## For the subject to be very satisfying.

For as long as I can remember, I have been captivated

by the mathematical sciences and, after discovering I had a natural talent for

the subject, promptly chose mathematics as a career. I love learning about the

history and evolution of such an important aspect of life. I find tutoring and

helping others with the subject to be very satisfying. Mathematics is a perpetually

intriguing subject to me and, as the discipline is ever expanding, it allows

significant room for additional study and research.

During my bachelor’s degree, I researched two topics

that I presented to the Mathematics Department at Alcorn State University. First,

I looked into the fascinating concept of the Golden Ratio, a special number that

approximately equates to 1.618. The Golden Ratio is used to describe the unique

scenario between two lengths when the ratio of the shorter length to the longer

length equals the ratio of the longer length to the sum of both lengths.

Later, I delved into Bézier curves, parametric curves

that are described by polynomials based on control points. A Bézier curve can

be thought of as a single function f: if given a number, then it returns a

point. Engineer Pierre Bézier widely publicized these curves in 1962 and used

them to design automobile bodies at Renault.

One of my research interests is the mathematics of the

stock market. The foundation for the area of mathematical finance was presented

in 1952 with Harry Markovitz’s Ph.D. thesis “Portfolio Selection”. In 1969, stochastic

calculus was introduced to mathematical finance by Robert Merton. Fischer Black

and Myron Scholes developed the Black-Scholes formula, the first widely

used model for option pricing, and published it in their 1973 article, “The

Pricing of Options and Corporate Liabilities”. The study of finance is

compelling in that it draws from many other mathematical disciplines such as probability

and partial differential equations to derive relationships between interest

rates, asset prices, and market movements.

I enjoy learning about new areas of study and applying

my experience from one field into another. I truly believe that one’s academic

and research interests should be pliable, as research areas tend to grow and

change rapidly. After eventually finishing PhD, my goal is to become a

professor at a research university. I look forward to a life of active

mathematical research, one in which I hope Simon Fraser University can play a vital

role.