I first enrolled in UAB in the fall of 2005 as a mechanical engineering major. I soon took up a double major in mathematics, being selected to enter the Fast-Track Mathematics Program, an accelerated five-year Masterís program. In this program, I studied one-on-one with Dr. James Ward over the course of two years in small research projects in the areas of differential equations, dynamical systems, bifurcation theory, and topological degree theory. In the spring of 2008, my last year as an undergraduate, I began a more intense study which culminated in this expository paper. I am most grateful to Dr. Ward for all the help he was in the process of writing this paper and answering my many questions. Send Email

Faculty Sponsor: James Ward, Professor of Mathematics, University of Alabama at Birmingham