Date of Completion

5-10-2016

Degree Type

Honors Thesis

Discipline

Mathematics (MATH)

First Advisor

Alissa Crans

Abstract

In choosing a topic for my thesis, I wanted to choose a topic that would be relatable to those outside of the math community without sacrificing mathematical integrity nor rigor. Thus, I chose the Rubik’s Cube to be the lens through which I sought to view Group Theory. In taking this approach, while gaining a basic appreciation for the Rubik’s Cube, we gain a better understanding of fundamental concepts like permutations, groups, commutativity, order, and generators. Even more, we apply the Cube to deeper concepts within Group Theory, namely those that revolve around the notion of a group action like orbit, stabilizer, kernel, and faithfulness. Throughout, we also make conjectures and prove certain theorems in order to enrich our understanding of these concepts and shed more light on the Cube. Overall, though I entered into this paper thinking that Group Theory would help me learn more about the Rubik’s Cube, I now believe the Rubik’s Cube is the perfect springboard by which anyone can learn more about Group Theory!

Included in

Algebra Commons

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