Have you ever played the addictive card game SET? Have you ever wondered about the connections between games and mathematics? If the answer to either question is "yes," then The Joy of SET is the book for you! The Joy of SET takes readers on a fascinating journey into this seemingly simple card game and reveals its surprisingly deep and diverse mathematical dimensions. Absolutely no mathematical background is necessary to enjoy this book—all you need is a sense of curiosity and adventure!
Originally invented in 1974 by Marsha Falco and officially released in 1991, SET has gained a widespread, loyal following. SET's eighty-one cards consist of one, two, or three symbols of different shapes (diamond, oval, squiggle), shadings (solid, striped, open), and colors (green, purple, red). In order to win, players must identify “sets” of three cards for which each characteristic is the same—or different—on all the cards. SET’s strategic and unique design opens connections to a plethora of mathematical disciplines, including geometry, modular arithmetic, combinatorics, probability, linear algebra, and computer simulations. The Joy of SET looks at these areas as well as avenues for further mathematical exploration. As the authors show, the relationship between SET and mathematics runs in both directions—playing this game has generated new mathematics, and the math has led to new questions about the game itself.
The first book devoted to the mathematics of one of today’s most popular card games, The Joy of SET will entertain and enlighten the game enthusiast in all of us.
Liz McMahon and Gary Gordon are professors of mathematics at Lafayette College. Hannah Gordon is a SET Grand Master and is studying health and nutrition. Rebecca Gordon teaches mathematics at Newark Academy. As a family, the coauthors have played SET together for more than twenty years.
"[A] model of mathematical exposition. The quality of writing is consistently high: clear but not condescending, humorous, chatty, and a genuine pleasure to read. . . . I doubt it will be very long before I find something from [The Joy of SET] to use in one of my classes."--Mark Hunacek, MAA Reviews
"[The Joy of SET] shows how budding interest in mathematics can be fostered and developed. . . . If [middle and high school teachers] ever try to enliven their classes or just interaction with curious students, this book is one they may depend on."--Alexander Bogomolny, Cut the Knot blog
"[A]mazing. . . . What I love about The Joy of SET is that it is written in such a way that it can be read and enjoyed by both SET enthusiasts and someone that has never played SET before. . . . Really and truly, there is enough math in this book to keep you busy for a lifetime! . . . I definitely recommend this book."--Sarah Carter, Math Equals Love blog
"[The Joy of SET] takes readers on a fascinating journey into this seemingly simple card game. . . . The book is in my view just the right way to talk about math as fun, and intellectually challenging."--Robert Harington, Scholarly Kitchen
"[A]s the authors convincingly demonstrate . . . the mathematics behind SET actually goes very deep. . . . [The Joy of SET] would make a fantastic resource for a middle school, high school, or undergraduate math club."--Brent Yorgey, Math Less Traveled blog
"This book, written by a mathematically inclined family, is the first and only work to explore the connection between the game and mathematics. . . . [The Joy of SET] will attract those who play SET and those who want to explore mathematically related subjects."--Choice
Table of Contents:
1 SET and You 1
2 Counting Fun! 27
3 Probability! 52
4 SET and Modular Arithmetic 72
5 SET and Geometry 98
Interlude: How to Improve at SET 136
6 More Combinatorics 149
7 Probability and Statistics 171
8 Vectors and Linear Algebra 197
9 Affine Geometry Plus 229
10 Computing and Simulations 256
Solutions to Exercises 289