Summary Description By
the time a graduate student finishes the mathematics program at Stony
Brook University, he or she is usually ready to pursue a career as a
researcher and scholar. This is accomplished by assisting the students
to specialize while encouraging them to maintain a very broad
perspective on mathematics as well as its applications. The
department's comprehensives are required written exams that test people
on basic general knowledge necessary in almost any area of mathematical
research. This basic knowledge is essential not only for students to
write a thesis but also to be able to become a part of the larger
mathematical community. After
passing them, the graduate student begins to specialize. However,
before being asked to pick a specific problem to work on, the student
is allowed time to inspect the available possibilities and choose his
or her field and thesis advisor from among these. For a period of about
a year the student is encouraged to read, understand and assimilate as
much material as he or she can in order to give him or her a better
base for making this choice and for putting it into perspective. This
perspective prepares the student not only for one particular problem,
but for a lifetime of research. Students
then take an oral exam on a major and a minor topic. The major topic
will generally be the topic of the student's thesis, while the minor
topic is chosen to provide relevant techniques and a broader
perspective. From
this point on, the student has regular meetings with his or her
advisor, to discuss progress and get advice. At the same time he or she
can ask any other faculty members for additional advice. He or she is
encouraged to attend departmental seminars and minicourses, and to
share what they have learned, with peers, in the Graduate Student
Seminar. More
advanced students are encouraged (and given money) to attend relevant
workshops, conferences and summer courses at other institutions. This
is helpful in many ways: students gain more knowledge of their field,
start the process of building a professional network, and also
experience how other institutions function. Seminars
and minicourses allow people to keep a broad view on seemingly
unrelated areas of research and to know what their colleagues'
interests are. Student seminars in particular prepare graduate students
to discuss mathematics in front of an audience. The thesis defense is
then a natural continuation of this.



Goals for Students A
fresh Stony Brook mathematics PhD should be able to conduct research
individually or in collaboration with other mathematicians, to write
readable mathematical papers, to present research at conferences, and
to teach undergraduate and graduate classes in mathematics and in
mathematicsrelated fields. He or she should have a good idea of
further directions for research and the knowledge and confidence to set
up good working relations with the others in the field. They should
also have a good idea of how a mathematician functions professionally.
In short, they should be ready to act in the more independent way
expected of a postdoc, and be well on the way to becoming as a
fullyfledged researcher and faculty member. They
should have an intimate understanding of their own specialized area,
but they should also have a general understanding of a vast array of
mathematics, so that they can spot the connections that are vital to a
research career. They
should have learned to think very precisely and without error. They
should have learned that they must seek out and fully understand the
underlying ideas behind mathematical arguments. They
should have learned how to effectively communicate mathematical ideas
to others. This is a vital skill for a researcher. It also is a vital
skill for a teacher, and a major goal of our program is to develop
highly effective teachers. Moreover it is a vital skill for any
mathematician working in industry, so our students can have a flexible
choice of careers. They
should have learned to have rigorous high standards, and to apply those
standards both in research and teaching. (There is an acute need for
people who are determined to assess new ideas in pedagogy in a rigorous
manner, and we encourage students to work with our Director of
Mathematics Education on this.)


Program Context The
Mathematics Department at Stony Brook is one of the best departments in
the country in geometry and in dynamical systems. The interrelation of
these fields with physics and biology is emphasized in our graduate
program. This past year, we had a very active seminar on mathematical
problems arising from general relativity, and we had talks in our
dynamical systems seminar on mathematical biology. During the summer,
many of the country's top theoretical physicists are at Stony Brook for
our annual Simons Workshop on Mathematics and Physics. In connection
with this workshop, we are running a daily "Physics clinic" for
graduate students in the math department. In this seminar, math
students are learning many fundamental concepts in modern theoretical
physics, including renormalization, quantization and supersymmetry.
Students wishing to establish ties with the Physics or Biology
departments are encouraged to do so. Moreover, The Mathematics
Department has just been awarded a Research Training Group grant from
the National Science Foundation in Geometry and Physics. This will
further strengthen the ties between geometry and physics, and new
curricula are being developed to enhance this.



How Do We Know? The
testing system at Stony Brook, consisting of comprehensives, an oral
exam and a thesis defense, is geared toward achieving our goals.
Questions on the comprehensives and orals frequently attempt to get to
the heart of the matter by confronting the student with specific
examples to which highly abstract theorems need to be applied. In this
way we can evaluate students' level of understanding. We
have introduced a more interactive style of teaching the intermediate
courses that are taken by students while studying for and just after
passing the orals.) Students are often asked to contribute short
lectures or to do some challenging homework problems. Students
also often participate actively in various learning seminars,
minicourses and working seminars, getting practice in presenting
material and feedback on how they are doing. Almost all final year
students give more formal talks as preparation for job interviews. Questions
during these talks and the thesis defense itself often probe as to
whether the student understands how his or her work fits into a much
broader picture. Since most of our students get good jobs, we believe
that our program is quite effective.


Unanswered Questions The
nature of mathematical research is constantly changing. New
applications are constantly being found, and opportunities for
collaboration with researchers in other fields are constantly
increasing. Many mathematical programs in the USA prepare students well
for conventional careers as researchers in pure mathematics; but they
need to assess whether they are adequately preparing students for less
conventional careers in the sciences and in industry, where
mathematicians with the proper training are increasingly in demand.
Some advisors at Stony Brook already make a special effort to ensure
that their students have the skills needed to get jobs in industry.


Contact Information Contact person: Daryl Geller Email address: daryl@math.sunysb.edu


