Acknowledgements

First and formost I would like to thank the Lord for giving me all the wonderful people who were there for me at some point or the other throughout this entire journey.

To name a few who I can remember right now. Appa and Amma, I would not be where I am without you both. Thank you for your constant support regardless in what state I was. It was your encouragement that got me through this.

Varsha, Anu and Viha, college life would not mean what it means without you guys. I am also grateful to all my close friends who were there to give me that one little push when I needed it the most. You have no idea how much that helped me. I love every single one of you.

I would also take this oppurtunity to thank Michelle and Anirudh, who both without second thought, extended their help in converting my thesis from a PDF to a website, even when the request was pretty last minute.

Last but not the least, I would like to thank all the math faculty, and most definitely my mentor Dr. Shailaja Sharma for providing me with the oppurtinity to pursue such a non-traditional topic, that I would have never thought possible in my Math degree. A heartfelt thanks to all of you for giving me the space that I needed; providing me with guidance; and never failing to check up on me.

Actually, I would like to give one more thanks: to you the reader. Thank you for taking the time to read this project of mine (no matter how you came upon it)