PhD program

PhD degree requirements


  • Four graduate courses, including a breadth requirement. Candidates for the PhD degree must achieve an average grade of at least 70% in their courses. Note: students who transfer directly into the PhD program (without completing the Master's degree), must take a total of eight courses.
  • Comprehensive examination
  • PhD thesis
  • Lecturing requirement

Course restriction: Students may not count more than one graduate course that is cross-listed with an undergraduate course for credit towards their PhD degree. This restriction applies to all 600-level AMATH courses and any cross-listed courses offered by other departments. Note: students who transfer directly into the PhD program (without completing the Master's degree) may take up to two cross-listed courses.

Selection of courses: Courses are selected in consultation with the student's supervisor. Beyond the breadth requirement, there are no other constraints on course selection. We encourage students to select courses that will help them develop a broad knowledge of Mathematics and its applications: appropriate courses are often offered by other departments in the Faculties of Mathematics, Science and Engineering.

Advisory committee: The program of studies of a PhD student is directed by a PhD advisory committee consisting of the supervisor(s) and two other faculty members. This committee should be approved (by the graduate officer) within three terms of enrolment. At least one of the two other members should be from (or cross-appointed to) the Department, and it is recommended that one of the members be from outside the research group of the supervisor(s).

Pre-comprehensive seminar: During the third term of enrollment, the candidate will give a 30-minute pre-comprehensive seminar on the proposed research area, emphasizing background material. Shortly thereafter the advisory committee shall decide on the background topics that will comprise the candidate's comprehensive exam. These topics are normally chosen to extend beyond the specific research project. This material should be at the level of a 400-700 course, but need not correspond to a specific course. The list of topics (and corresponding examiners) should be submitted to the graduate coordinator not more than two weeks after the pre-comprehensive seminar. Once approved by the graduate officer, the list will be provided to the student.

Comprehensive examination: The comprehensive examination is to be completed by the end of the student’s fifth term. The candidate will prepare a written research proposal (approximately 25 pages) that will be submitted to the members of the advisory committee and the examination chair (normally the graduate officer) at least two weeks prior to the comprehensive examination. The proposal should describe the research problem, together with motivation, literature review, an indication of methodology, any progress made to date, and a research plan with timeline.

Shortly before the comprehensive examination, the examination chair (through the graduate coordinator) will consult with the advisory committee to determine whether the committee wishes the exam to proceed and, if so, whether the committee wishes to meet to discuss the questions to be asked on background material. Each committee member will provide a typeset list of questions to the graduate coordinator four business days before the exam (about 3-5 questions, which can all be answered at a whiteboard in about 15 minutes). This list of questions will be provided to the candidate one hour prior to the start of the exam. The candidate will use this time to prepare answers, with no access to outside materials.

The examination will consist of a 20 minute presentation of the proposed research followed by two rounds of questions: the first on the prepared background questions, the second on the research proposal and the relevant literature. Each examiner shall question the candidate for approximately 15 minutes in each round. If there is more than one supervisor, they will share the allotted 15 minute time-slot. The comprehensive examination should normally be completed in two hours, after which the committee will consider the student’s progress to date, the proposal, and the student’s performance in the exam. They will then make one of the following assessments: pass (possibly contingent on some further action, such as completing a specific course); re-examination on background and/or proposal; or fail. Students who have not satisfactorily completed the comprehensive examination by the end of the fifth term will have their progress reviewed by the departmental graduate committee.

PhD Thesis: A PhD thesis contains original results that warrant publication in the research literature. Indeed, candidates are encouraged to publish papers based on their research before submitting their theses. Moreover, the Department expects a PhD thesis to be a scholarly work that is broad in scope. As such, it should contain a discussion of the history of the research problem and an analysis of the relevant literature. For University guidelines on co-authored material in PhD theses please visit the Graduate Studies and Postdoctoral Affairs (GSPA) website; additional departmental guidelines apply.  

The candidate shall defend the thesis in an oral examination before an examining committee, which shall consist of at least 5 voting members (External Examiner, Supervisor(s), Internal Member (from home department), Internal-external member (external to home department) and one other member). In the case that there is more than one supervisor, the co-supervisors shall count as one voting member. The external examiner should be familiar with the student's research field. 

For submission deadlines please consult the Math Graduate Office website. PhD thesis defence requirements and external examiner criteria can be found on the Graduate Studies website

Lecturing: This requirement is normally met by teaching a one-term undergraduate course, usually at the first or second year level, under the supervision of a faculty member. Students will satisfy this requirement after completing the comprehensive examination and after obtaining experience as a teaching assistant. If the department is unable to provide the student with a suitable undergraduate course to teach, the requirement may be met by giving a series of lectures of an introductory nature concerning the student's field of research. The University's Centre for Teaching Excellence provides support for all aspects of university teaching.

For more resources for graduate students, please visit the Math Graduate Office website.