Math Affinity Puzzles

Instead of treating mathematics as a collection of separate topics or isolated courses, this book highlights the patterns and relationships that appear throughout mathematics. Rather than keeping studies confined to a single field, the puzzles here look beyond boundaries and discover links among different areas of knowledge. Within the domain of mathematics, this book focuses on the fun of finding such connections through puzzles.

Math Affinity Puzzles uses analogies to explore connections between mathematical terms and concepts, where solving a puzzle requires unraveling the relationships between the mathematical ideas. Solving this kind of mathematical puzzle is thus not about assessing understanding but deepening it, making the connections, and having fun doing it.

Because there may be multiple relationships present, one answer is not claimed to be correct. Instead, which answer is best comes from one point of view. The short descriptions follow, touching on the different choices while going more deeply into historical or other aspects of the relationships.

The puzzles will deepen the reader’s understanding and appreciation of, as well as foster discussion about, the relationships among mathematical ideas.

The puzzles in this book can be enjoyed on their own or as supplements in a course setting. The authors have used them in calculus and upper-level classes as homework assignments and for in-class discussions. Students have been asked to justify the one they have chosen, offering opportunities for noncomputational critical thinking, speaking, and writing about mathematics.

Katie Ballentine is a software engineer at Guild Education. Previously, she was Director of Communications at Mathematical Sciences Publishers (MSP), and before that, she was a mathematical copy editor at MSP and Mathematical Reviews. She has taught a variety of undergraduate math classes.

Michael A. Jones is the Managing Editor and an Associate Editor at the American Mathematical Society’s Mathematical Reviews. He was a faculty member for 14 years, including as an Associate Professor in mathematics at Montclair State University, New Jersey. He served as the editor of the Mathematical Association of America’s Mathematics Magazine from 2014 to 2019. In the summers, he teaches high school students through the University of Michigan’s Michigan Mathematics and Science Scholars program. He is the author of approximately 70 research and expository articles in mathematics and its application to the social sciences.

Lon Mitchell is currently a professor at Eastern Michigan University, was previously an editor for the American Mathematical Society, and has taught for multiple gifted high-school enrichment programs, including for the University of Michigan.

Jennifer M. Wilson is an Associate Professor of Mathematics at The New School, where she has been a faculty member since 2003. She has taught most of the standard courses in the undergraduate mathematics curriculum and has published research in a variety of different journals, including Mathematics of Social Sciences, Mathematical Methods of Operations Research, the College Mathematics Journal, and Mathematics Magazine.