ChapterZero

You know how sometimes you write something, and it develops from an utter piece of crap into something that you’re actually proud of, an almost perfect expression of what you intended to say? I just had one of those moments, writing my personal statement for the NSF Graduate Research Fellowship. Here it:

The major impetuses for my decision to pursue an advanced degree in mathematics are my pleasure in working with mathematics, and my desire to elicit the same sense of wonder in others. Consequently, my career objective is to become a math professor. An NSF Graduate Research Fellowship would assist me in surmounting the financial obstacles I will encounter in pursuing this objective.

I have always felt an affinity for math, but I was initially more fascinated by the physical sciences and their applications. It was in high school that I realized there was deeper content to mathematics than arithmetic and symbol manipulation— the determinant raised puzzling questions: why is it defined in such a strange way, and why is it connected to the solvability of systems of equations? In the same vein, why does Descartes’ rule of signs work? These were my first memorable encounters with non-intuitive mathematical results (pi excluded).

In my junior year of high school, I became fascinated with neural networks; I enrolled in college, majoring in electrical engineering, to follow that interest. In my first two semesters, I took calculus courses taught by Dr. Johnson, who invited a couple of students to take a Special Problems course on Fractional Derivatives. We never got around to discussing them, but that course served as my initiation to higher mathematics: I learned why proofs are useful and necessary, and how to construct them, as well as the basics of analysis. At the same time, I got a feel for the internal motivations that drive a lot of mathematical research; before this it seemed to me that all the interesting mathematical questions had been addressed already. But even within the microcosm of our classroom, I saw that every significant discovery or definition opens up new panoramas of challenging questions.

The course was taught using the Moore style, in which the professor provides definitions, propositions, and occasional motivating comments, while the students provide proofs or refutations of the propositions, and critique each other’s proofs. For some time, I thought this was the optimal method of learning mathematics—so much so that I took 2 other courses taught in the same style, also by Dr. Johnson. Inevitably, I found that the Moore style is definitely not suitable for teaching every mathematics course– for one, it is virtually impossible to cover a sizable amount of material– but it was the fun I had puzzling over and defending proofs in these classes that motivated me to continue taking math courses past the requirements for my engineering degree.

In the summer of my sophomore year, I obtained an internship with the Adaptive Optics group at Lawrence Livermore National Laboratories. I took full advantage of my access to the LLNL library, and in the process of reading background material for my project, I discovered the world of image processing. I was thrilled to learn of this part of the electrical engineering spectrum, and I decided to focus on signal processing. On returning from California, I signed up for an EE analysis course dealing with the Fourier and Laplace transforms. The material was exciting, but I desired a more comprehensive, theoretical development of the mathematical tools we used. The next semester, I took the new “Mathematics of Signal Representation” course being offered in the mathematics department. In that course, I learned the mathematical principles— inner product spaces, Hilbert spaces, orthonormal bases with infinite elements, generalized Fourier series, and so forth– that underlie Fourier analysis. The most titillating classes were those in which the professor detailed the historical developments that culminated in modern harmonic analysis, or placed his research projects in the context of the material we were studying in class. For me, that was motivational material! Dr. Papadakis, the professor teaching the course, recognized my interest, and that summer, recommended I attend the Wavelets and Matrix Theory REU being conducted at Texas A&M University by Dr. David Larson.

The Wavelets REU consisted of two parts: in the first, we attended two three-hour seminars weekly, where we learned the basics of operator theory, sampling and frame theory, and Hilbert spaces. In the second, we continued to attend the seminars while working on our research projects. The material I learned that summer was fascinating, the problems were challenging, and I had fun working with people who felt the same degree of enthusiasm about the mathematics we were doing as I did. While at A&M I read two engaging books of essays by Gian-Carlo Rota: Discrete Thoughts and Indiscrete Thoughts; his discussion of the New Math and New New Math systems and the declining efficacy of the modern educational system in the former motivated me to seriously consider becoming a mathematics professor.

It was over the course of this summer that I made the decision to pursue a graduate degree in mathematics, with the goal of becoming a mathematics professor. This decision has only been reinforced by the research I’ve conducted and the mathematics I’ve learned since returning to my home university. Observing Johnson, Papadakis, Larson, and my other professors, I have seen how rewarding it is to work in the field you love while sharing your delight with students. At the same time, as a professor, I will have a unique opportunity to enhance the scientific, and in particular, mathematical, understanding of younger generations. I believe this is vital not only to ensure continued public understanding of the importance of mathematical research, but also to inspire future generations of mathematicians, engineers, and scientists. It was my professors who nurtured a lifelong interest in mathematics within me, and I’d like to do the same for other students.

I wanted to put a section in there about how I want to write really badly (please interpret that in the way I intended!), but I couldn’t think of any non-cheesy way to develop that within the two page limit. But I do… want to write really badly, that is. Just about every time I pick up or put down a well-written expository book, whether on science or math, I get bit by that bug.

This entry was posted on Thursday, November 3rd, 2005 at 2:15 pm and is filed under General. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.