Acknowledgments

I would like to express my gratitude to the many people who have helped me through the years. First of all, I would like to thank my adviser Dr. Robert Perlis. He has always known just what to say to challenge me and make me think, and he’s been supportive and understanding during the ups and downs of my graduate studies. I’ll never forget him telling me, “There are more important things in life than math. ” I will be a better teacher and mentor to my students because of him. I would like to thank Lisa Adams and Dr. Steve Agronsky for their faith in my mathematical abilities. If not for their encouragement to “go all the way with math”, I definitely wouldn’t be here right now. My parents and sister deserve special thanks for their support throughout the years. They never doubted that I would make it this far. I am grateful for my two best friends, Anthony and Paula. They have both given selflessly of themselves, and I know we will continue to be great friends no matter where life takes us. Finally, I dedicate this dissertation to my husband Charles and my daughte