Mathematical Induction (The Good Kind)
When I arrived at UCSB as a transfer student, my concerns mostly converged on one question: will I be able to do anything in my field ever? I psyched myself out well before arriving by looking ahead to the material I would inevitably learn and the work that professional mathematicians do. In short, I found myself daunted by the complexity that I faced. Our undergraduate years are fraught with episodes of imposter syndrome, even when it has been shown repeatedly that we arrive at such a stage in our lives on merit alone, and I am no exception to feeling this way.
Upon entering the INSET-V/STEEM program, I was suddenly on the frontline of math. There was no longer any question as to whether I could do anything with my skill set in my field; it was now required of me. So what exactly was required of me? I’ll boil it down to three categories.
First, doing research on these topics requires complete mathematical fluency. You can’t shy away from analysis arguments and bury your head in the sand when scary proofs come along. I have had to prepare myself by being comfortable with deltas and epsilons as well as being able to extract every wonderful detail from research papers and advanced textbooks. But that’s expected.
Second, studying dynamical systems requires an analytic eye for detail. Any mistake in my Matlab code has disastrous consequences for the validity of the subsequent mathematical work. Having to depend on semi-empirical evidence like the graphical output of a program seems like I could manufacture whatever results I want, but the end result comes from thousands of calculations performed in just five seconds. Needless to say, thank goodness for computers. And so, it’s necessary to pay attention to any errors in the output that arises from, say, a missing comma or coefficient in the code.
Lastly, being a computational mathematician requires a vast supply of coffee. A good strong home-brewed cup is best, but an iced latte in the afternoon serves as a crucial pick-me-up after scouring through the results of dozens of nearly identical programs. Should any land on earth prove to have an endless supply of coffee beans, I may have to move there permanently.
Most importantly, though, I don’t need reassurance as an undergraduate student that my math tool set will someday be put to use, where “someday” approaches infinity. What I have done in the past weeks is the creation and betterment of mathematics, in theory and in practice. Real-world applications in this field exist in general, but my specific work might not be of any direct benefit for many years or it might directly apply right now, relevant for some climatologist in Norway or economist in New York. The STEEM branch program has been my mathematical induction.