Copyright c © by Charles Nguyen

I owe much to the many friends, family, and peers that have supported me both in the devel-opment of this work and the ongoing educational journey that I have undertaken over the past four years. To begin, I must thank Professor Stephen Pankavich for extending an invitation to such a great experience. Professor Pankavich has been an outstanding mentor with his guidance, patience, and genuine concern for my growth as a mathematics student. Having such a motivational profes-sor to work under during my last year as an undergraduate researcher has been my greatest honor. I would also like to recognize Robert Allen and Dustin Brewer, my undergraduate colleagues, for their support within our joint research group. Additionally, I appreciate the support and guidance received from the Center for Undergraduate Research in Mathematics, as well as, the opportunity they have provided me to present my research and meet fellow mathematics majors at the 2010 CURM Spring Research Conference. Finally, I must recognize my family and friends for their support during my time working on this project and throughout my college career. Without them, the world is a difference place