Math Affinity Puzzles by Katie Ballentine

Math Affinity Puzzles by Katie Ballentine

Math Affinity Puzzles highlights the patterns and relationships that appear throughout mathematics. Rather than treating mathematics as a collection of separate topics or isolated courses, the puzzles here look beyond boundaries to discover links among different areas of knowledge.

The book 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.

Each puzzle is followed by a short description and further discussion, touching on the different choices while going more deeply into historical or other aspects of the relationships. In some cases, there may be multiple relationships present and the suggested answer is one of many.

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, offering opportunities for noncomputational critical thinking, speaking, and writing about mathematics. Regardless of their use, the puzzles will deepen the reader’s understanding and appreciation of the relationships among mathematical ideas.

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 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, NJ. He served as 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.

Lon Mitchell is currently an associate professor of mathematics 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.