Learning Permutation Group Theory via Puzzles
Learning Permutation Group Theory via Puzzles
John O. Kiltinen
Abstract of article: This article describes the author's use of computerized puzzles for helping students gain a deeper understanding of the theory of permutation groups in his abstract algebra course. The software, which he has developed using a cross-platform (Macintosh and Windows) development tool called MetaCard, presents several puzzles to the student that require aspects of group theory (such as commutators and conjugates) to obtain a solution. The puzzles range from a simple one that creates an environment for exploring transpositions to several very challenging ones that are modeled after commercial physical puzzles. All of the puzzles are two-dimensional for ease in understanding and to avoid orientation issues such as those that arise with Rubik's Cube. The article describes the puzzles and their computerized implementation, outlines the mathematical ideas that they illuminate, and describes the use the author has made of them in teaching his introductory undergraduate abstract algebra course.
About the author: John O. Kiltinen, Professor of Mathematics at Northern Michigan University, earned his Ph.D. in topological algebra at Duke University in 1967, and then taught four years at the University of Minnesota. He was a Fulbright lecturer at the University of Joensuu and a visiting professor at the Tampere University of Technology in 1978-79. As the first acting director of NMU's Glenn T. Seaborg Center for Teaching and Learning Science and Mathematics, he directed the Michigan Mathematics Early Placement Test, and several other grant-funded projects. His research has been in the areas of topological and pure algebra.
Software used: MetaCard
Files to download: Below are demonstration versions of one of the puzzles discussed in this article. Choose the platform of your choice. The files are approximately 1.5 Mb and 2.5 Mb (Windows and Macintosh, respectively) in size as downloads.
Other links: Project's home page.