- #1

- 56

- 8

Since I was a kid I had great interest in science, which at the end of high school led me to decide to study chemistry. At the faculty of chemistry I discovered higher mathematics and physics and became fascinated by them. After showing some aptitude for these subjects I was encouraged by several professors to switch majors, which I did a year later. Although my actual degree is in physics, I took simultaneously many mathematics courses (I did not receive a double degree due to bureaucratic issues). From the very beginning of my studies, PDEs and calculus of variations sparked my interest; I found intriguing the idea of doing calculus in infinite dimensions. When I finally studied these subjects at a greater depth, I was far from disappointed. A feature I love about them is their broadness; they range from the very abstract and theoretical to the very applied and computational. My background in physics was very helpful to realize the applicability of partial differential equations and to gain some intuition behind the theory.

As for the theoretical side, I first took a course on basic PDEs which covered the classical theory and later learned the foundations of the modern theory when I took functional analysis. I also attended a course on variational methods, which dealt primarily with semilinear elliptic equations, and a course on control theory (for which I later became the teaching assistant). I became interested in the numerical side somewhat late in my studies and actually the first related course I attended was a graduate course on the finite element method I took as an exchange student at the YYY [it's a university in the same country]. Later I took a graduate course on methods based on radial basis functions and another on finite differences. I joined the research group of Professor X, where I worked on several small projects, but perhaps my main contribution was writing notes to make the subject accessible to advanced undergraduates and beginning graduate students (available at URL). My bachelor thesis combined both theory and numerics; in this work I studied an algorithm to find numerically ground states of a Nonlinear Schrödinger Equation, but also addressed the question of existence of such ground states using variational methods.

As a teaching assistant my main duty was to deliver tutorials and grade assignments, but I was often given lecturing responsibilities. I am grateful because the professor gave me a lot of freedom to choose how to lecture a given topic and which problems to solve at tutorials. This helped me to develop independence and gain maturity as a lecturer.

At the moment I am not in contact with any professor from the University, but I would be very interested in working with Professor A because he combines the subjects I am interested in and works on some exciting applications (e.g. shape-memory alloys); to my taste his research strikes the perfect balance between theory and application, which is something I always strive for (his paper "..." is a perfect example of this). I would also be interested in working with Professor B; his research on meshless methods and generalizations of the finite element method has caught my interest. Furthermore, I believe my background on radial basis functions would be a nice complement. With that said, there are other Professors at the department whose research appeals to me and with whom I would gladly work (e.g. Professor C).

I believe that, because of the numerous research faculty with very interesting projects in my intended area of research, XXX would be an amazing place to pursue my studies, and that, for the reasons stated above, I would be a great fit for the program. Moreover, I believe my experience as an exchange student in YYY is an advantage, because it increased my adaptability and provided first hand experience with the educational system in the country. I very much look forward to hearing from you.

Thanks in advance!