New Ph.D. Program in Applied Mathematics:

An Exemplary Element Snapshot

Department of Mathematics, University of Southern California

Description of the new Ph.D. program

The Department of Mathematics has redesigned its doctoral program in Applied Mathematics. The former program was similar to traditional Ph.D. programs in core mathematics that can be found at any major research university in the country. Students took a year of courses and then took a screening examination in real analysis. They then took another year of courses followed by a written and oral qualifying examination in two other subjects. They would begin their research only after successfully completing their qualifying exams. Moreover, this research would be carried out in the traditional way: primarly as a solitary enterprise, with only relatively minor cooperation with the student's advisor. The new program in Applied Mathematics is designed to have the students begin research much sooner in their graduate education. The program is also more compatible with the interdisciplinary flavor of the applied mathematics research that currently goes on in this department. Furthermore, it allows for a research apprenticeship, in which the student is able to make the transition from taking courses to doing original research more gradually while learning how one actually does research in applied mathematics.

The new Applied Math Ph.D. program in detail

The Applied Math Ph.D. student takes courses for the first year. At the beginning of their second year, the student takes four one hour screening exams in Real Analysis, Numerical Analysis, Probability, and Statistics. Once they have successfully completed the screening procedure, the student chooses an advisor and dissertation committee. While continuing to take courses the second year, the student begins to get involved in a research project closely supervised by his or her advisor, and, typically, that advisor's interdisciplinary and/or industrial research group. This period serves as a research apprenticeship. After another 12 to 18 months the student produces a written document in the form of a research proposal. This document contains a statement of the problem upon which the student is working, background material, a survey of the literature, proposed research, and any preliminary results or joint publications that may have been produced by the student and the advisor during the research apprenticeship period. The student then makes a formal presentation of the proposal to his or her committee and is orally examined on the material contained in the proposal. This serves as the qualifying examination. Once the qualifying exam has been passed, the student is entered into candidacy, completes the research outlined in the proposal, and produces and defends a dissertation.

Educational purpose of the new program

The primary motivations for re-designing our Ph.D. program in Applied Mathematics were to

  • Get the student involved in research at an earlier stage in his or her graduate career;
  • Expose the student to interdisciplinary and collaborative research;
  • Provide the student with a research apprenticeship in order to make the transition from taking courses to doing original research more gradual and more closely supervised;
  • Streamline the qualifying procedure;
  • Provide the student with additional opportunities to present his work in both written and oral form prior to the writing and defending of the dissertation; and
  • Adapt what is the standard way of training new researchers in the laboratory sciences and engineering to applied mathematics. Applied Mathematics is a discipline in which the way research is carried out now, in many ways, has more in common with these areas of intellectual pursuit than it does with traditional core mathematics.

  • Evidence that the new program works

    The newly designed Applied Mathematics program is just producing its first group of Ph.D.s, so it is difficult at present to provide any kind of quantitative evaluation of how well it is working. We can say, however, that both faculty and students seem pleased with the new program and that our core colleagues are considering adapting this approach to training new Ph.D.s in core mathematics.

    Reflection from a faculty member

    by Gary Rosen, Professor and Graduate Vice-Chair

    The new Ph.D. program in Applied Mathematics and, in particular, the research apprenticeship period, has afforded me the opportunity to work closely with my students and to teach them how one actually goes about doing research in mathematics. I can now do this without feeling that I am writing their dissertation for them. Also, by gradually getting them more and more involved in my interdisciplinary research program, I have been able to train them in the finer points of working as part of a team of scientists with rather diverse backgrounds with the common goal of solving a problem. They have come to appreciate the importance of, and benefits derived from, learning to speak different scientific languages and being exposed to a variety of scientific cultures and research protocols.

    Student reflections on the new program

    by Asher Shamam, Graduate Student

    Having the benefit of the perspective of a former UCLA PhD Applied Math student, I can state without reservation that the format provided at USC is superior to the hands-off approach I experienced at UCLA. Working hard, I was able to pass the 4 screening exams within my first year. Shortly thereafter, working closely with a thesis advisor who played the role of a true mentor, I was able to focus my efforts on a very specific problem. This resulted in rapid progress, so that 2.5 years into the program, and with preliminary results at hand, I can say with confidence that the light at the end of the tunnel is visible. Thank you USC!

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