities.
