Proofs that Really Count
Proofs that Really Count
Jennifer J. Quinn, Occidental College, Los Angeles
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.
- Accessible to mathematicians at a wide range of levels
- All exercises with hints and references
- Explains well known number patterns familiar to all students
Reviews & endorsements
'This book is written in an engaging, conversational style, and this reviewer found it enjoyable to read through (besides learning a few new things). Along the way, there are a few surprises, like the 'world's fastest proof by induction' and a magic trick. As a resource for teaching, and a handy basic reference, it will be a great addition to the library of anyone who uses combinatorial identities in their work.' Society for Industrial and Applied Mathematics Review
Product details
No date availableHardback
9780883853337
206 pages
262 × 185 × 17 mm
0.518kg
100 b/w illus.
Table of 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.
