Softcover ISBN:  9781470463038 
Product Code:  MBK/146 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
eBook ISBN:  9781470472900 
Product Code:  MBK/146.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Softcover ISBN:  9781470463038 
eBook: ISBN:  9781470472900 
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 
Softcover ISBN:  9781470463038 
Product Code:  MBK/146 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
eBook ISBN:  9781470472900 
Product Code:  MBK/146.E 
List Price:  $79.00 
MAA Member Price:  $71.10 
AMS Member Price:  $63.20 
Softcover ISBN:  9781470463038 
eBook ISBN:  9781470472900 
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 

Book Details2023; 346 ppMSC: 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.
ReadershipGraduate 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 is the ultimate book on cardshuffling, "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


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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.
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 is the ultimate book on cardshuffling, "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