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Guidelines for Students Enrolled in the Ph.D. Program in Mathematics

What follows is drawn from departmental rules, regulations, and practices, and from the regulations of the School of Graduate Studies.

More details can be obtained from the Mathematics Graduate Student Advisor ( and from the regulations in Sections 1-6 of the current Graduate Calendar.

The guidelines below should explain general procedures, although they may at times be adjusted in particular cases.

All Ph.D. students must:

  • Choose a thesis supervisor and develop a research program.
  • Complete the course requirement, which is a minimum of two one-term graduate courses in Mathematics at the 700 level beyond the M.Sc. requirement.
  • Complete the comprehensive examinations requirement, which means passing a written comprehensive exam and an oral comprehensive examination.
  • Are responsible for the organization of the annual meetings of the supervisory committee and the timely submission of the written report to the department.
  • Write an acceptable thesis based on original research and present an oral defense of the thesis.

Supervisor and Supervisory Committee

Graduate students should choose a thesis supervisor by the end of the first year. (Before that time, the Mathematics Graduate Advisor will serve as provisional supervisor.) Also by the end of the first year a supervisory committee should be formed. Supervisory committees consist of the supervisor and two or three other faculty members, usually chosen from faculty in the Department of Mathematics & Statistics. The supervisory committee meets annually to evaluate the student’s progress and provide advice for further research. Before these meetings, students are asked to prepare a written report summarizing the progress made since the last meeting. After the meeting, the supervisory committee submits a written report to the Chair which is due by July. Students should read carefully Sections 2.6 and 4.5 of the Graduate Calendar about supervision


Students choose their courses in consultation with the Mathematics Graduate Advisor, their Supervisor, and/or other members of the supervisory committee. A student may be asked to take courses beyond the minimum requirement, and the minimum course requirement should be completed in the first year of study. A student who fails a prescribed graduate, prerequisite undergraduate, or required extra course, must withdraw from the university unless the Faculty Committee on Graduate Admissions and Study approves a suitable recommendation from the Department of Mathematics & Statistics.


Each Ph.D. student is expected to attend regularly the Departmental Colloquium and one of the weekly seminars in their area of interest.

Ph.D. Comprehensive Examination

The comprehensive exam consists: (a) the preliminary exam, and (b) the oral exam. The preliminary exam is offered in January and May and should be completed within eight months of entering the graduate program. Students who do not successfully complete all the comprehensive exam requirements within 16 months of entering the program may be asked to withdraw due to lack of progress.

A. Preliminary Exam.

All Ph.D. students must pass one preliminary exam, which is a written exam covering basic material that is normally taught at the undergraduate level. Preliminary exams are offered in the following three areas:

  1. Pure Mathematics
  2. Applied Mathematics
  3. Probability and Statistics

Students who do not pass the preliminary exam on their first attempt are permitted a second attempt at the same exam.

B.Oral Exam.

All Ph.D. students must pass an oral examination in the general area of their proposed research. The subject matter for the oral exam is based on a body of knowledge agreed upon by the student and his or her supervisor. Material can chosen from advanced textbooks and published papers. The examining committee consists of three faculty members, including the supervisor, who is the chair of the examining committee. All members of the examining committee must be informed of the subject matter well in advance of the exam, which should not exceed two hours. Student who do not pass the oral exam on their first attempt are permitted a second attempt at the same exam.


It is absolutely essential that a student submitting a Ph.D. thesis follows the procedures set forth in Section 2.7 and 4.4 of the Graduate Calendar. In particular, note that authorization of the supervisory committee must be obtained BEFORE preparing the final version of the thesis, and that the format of the typed thesis should be exactly as specified in the “Guide for the Preparation of Theses”, which can be obtained from the Graduate Studies Office. The thesis is submitted to Graduate Studies, which will then arrange the Oral Thesis Defense and appoint an external examiner, normally recommended by the Supervisory Committee and the Department Chair. It is important that students submit their theses by the appropriate deadline given in the Calendar in order to be able to graduate at a particular convocation.

Note also that the Oral Defense normally cannot be held between July 1 and the first Monday in September.

Part-time Students

The time limits for part-time students to pass the Comprehensive Examination or to fulfill their course requirements have been interpreted by the Graduate School to be 4/3 times the corresponding limits for full-time students.