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Proofs that Really Count: The Art of Combinatorial Proof (Dolciani Mathematical Expositions), by Arthur T. Benjamin, Jennifer Quinn
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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.
- Sales Rank: #320332 in Books
- Brand: Brand: The Mathematical Association of America
- Published on: 2003-08-01
- Original language: English
- Number of items: 1
- Dimensions: 6.97" h x .67" w x 9.96" l, 1.15 pounds
- Binding: Hardcover
- 208 pages
- Used Book in Good Condition
Review
'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
About the Author
Arthur T. Benjamin received his PhD in Mathematical Sciences from John Hopkins University. He is currently Professor and Chair of the Mathematics Department at Harvey Mudd College.
Jennifer J. Quinn received here PhD in Combinatorics from the University of Wisconsin, Madison. She is currently Associate Professor and Chair of the Mathematics Department at Occidental College.
Most helpful customer reviews
19 of 22 people found the following review helpful.
Winner of the 2006 Mathematical Association of America Beckenbach Book Prize
By Joshua Jordan
"Thoroughly engaging... Accessible to a very broad audience... While the theorems covered may not be new to research mathematicians, I would wager that very few of us have seen them proven in quite this way." -- American Mathematical Monthly [[...]
I am not a mathematician and I learn something cool and useful from this book every few paragraphs. Highly recommended.
34 of 37 people found the following review helpful.
Outstanding exposition
By Brian Borchers
I was introduced to this book by a talk that one of the authors (Arthur Benjamin) gave at the MAA Mathfest in Albuquerque in August of 2005. The talk was one of the very best mathematics talks that I've ever attended. Everyone in the audience could follow what was going on, and we all left with an understanding of the basic approach to combinatorial identities used in this book. The authors' approach is to prove combinatorial identities by defining a quantity and then obtaining different formulas for that quantity. One formula becomes the left hand side of an identity while another formula becomes the right hand side.
When I read the book I found that it was just as clearly written, with lots of beautiful examples.
16 of 17 people found the following review helpful.
easy to understand and full of insights
By Bennett Haselton
The proofs in this book are easy enough for a bright high schooler or even an exceptional middle schooler to understand, while still making use of insightful tricks that keep the solutions far from being obvious.
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