Magical Mathematics reveals the secrets of fun-to-perform card tricks―and the profound mathematical ideas behind them―that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge.
Diaconis and Graham tell the stories―and reveal the best tricks―of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick―and much more.

Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks

Humor & Entertainment

Persi Diaconis

Ron Graham

Puzzles & Games

Princeton University Press

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.

The Mathematics of Shuffling Cards

Science & Math

Jason Fulman

Mathematics

American Mathematical Society

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Books by Persi Diaconis