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Proofs that Really Count: The Art of Combinatorial Proof
 
Proofs that Really Count
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-88385-333-7
Product Code:  DOL/27
List Price: $58.00
MAA Member Price: $43.50
AMS Member Price: $43.50
Softcover ISBN:  978-1-4704-7259-7
Product Code:  DOL/27.S
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-61444-208-0
Product Code:  DOL/27.E
List Price: $60.00
MAA Member Price: $45.00
AMS Member Price: $45.00
Softcover ISBN:  978-1-4704-7259-7
eBook: ISBN:  978-1-61444-208-0
Product Code:  DOL/27.S.B
List Price: $125.00 $95.00
MAA Member Price: $93.75 $71.25
AMS Member Price: $93.75 $71.25
Proofs that Really Count
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Proofs that Really Count: The Art of Combinatorial Proof
MAA Press: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-88385-333-7
Product Code:  DOL/27
List Price: $58.00
MAA Member Price: $43.50
AMS Member Price: $43.50
Softcover ISBN:  978-1-4704-7259-7
Product Code:  DOL/27.S
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
eBook ISBN:  978-1-61444-208-0
Product Code:  DOL/27.E
List Price: $60.00
MAA Member Price: $45.00
AMS Member Price: $45.00
Softcover ISBN:  978-1-4704-7259-7
eBook ISBN:  978-1-61444-208-0
Product Code:  DOL/27.S.B
List Price: $125.00 $95.00
MAA Member Price: $93.75 $71.25
AMS Member Price: $93.75 $71.25
  • Book Details
     
     
    Dolciani Mathematical Expositions
    Volume: 272003; 194 pp
    Recipient 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, 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.

  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 272003; 194 pp
Recipient 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, 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.

  • 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
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