For ever expanding, it allows significant room for additional

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 material 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.

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Later, I delved into Bézier curves, which are 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. Pierre Bézier 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 created the Black-Scholes formula, the
first model widely used 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 area 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 my Ph.D., 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.