*By Daniel Hobbs*

After earning a master’s degree in physics and taking a high school mathematics and physics teaching job overseas in South Korea, I kept telling other people and myself that I was planning to go back to graduate school to do a PhD. One year turned into two years and eventually into twelve years. At that point in time in 2019, I was still teaching mathematics and physics albeit in Shenzhen, China, and note that over the years, I had gone on many travel adventures in various countries. The extended Chinese New Year winter holiday in 2019 was no exception, and at that time, a mathematics friend invited me to visit his university in Bangladesh. On the first day of my arrival, I found myself being asked by many ambitious engineering and science students about possibilities of doing graduate degrees in the United States. It was suddenly then that I realized I had been putting my own dream of doing PhD dissertation research on hold for far too long.

It was then that I thought long and hard about what I wanted. In truth, mathematics had always been a big passion of mine, but I particularly liked the idea of doing applied mathematics especially given its wide interdisciplinary umbrella. Doing a google search, I quickly found out about UW’s applied mathematics master’s online program. Consequently, it became my idea to join the master’s program in order to build a more recent academic record and then hopefully enter a PhD program in applied mathematics.

After being accepted into the master’s program for the Autumn 2019 entry, I was visiting family in the US and decided to visit the University of Washington Seattle campus in August before flying back to China. Although it was still the summer holiday, Professor Tom Trogdon agreed to meet with me and talked to me about some of what I could expect in the master’s program and gave me advice in general. Furthermore, I must say that the summertime weather makes for a wonderful experience when visiting the campus.

Probably around early December 2019, Near the end of the first course “Vector Calculus and Complex Variables” AMATH 501, it was particularly clear that I was thoroughly enjoying the course. In fact, I was having a lot of fun finding more than one way to solve various homework problems simply for the intellectual fun of it. Just to give an example, at one point in time, I was working on the office marker board at work on an integral problem related to one of my final homework problems. I had already solved it with the Cauchy Residue Theorem, and so, I was working on finding an alternative solution to it with only real analytic methods on the office marker board. After trying several ideas, I eventually found a way to solve it by initially manipulating a Laplace-like Transform along with a series expansion followed by a final integration using a Cauchy-Schlömilch transformation substitution (which I learned from a Hong Kong mathematics friend). In fact, a colleague saw me working on the problem. He then asked me about it, and we got into an involved discussion in which I was explaining various aspects about the problem. His final comment was that the applied mathematics program seems to have “ignited something” in me.

In general, it was my observation that the applied mathematics department had set a high standard of quality for its online program. So, when the pandemic began, the department was especially well prepared in my opinion. While taking “Introduction to Dynamical Systems and Chaos” AMATH502 in Winter 2020, I ended up temporarily staying in Vietnam while also teaching my Chinese students online during the initial epidemic that later became a pandemic. At the time, due to the unusual situation and associated difficulties, the professor of the course (AMATH502) was reasonably flexible with me. More importantly, I had the fascinating subject of dynamical systems and chaos to occupy my time thereby taking my mind off of the myriad of uncertainties caused by the epidemic morphing into a pandemic. To add to that, following my return from Vietnam to China through border crossing on March 27th, 2020, working on homework problems from “Methods for Partial Differential Equations” AMATH 503 was an excellent way to occupy some of my time during the two-week hotel quarantine.

Incidentally, while taking the courses AMATH 584 and AMATH 568 both with Professor Nathan Kutz, in addition to learning important analytical techniques and ideas, this was also a time during which I worked hard on reviving my nearly forgotten computer programming skills which were needed for many of his course assignments. So, by the time that I started taking the course “Scientific Computing” AMATH 581, I felt reasonably proficient in MATLAB. Still, debugging code can at times be frustrating, and I think Professor Eli Shlizerman said it best in making a comparison to “good wine” when essentially saying that both mathematics homework and scientific programming assignments require time to mature in the mind.

To mention some other highlights from the master’s program as part of “Advanced Methods for Ordinary Differential Equations” AMATH 568, I did a computational analysis of the driven inverted pendulum equation showing fractal aspects in the parameter space governing when it is stable. Furthermore, in AMATH 581, the course culminated in programming part a simple simulation of the Bose-Einstein condensate modeled by the Gross-Pitaevskii Equation by employing the Fast Fourier Transform technique. Finally, I also took AMATH 500 with Professor Bernard Deconinck’s section which is the Applied Partial Differential Equations Seminar in which I got to listen to various expert guest speakers give talks on their research in various applications of the field.

As for my original goal of entering a PhD program, a couple professors from the UW applied mathematics department wrote letters of recommendation for me, and I recently returned to the U.S. to enter the Mathematical Modeling PhD program at the Rochester Institute of Technology. Even more importantly, I believe UW has given me excellent preparation to continue challenging myself.