Acknowledgments

I would ¯rst like to thank my advisors, Tasso Kaper and Gene Wayne, for their exten-sive support and encouragement over the last several years. I would also like to thank the additional members of my committee: Arjen Doelman for his helpful suggestions and ad-visement regarding my current research, Kreso Josi¶c for guidance in my earlier research and also for preparing detailed comments on this document, and Tom Hawkins for providing me with a solid analytical foundation that has been instrumental in all aspects of my work. In addition, I have had many enlightening mathematical discussions with David Fried and Nikola Popovic during the course of my studies. I would also like to thank my friends and family for their continual support, both mathematical and otherwise, throughout the years. Finally, I would like to thank Jason Ritt, for providing everything else I needed along the way. ii