Building Geometrical Models for Biological Molecules

Dedication To my Father, Who is in heaven. To my Brother, through Whom all things came into being. To my Helper, Who teaches me all things. I will lift up my eyes to the mountains; From where shall my help come? My help comes from the LORD, Who made heaven and earth. Acknowledgements First, I would like to thank Dr. Daniel Dix, my thesis advisor, who has patiently guided me through this long process of completing the thesis, encouraging me through the Scripture when I felt that I could not go on any more and bearing with me in my ignorance and frustration. I recognize and thank his family for the sacrifices that they made for him to do so. Also, I am grateful to Dr. László Székely, my second reader, for being a second reader, waiting quietly without pressuring at all till I was able to hand the thesis for his reading, and his insightful suggestion and uplifting words. I would like to express special thanks to Dr. George McNulty, who has been not only the technical support, but more than that, has been a support throughout my time here in this school, even from my undergraduate time, and encouraged me to go on to graduate school. I am thankful for Dr. Anton Schep, the director of the Department of Mathematics , for his advise and guidance and help in many ways, going beyond his duty as to look for an office space for my last semester. To all the staff in the Department, I give thanks for what they have done and are doing and the care that they show to us. And many thanks to my fellow graduate students and office mates for various ways of support and kindness. I am deeply grateful for my family and the Family for their deep love, continous support, care and labor, taking part in this project for His glory. By His power through their labor, this servant was enabled to persevere. His grace was and is sufficient. May He reward and bless each one. iii And most of all, I give thanks to my Lord, my Creator, the living God for sustaining and teaching me and for His great love.