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The Mathematics of Shuffling Cards
 
Persi Diaconis :  Stanford University, Stanford, CA
Jason Fulman :  University of Southern California, Los Angeles, CA
Softcover ISBN:  978-1-4704-6303-8
Product Code:  MBK/146
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-7290-0
Product Code:  MBK/146.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
Softcover ISBN:  978-1-4704-6303-8
eBook: ISBN:  978-1-4704-7290-0
Product Code:  MBK/146.B
List Price: $158.00 $118.50
MAA Member Price: $142.20 $106.65
AMS Member Price: $126.40 $94.80
Add to cart
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The Mathematics of Shuffling Cards
Persi Diaconis :  Stanford University, Stanford, CA
Jason Fulman :  University of Southern California, Los Angeles, CA
Softcover ISBN:  978-1-4704-6303-8
Product Code:  MBK/146
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
eBook ISBN:  978-1-4704-7290-0
Product Code:  MBK/146.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $63.20
Softcover ISBN:  978-1-4704-6303-8
eBook ISBN:  978-1-4704-7290-0
Product Code:  MBK/146.B
List Price: $158.00 $118.50
MAA Member Price: $142.20 $106.65
AMS Member Price: $126.40 $94.80
Add to cart
  • Book Details
     
     
    2023; 346 pp
    MSC: Primary 05; 60

    2023 CHOICE Outstanding Academic Title

    This book gives a lively development of the mathematics needed to answer the question, “How many times should a deck of cards be shuffled to mix it up?” The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table.

    The mathematics ranges from probability (Markov chains) to combinatorics (symmetric function theory) to algebra (Hopf algebras). There are applications to magic tricks and gambling along with a careful comparison of the mathematics to the results of real people shuffling real cards. The book explores links between shuffling and higher mathematics—Lie theory, algebraic topology, the geometry of hyperplane arrangements, stochastic calculus, number theory, and more. It offers a useful springboard for seeing how probability theory is applied and leads to many corners of advanced mathematics.

    The book can serve as a text for an upper division course in mathematics, statistics, or computer science departments and will be appreciated by graduate students and researchers in mathematics, statistics, and computer science, as well as magicians and people with a strong background in mathematics who are interested in games that use playing cards.
    Readership

    Graduate students and researchers interested in applications of mathematics to card shuffling.
  • Table of Contents
     
     
    • Chapters
    • Shuffling cards: An introduction
    • Practice and history of shuffling cards
    • Convergence rates for riffle shuffles
    • Features
    • Eigenvectors and Hopf algebras
    • Shuffling and carries
    • Different models for riffle shuffling
    • Move to front shuffling and variations
    • Shuffling and geometry
    • Shuffling and algebraic topology
    • Type B shuffles and shelf shuffling machines
    • Descent algebras, $P$-partitions, and quasisymmetric functions
    • Overhand shuffling
    • “Smoosh” shuffle
    • How to shuffle perfectly (randomly)
    • Applications to magic tricks, traffic merging, and statistics
    • Shuffling and multiple zeta values
  • Additional Material
     
     
  • Reviews
     
     

    • This book can be considered a life’s work by two outstanding mathematicians...Anyone looking for an exciting introduction to the world of mathematics of card shuffling will find it in this book by Diaconis and Fulman.
      Dominik Schmid, Semesterberichte (translated from German)

    • This is the ultimate book on card-shuffling, "a report on two lifetimes' work."...What is astonishing is the sheer bulk of connections to all kinds of mathematics beyond combinatorics and probability, from "carries" in ordinary addition to algebraic topology, hyperplane arrangements, Hopf algebras, and using shuffling to prove a theorem about zeta values.
      Mathematics Magazine

    • . . . this book is a great resource for those with a strong background in mathematics who are interested in the deeper mechanics of the familiar card shuffle.
      Tricia Muldoon Brown, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
2023; 346 pp
MSC: Primary 05; 60

2023 CHOICE Outstanding Academic Title

This book gives a lively development of the mathematics needed to answer the question, “How many times should a deck of cards be shuffled to mix it up?” The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table.

The mathematics ranges from probability (Markov chains) to combinatorics (symmetric function theory) to algebra (Hopf algebras). There are applications to magic tricks and gambling along with a careful comparison of the mathematics to the results of real people shuffling real cards. The book explores links between shuffling and higher mathematics—Lie theory, algebraic topology, the geometry of hyperplane arrangements, stochastic calculus, number theory, and more. It offers a useful springboard for seeing how probability theory is applied and leads to many corners of advanced mathematics.

The book can serve as a text for an upper division course in mathematics, statistics, or computer science departments and will be appreciated by graduate students and researchers in mathematics, statistics, and computer science, as well as magicians and people with a strong background in mathematics who are interested in games that use playing cards.
Readership

Graduate students and researchers interested in applications of mathematics to card shuffling.
  • Chapters
  • Shuffling cards: An introduction
  • Practice and history of shuffling cards
  • Convergence rates for riffle shuffles
  • Features
  • Eigenvectors and Hopf algebras
  • Shuffling and carries
  • Different models for riffle shuffling
  • Move to front shuffling and variations
  • Shuffling and geometry
  • Shuffling and algebraic topology
  • Type B shuffles and shelf shuffling machines
  • Descent algebras, $P$-partitions, and quasisymmetric functions
  • Overhand shuffling
  • “Smoosh” shuffle
  • How to shuffle perfectly (randomly)
  • Applications to magic tricks, traffic merging, and statistics
  • Shuffling and multiple zeta values

  • This book can be considered a life’s work by two outstanding mathematicians...Anyone looking for an exciting introduction to the world of mathematics of card shuffling will find it in this book by Diaconis and Fulman.
    Dominik Schmid, Semesterberichte (translated from German)

  • This is the ultimate book on card-shuffling, "a report on two lifetimes' work."...What is astonishing is the sheer bulk of connections to all kinds of mathematics beyond combinatorics and probability, from "carries" in ordinary addition to algebraic topology, hyperplane arrangements, Hopf algebras, and using shuffling to prove a theorem about zeta values.
    Mathematics Magazine

  • . . . this book is a great resource for those with a strong background in mathematics who are interested in the deeper mechanics of the familiar card shuffle.
    Tricia Muldoon Brown, MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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