What is applied math? Before this semester, my answer to this question would have been a resounding, "more or less physics." After the first day and seeing the results of the survey about what my peers were interested in, my answer expanded to "more or less physics or finance." Then, after a semester of attending guest lectures and senior presentations, I gained a better sense of the breath of math in explaining so many phenomenon in this world. I got to see how individual concepts such as symmetric matrices are applied to fields as diverse as cardiovascular valve movement and mate selection.

In addition to breadth of applications, I also noticed the trend that the real-world problems that each presentation explored necessitated mathematical models, at least in part, because data was extremely large. In particular I remember the first presentation about interpreting viewer behavior on Buzzfeed and a later presentation about filtering junk emails using conditional probabilities based on key words.

Based on comments and questions from other students and Professor Wiggins, I also began to question the reason behind building models. Before, I took complicated-looking formulas at face value and assumed they explained real-life based on empirical evidence. I didn't really question whether a specific model chosen to answer a specific problem was truly the best model for the particular purpose. Then, there was one class I remember in particular when the topic of cross-validation was raised. I learned that many times, the purpose of building a model is to predict, and if that is the case, then you should confirm your final model has good predictive power by using it on a set of data different from the training set. In short, I realized that there's always a method to the madness of mathematics, and figuring out this method or intention should be the first step in the problem solving process.

Thirdly I learned that complex math problems and complex formulas are, for the most part, constructed out of simpler problems and formulas. Namely, I remember one lecture about space-time and the presenters were trying to show through derivations that the four-dimensional equation could be collapsed down to three dimensions, which could then be collapsed down to two dimensions, thereby becoming more intuitive.

Fourthly, I learned that the field of applied math, like any other field, is critically dependent on effective communication. I think the style of the seminar--presentation-based rather than paper-based--really highlights the absurdity of the layman's perception of a mathematician (think Albert Einstein, scribbling away alone into a notebook with his office door closed for days on end). Nowadays, math is all about sharing ideas, debating, revising models, fixing bad assumptions, an working in teams.

Fifth, I realized how subjective math can be and that there isn’t always one right or best answer. The outputs of models depend on assumptions, which can be taken into consideration as constraints to the initial equations. For instance, for the optimal mate matching problem, when like-attracts-like was assumed, this was a very different initial problem than when opposite-attract was assumed. In that same presentation, it was mentioned that associated with each maximization problem there is a corresponding dual

minimization problem whose results are the same. This duality likewise draws attention to the importance of phrasing of questions and phrasing of constraints.

In conclusion, this essay list some of my key realizations about applied math, a subject I have come to understand better this semester after listening to several diverse presentations from my peers as well as from professionals.