Department of Mathematics
Each student must prepare for and successfully pass a topics examination on an advanced subject. A graduate student initiates the examination process in conjunction with a willing faculty member, called a topics advisor . The faculty member determines the scope of the examination and the reading list in consultation with the student, and they agree on the date by which the examination will take place. An advanced topic is one that goes beyond the scope of the basic graduate courses in a single subject or area. The reading list should normally include:
- some portion of a text or monograph, and
- one or two research papers, depending on length or difficulty.
The reading list should be designed so that it can be completed in a reading period of three to four months. Preparation by the student is expected to be a fairly independent process; consultation with the topics advisor is expected occasionally, not regularly. The preparation for this examination is not supposed to substitute for the regular coursework that is expected of the students.
The topics examination is administered by the topics committee, which consists of the topics advisor and two other faculty members, who will have been invited to join the committee by the advisor. The examination itself may be attended by mathmatics faculty members only, and consists of two parts. First, there is a 45 minute presentation based on a research paper from the reading list. The subject of the presentation will have been determined during the reading period by the student and the topics advisor. Then there is a period of questions by the committee of three for the student on topics closely related to the reading list, which will last not more than 45 minutes. After the questioning, the committee will consult briefly in private and vote to determine whether the student has passed. The results of the decision are then recorded in the Department records.
Students are encouraged to talk with faculty during the first semester of their second year to discuss possible subjects of the topics examination. The student is normally expected to pass the topics examination before the end of the second year of study at Brown. In any case, the student must take the examination before November 15 of the third year. In case of failure at the first attempt, the student's second and last attempt must be made before February 15 of the third year of study.
A faculty member may be the topics advisor to any graduate student. The topics advisor is, however, not presupposed to be the eventual thesis advisor, and the reading topic is not necessarily the topic of the student's eventual dissertation, although either of these may become the case. A student retaking the topics examination may select a different subject with a new topics advisor.