To my family and friends ii ACKNOWLEDGMENTS I am grateful to my advisor, Professor Igor Markov, for all the advice and countless ideas he gave me throughout my graduate career. He provided me with many opportunities to improve my research and teaching skills, and taught me the true meaning of academic dedication and perseverance. I would like to thank all my colleagues for their helpful contributions. In particular, I would like to thank Jarrod Roy, who mentored me and gave me valuable advice during my first few years, and Myung-Chul Kim, who was my primary collaborator during my last few years. I would also like to thank all past and current students that I met in Pro-fessor Markov’s group, including Hector Garcia, Dong-Jin Lee, Johann Kne...