Mathematics of Tabletop Games

Aaron Montgomery received his B.A. in Mathematics from Pomona College and his Ph.D. in Mathematics from the University of Wisconsin-Madison. He is currently employed by Central Washington University, where he teaches in the Mathematics Department and the Douglas Honors College. He has taught various traditional courses in mathematics, mathematics education, and computer programming. He has also taught special topics courses such as Games and Politics and The Mathematics of Recreational Boardgames. He is an omnigamer whose favorites include Arkham Horror: The Card Game, Undaunted: Stalingrad, Mage Knight, and the Soulsborne video games from FromSoftware.

“A seminal and groundbreaking study that will of be particular interest to gamers wanting an introduction to the mathematics behind their gaming pastime pursuits, "Mathematics of Tabletop Games" by mathematician and educator Aaron Montgomery is especially and unreservedly recommended for personal, professional, and college/university library Recreational Mathematics collections.”—Midwest Book Review“This book undoubtedly fits into recreational mathematics, as it combines gaming with topics such as combinatorics, graph theory, group theory, logic, probability, and number theory. The mathematics presented is straightforward and accessible to undergraduates. Besides learning about games that have a mathematical flair, I found the main draw of the book to be that it offers unique examples to use in courses that cover any of the aforementioned topics. A motivated undergraduate could use this for an independent study or even spark a project exploring the mathematics behind their favorite games.”—Notices of the American Mathematical Society“Don’t be intimidated: the book is surprisingly accessible. Aaron Montgomery guides the reader with clarity, starting from the basics and never taking anything for granted, nor requiring prior knowledge.The game chosen as an example in each case is introduced just enough to follow the references, and every mathematical concept is explained patiently, step by step. Credit also goes to smart editorial choices: short paragraphs, summary diagrams, and tables that condense key points, making the reading pleasant and straightforward.”—Volpe Giocosa, boardgamegeek.com

• 1. Combinatorics. 2. Geometry. 3. Group Theory. 4. Graph Theory. 5. Probability. 6. Game Theory. 7. Auctions. 8. Logic. 9. Number Theory.