Getting started in mathematical research.
One of the best things about attending Franklin & Marshall College was the opportunity to do research with well renowned faculty. As early as the end of my freshman year, as a potential Math Major, I had started research in the Earth and Environment department with Drs. Dorothy Merritts and Robert Walter on a project studying Milldam erosion in the Susquehanna watershed. Later in my college career, taking full advantage of a Liberal Arts setting, I was also able to work with Dr. Eigen in the Sociology department looking at the history of the insanity plea at the Old Bailey. Starting junior year, I was able to do a directed reading with Dr. Nimershiem on the fundamental concepts of topology, which culminated with a small project connecting topology to analysis. While very similar to a topology class, the thing that I got most from this experience was how to perfect my mathematical proof writing. Dr. Nimershiem was extremely patient and helped me transition into writing proofs. With Dr. Crannell, I was able to go further from the "normal", with a project on Godel's incompleteness theorem that ended with my writing an expository paper about Godel's research. Both these junior year experiences expanded and perfected my ability to express myself mathematically.
What I did in my research experience.
By senior year, I had pretty much decided that I was in love with mathematical analysis and wanted to explore diverse subjects within it. Once again, I was able to find two stimulating projects with two different professors who let me excel in diverse ways. Dr. Gethner introduced me to the idea of looking at successive derivatives of a certain class of differentiable functions and let me run with the idea. At times when I would lose track, or even lose interest, he was very quick and eloquent at guiding me into the right direction. Dr. Crannell guided me through the theory of dynamical systems, and cleverly when I wasn't expecting it, showed me a problem that had been solved by using a measure-theoretic approach but not a topological approach. When I inquired about connecting these approaches, she let me discover by myself the wonder of quasi-continuous functions and how their theory could be used to solve this problem in a topological setting. She guided me all the way through this completely new theory I had never seen before, and the project ended with my going for Honors. I have to say, with the preparation Dr. Crannell and my entire honors committee gave me through the process, the defense was the most rewarding experience of my senior year.
What I'm doing now.
I received my Ph.D. in Applied Mathematics & Statistics, and Scientific Computation from the University of Maryland, and am currently an assistant professor of Civil Engineering at Johns Hopkins University. My research now uses optimization, game theory, and probabilistic techniques to study large-scale systems. Such systems arise when modeling problems in energy and environmental markets, transportation, and public health. I also model engineering design and develop novel algorithms along with supporting mathematical theory.
As a mathematics grad student at the University of Maryland, I was comfortable interacting with professors since through my research at F&M I had one-on-one interaction with professors. Many of my fellow grad students had never had this experience; however, I was already comfortable being proactive and inquiring about research opportunities. The graduate professors that I worked with quickly realized that I had been trained in the methods of research and methods of writing. I was able to start two different projects within my first year, and one of them was outside the math department. At the end of my first year, I presented a poster on one of the projects I was working on.
While Franklin & Marshall College gave me many other experiences and memories that I cherish, working closely with professors on research projects was one of my most memorable and rewarding experiences. I am indebted to the faculty for that, and I hope many other students take advantage of this wonderful opportunity.