CID Summer 2005 Convening: Developing Researchers and Scholars

Topic 4: Developing a Professional Identity as a Researcher and Scholar

Stony Brook University

In the Mathematics Department's doctoral program, students are trained to become researchers and scholars, to become highly effective teachers, and to have the flexibility needed to pursue a variety of careers. This Snapshot specifically describes how the doctoral program in the Mathematics Department helps teach students to become researchers and scholars.

Making the shift from considering oneself a student to seeing oneself as an active and contributing member of the discipline is an important change in professional identity. Self-identifying as a mathematician implies active participation in a broad disciplinary community of researchers and scholars. It means embracing the identity of a steward of the discipline, responsible for the future of the field and the next generations of scholars.

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.

Tools and Resources

Graduate Student Seminar
All the speakers in this seminar were Stony Brook Mathematics graduate students.

General Relativity Seminar
Many speakers in this seminar were Stony Brook Mathematics graduate students.

Columbia-Stony Brook junior algebraic seminar
A joint seminar at which graduate students speak.

Stony Brook RTG program in Geometry and Physics
A program starting Fall 2006 to train graduate students and postdocs in geometry (broadly construed) and mathematical physics.

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 mathematics-related 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 fully-fledged 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:

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