The Mathematics of Shuffling Cards

Persi Diaconis, Jason Fulman

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Paperback

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English

American Mathematical Society
28 June 2023

Discrete mathematics; Algebra; Algebraic geometry; Probability & statistics; Combinatorics & graph theory

Series: Miscellaneous Book Series

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.

By: Persi Diaconis, Jason Fulman
Imprint: American Mathematical Society
Country of Publication: United States
Dimensions: Height: 254mm, Width: 178mm,
Weight: 226g
ISBN: 9781470463038
ISBN 10: 1470463032
Series: Miscellaneous Book Series
Pages: 346
Publication Date: 28 June 2023
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Persi Diaconis, Stanford University, CA. Jason Fulman, University of Southern California, Los Angeles, CA.