2018 Major: Mathematics and Computer Science
"My intention as a high school senior was to study neuroscience at Duke and become a neurosurgeon. This plan was utterly derailed by the math faculty in my very semester of college. I had a chance encounter with Prof. Kraines and Prof. Schott who both encouraged me to take linear algebra; I had also already decided to enroll in the mathematical modeling FOCUS cluster, so I ended up with three math courses in my very first semester. These classes were not easy. I had never written a proof before: in the first six weeks of linear algebra, I had no idea what was happening. In the last six weeks of linear algebra, I still had no idea what was happening. But, I muddled through the material as best I could. Simultaneously, my FOCUS classes also required me to immediately apply mathematical ideas to interesting problems in biology and neuroscience. All three of my professors were brilliant, motivated, and tough---I was a little scared of them. But, I survived the semester and immediately decided that I was going to continue as a math major. From there, I learned a wide array of mathematical ideas. However, the core of the education, namely the rigor and the ability to think at multiple levels of abstraction, are indispensable skills. No matter what I do, I always activate my mathematical education.
"I had a very broad liberal arts education at Duke, which resulted in a secondary major in computer science, study abroad in Oxford and Paris, and four years of instrumental conducting lessons, on top of courses in history, law, literature, chemistry, economics, philosophy, geology, and more. I cannot stress how valuable this allied liberal arts is. Learning different ways and modalities of thinking about the world provides more context, resources, and skills to confront professional (and, frankly, personal) problems."
"For an undergraduate degree: go broad, focus on theory courses, do research, and work hard. Breadth: even if you fall in love with a particular area of math, as an undergraduate, you should explore as many options as possible. If you really want to specialize in a certain area, this is a sign that a PhD might be a good path for you. However, you should sample as many different types of math, even if you think you'll dislike a certain topic. Theory: in your coursework, focus on theory/pure courses. My research is squarely applied math (maybe even *really* applied math), but I would not be able to do this research without a solid theory foundation. I think theory is the hardest to learn on your own and where you get the biggest benefit in taking a class. Applied classes are a lot of fun, but you will likely learn a lot more about applied math through research or an internship. Research: not all math research has to result in a Fields Medal. However, engaging in math research is an amazing way to gain some insight into current trends in math, to work closely with the brilliant math faculty, and to sharpen your mathematical skills beyond the classroom. Work Hard: perhaps very trivial or obvious advice, but I think every hour invested in the math degree is completely valuable. Even if you don't directly use a particular mathematical topic in the future, mathematical reasoning is a powerful and rare skill. However, it is not a magical or innate skill: it is something that you need to learn, which you can do by working hard. It's easy to get intimidated by your peers who seem to just "get" math more than you do, but you can be an excellent mathematician through the appropriate training. For what it's worth, the people I know who do really "get" math are the ones who work the hardest."
