Honors Senior Theses/Projects

Date of Award

6-1-2016

Department

Honors Program

Faculty Advisor

Michael Ward,

Honors Program Director

Gavin Keulks

Abstract

My area of research focuses on a _eld in mathematics called group theory. More speci_cally I will look at commutativity of pairs of elements in particular groups and the probabilities associated with them. My thesis will have both general and speci_c sections. This will allow me to generalize commutativity and more importantly, the probability associated with commuting pairs, before applying those generalizations to speci_c groups. Two groups will be focused on primarily, namely the dihedral groups and the matrix group GL(2; Zp). My hope is that my work will be presented in a manner that allows mathematicians to obtain a better understanding of the theory involved. I will represent the theory with mathematical proof, both adapted from other papers and original ones as well. I enjoyed studying group theory previously and am looking forward to diving deeper into its application.

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