My Favorite Abstract Algebra Projects
I have written a couple of Abstract Algebra projects that have been particularly popular with students. The most recent project guides students through an algebraic formulation of the card game SET. There are many interesting mathematical questions one can ask about this game. The second project uses the software package GAP (Groups, Algorithms, and Programming) to investigate the transformation group of the familiar Rubik's Cube. You can access the two projects below.
Product-Free Sets and the Card Game SET
Exploring Rubik's Cube with GAP
Why are these projects successful?
I believe these projects are successful because they illustrate that Abstract Algebra is not just about clever tricks and abstract objects/properties that generalize the integers (as, I fear, too many undergraduates believe.) Rather, Abstract Algebra is a rich set of tools that allow us to define useful frameworks on a wide range of situations, making computation and problem-solving possible - even easy. By applying algebraic tools to familiar games, students see for themselves how useful and concrete Abstract Algebra really is.
Do you want to see more of my GAP projects? Click here.
Abstract Algebra Students working on the Rubik's Cube Project
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