I want to solve puzzles and resolve problems, and help others to learn how to do the same. My goal, of course, is eventually to do this as a tenured professor at a respected university. And although this will not all happen automatically, I do not feel any trepidation or hesitancy in approaching the sometimes hard work which will bring this about; it is the sort of work I would want to do, and find myself doing, anyway. It's hard for me to understand that some people do research only because it is a requirement for finishing a degree or obtaining tenure. Even in a different career, nothing would keep me from continuing to learn new mathematics, to solve problems, and even to publish. I've always spent time especially on particularly challenging problems or original research topics. (Sometimes to the exclusion of assigned homework problems, as I'm afraid has sometimes been apparent in my academic record.) It was a revelation to me to realize that this could be the basis of a career--that it is possible to earn a living merely researching and teaching in mathematics.
After completing my BS in Mathematics here at Brigham Young University, I stayed for another two years to complete a master's degree. I did this both in order to gain a solid foundation in combinatorics, algebra, analysis, and topology before starting a doctoral program, and in order to complete problems which I had already started working on with faculty here, as well as on my own. This has given me the chance to do some original research, particularly in the field of linear algebra. It has also given me the chance to be in charge of a classroom, teaching college algebra and second semester calculus. And it led to the valuable experience I had last summer of being a research mentor in the REU program in mathematics held annually at the College of William and Mary.
In another year, I could probably have turned my master's thesis into a doctoral dissertation, and perhaps I should have chosen that route, considering the semester I spent working full-time, the two years I earlier spent serving a mission in Haiti for the Church of Jesus Christ of Latter-day Saints, and the two years it has taken me to complete a master's degree. But although I've been able to solve some interesting problems in matrix analysis, there are deeper problems that I want to understand and tackle, particularly in fields relating to low-dimensional topology, and I want to take the opportunity to participate in a doctoral program at another institution before looking for a permanent teaching position. I have chosen to apply to Berkeley because of its reputation in the area of mathematics, and specifically because I would welcome the opportunity of working with such leaders in the field of low-dimensional topology as Andrew Casson, Robion Kirby, [Vaughan Jones, John Stallings,] and Nicolai Reshetikhin. (I have also heard good things about Berkeley from my brother-in-law Dean Wheeler, who is now working on a doctorate in Chemical Engineering.) I look forward to the possibility of furthering my learning and research with a group of mathematicians of great imagination and ability.