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William Paterson University mathematics professor David Nacin has just released his second book, and this one, like his first, teaches math through puzzles.
The Group Theory Puzzle Book is both a book of more than 250 math puzzles and an introduction to group theory—the building block of abstract algebra that arises in almost every branch of mathematics and the sciences. Nacin’s is the first known book to introduce group theory through puzzles.
“No prior background is needed, as every mathematical concept is clearly explained within the book, making it ideal for anyone looking to explore new types of puzzles,” says Nacin, who also serves as director of the University’s master of science (MS) program in applied mathematics.
He created the 250-plus unique puzzles in his book, which are similar to KenKen puzzles. However, instead of using the whole numbers 1 through n in playing grids, Nacin’s puzzles use elements from the mathematical structures known as groups.
Nacin is a prolific creator of math-infused puzzles related to partition identities, the motion of chess pieces, finite groups, and other mathematical structures, with over 1,000 puzzles to his name. Nacin’s puzzles have appeared in many magazines and academic journals, and he has maintained a puzzle blog since 2016.
He also uses puzzles in class to help his students approach their learning in new ways.
“I don’t like to assign puzzles to anything that will get a grade. Puzzles should never be required since that can take some of the fun out the experience. They should always be an optional challenge,” Nacin says.
The early sections of Nacin’s new book demonstrate 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 additional 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, Nacin says.
“In a first class in group theory, students learn and prove lots of facts about groups, but they sometimes leave the course without feeling like they have any sort of hands-on understanding at all,” he explains. “I wanted to make groups less mysterious and more fun.”
“In addition, for people who already know group theory and like groups, the book is just a large collection of exciting puzzles for them,” Nacin continues.
The Group Theory Puzzle Book is available through the publisher, Springer, as well as through Amazon and other major retailers.
12/11/24
