The Group Theory Puzzle Book

This book introduces readers to key concepts in group theory through engaging puzzles. The early sections of the book show how the rules of group theory emerge naturally from solving puzzles. Different classes of groups, such as cyclic, dihedral and permutation groups are introduced, accompanied by numerous puzzles to facilitate the understanding of the underlying group structures. Later chapters explain how further group theory principles can be applied to puzzle-solving.

This book is intended as a highly motivating supplementary text for an undergraduate abstract algebra course. It is also ideal for anyone seeking a fun, hands-on approach to learning group theory. Additionally, the book’s many puzzles will be enjoyable for readers already familiar with group theory.

David Nacin is a professor of mathematics at William Paterson University, where he also serves as director of the M.S. in Applied Mathematics graduate program. He received his Ph.D. from Rutgers University in 2005. His research interests include non-commutative algebra, discrete mathematics, and recreational mathematics. He enjoys designing and studying puzzles related to partition identities, the motion of chess pieces, finite groups, and other mathematical structures. Author of the book Math-Infused Sudoku, published by the American Mathematical Society in 2019, his mathematical puzzles have appeared in many magazines and academic journals. Since 2016, he has maintained a puzzle blog at quadratablog.blogspot.com.