For my senior year at F&M, I decided to do a two-semester independent study with Professor Feldman. The subject was cryptography, and although I had no previous knowledge in the topic aside from unscrambling word puzzles, I was excited to start the project. I was also interested in the subject because of its useful application in so many areas of today’s hi-tech society. After all, cryptography is a mathematical science involving the study of how to keep and transfer data securely. Starting with this basic definition, I began learning about the principles of modern cryptography. With the encouragement of Professor Feldman, it wasn’t long before I was reading theoretical proofs of definitions such as perfectly secret encryption and eventually studying the application of group rings in algebraic coding theory.
Doing research is an experience that I highly recommend for students. Fortunately, F&M makes this opportunity very accessible, whether by doing a summer Hackman scholarship or an independent study. For me, I had actually started doing research in the chemistry department as early as my first year at F&M. I quickly learned that research in a subject is very different from taking classes, and so I was eager to see this side of mathematics as well. Independent research gives you the freedom to explore new topics and study your own project while having the guidance from working one-on-one with a professor. This type of work is challenging because results hardly ever come as planned or hoped, but that’s what makes it interesting and rewarding when you do finally see results.
Although I have not continued doing research in cryptography, my independent study was one of the most valuable experiences for me at F&M. I am currently pursuing a route in applied mathematics by working full-time as an Actuarial Assistant for GEICO. While my job does not involve reading through complex theoretical proofs, it does require a strong sense of problem-solving and analytical ability. Being a math major obviously builds these skills, but the creativity involved with doing research adds a whole new level that is useful for any mathematical career path.