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 redesigning 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 ViceChair 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 handsoff 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!


