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The Unity of Combinatorics
 
Ezra Brown Virginia Polytechnic Institute and State University, Blacksburg, VA
Richard K. Guy University of Calgary, Calgary, AB, Canada
The Unity of Combinatorics
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6509-4
Product Code:  CAR/36.S
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
Sale Price: $39.00
eBook ISBN:  978-1-4704-5667-2
EPUB ISBN:  978-1-4704-6829-3
Product Code:  CAR/36.E
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
Sale Price: $39.00
Softcover ISBN:  978-1-4704-6509-4
eBook: ISBN:  978-1-4704-5667-2
Product Code:  CAR/36.S.B
List Price: $130.00 $97.50
MAA Member Price: $97.50 $73.13
AMS Member Price: $97.50 $73.13
Sale Price: $78.00 $58.50
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
The Unity of Combinatorics
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The Unity of Combinatorics
Ezra Brown Virginia Polytechnic Institute and State University, Blacksburg, VA
Richard K. Guy University of Calgary, Calgary, AB, Canada
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6509-4
Product Code:  CAR/36.S
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
Sale Price: $39.00
eBook ISBN:  978-1-4704-5667-2
EPUB ISBN:  978-1-4704-6829-3
Product Code:  CAR/36.E
List Price: $65.00
MAA Member Price: $48.75
AMS Member Price: $48.75
Sale Price: $39.00
Softcover ISBN:  978-1-4704-6509-4
eBook ISBN:  978-1-4704-5667-2
Product Code:  CAR/36.S.B
List Price: $130.00 $97.50
MAA Member Price: $97.50 $73.13
AMS Member Price: $97.50 $73.13
Sale Price: $78.00 $58.50
Please Note: Purchasing the eBook version includes access to both a PDF and EPUB version
  • Book Details
     
     
    The Carus Mathematical Monographs
    Volume: 362020; 353 pp
    MSC: Primary 05; 11; 20; 51; 52; 91; 94

    Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable.

    Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Blocks, sequences, bow ties, and worms
    • Combinatorial games
    • Fibonacci, Pascal, and Catalan
    • Catwalks, sandsteps, and Pascal pyramids
    • Unique rook circuits
    • Sums, colorings, squared squares, and packings
    • Difference sets and combinatorial designs
    • Geometric connections
    • The groups $PSL(2,7)$ and $GL(3,2)$ and why they are isomorphic
    • Incidence matrices, codes, and sphere packings
    • Kirkman’s Schoolgirls, fields, spreads, and hats
    • $(7,3,1)$ and combinatorics
    • $(7,3,1)$ and normed algebras
    • $(7,3,1)$ and matroids
    • Coin turning games and Mock Turtles
    • The $(11,5,2)$ biplane, codes, designs, and groups
    • Rick’s Tricky Six Puzzle: More than meets the eye
    • $S(5,8,24)$
    • The miracle octad generator
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 362020; 353 pp
MSC: Primary 05; 11; 20; 51; 52; 91; 94

Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable.

Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

  • Chapters
  • Introduction
  • Blocks, sequences, bow ties, and worms
  • Combinatorial games
  • Fibonacci, Pascal, and Catalan
  • Catwalks, sandsteps, and Pascal pyramids
  • Unique rook circuits
  • Sums, colorings, squared squares, and packings
  • Difference sets and combinatorial designs
  • Geometric connections
  • The groups $PSL(2,7)$ and $GL(3,2)$ and why they are isomorphic
  • Incidence matrices, codes, and sphere packings
  • Kirkman’s Schoolgirls, fields, spreads, and hats
  • $(7,3,1)$ and combinatorics
  • $(7,3,1)$ and normed algebras
  • $(7,3,1)$ and matroids
  • Coin turning games and Mock Turtles
  • The $(11,5,2)$ biplane, codes, designs, and groups
  • Rick’s Tricky Six Puzzle: More than meets the eye
  • $S(5,8,24)$
  • The miracle octad generator
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.