SoftcoverISBN:  9781470472597 
Product Code:  DOL/27.S 
List Price:  $58.00 
MAA Member Price:  $43.50 
AMS Member Price:  $43.50 
eBookISBN:  9781614442080 
Product Code:  DOL/27.E 
List Price:  $58.00 
MAA Member Price:  $43.50 
AMS Member Price:  $43.50 
SoftcoverISBN:  9781470472597 
eBookISBN:  9781614442080 
Product Code:  DOL/27.S.B 
List Price:  $116.00$87.00 
MAA Member Price:  $87.00$65.25 
AMS Member Price:  $87.00$65.25 
Softcover ISBN:  9781470472597 
Product Code:  DOL/27.S 
List Price:  $58.00 
MAA Member Price:  $43.50 
AMS Member Price:  $43.50 
eBook ISBN:  9781614442080 
Product Code:  DOL/27.E 
List Price:  $58.00 
MAA Member Price:  $43.50 
AMS Member Price:  $43.50 
Softcover ISBN:  9781470472597 
eBookISBN:  9781614442080 
Product Code:  DOL/27.S.B 
List Price:  $116.00$87.00 
MAA Member Price:  $87.00$65.25 
AMS Member Price:  $87.00$65.25 

Book DetailsDolciani Mathematical ExpositionsVolume: 27; 2003; 194 ppRecipient of the Mathematical Association of America's Beckenbach Book Prize in 2006!
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, awardwinning 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.

Table of Contents

Chapters

Chapter 1. Fibonacci Identities

Chapter 2. Gibonacci and Lucas Identities

Chapter 3. Linear Recurrences

Chapter 4. Continued Fractions

Chapter 5. Binomial Identities

Chapter 6. Alternating Sign Binomial Identities

Chapter 7. Harmonic and Stirling Number Identities

Chapter 8. Number Theory

Chapter 9. Advanced Fibonacci & Lucas Identities


Additional Material

Reviews

'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


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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, awardwinning 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.

Chapters

Chapter 1. Fibonacci Identities

Chapter 2. Gibonacci and Lucas Identities

Chapter 3. Linear Recurrences

Chapter 4. Continued Fractions

Chapter 5. Binomial Identities

Chapter 6. Alternating Sign Binomial Identities

Chapter 7. Harmonic and Stirling Number Identities

Chapter 8. Number Theory

Chapter 9. Advanced Fibonacci & Lucas Identities

'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