The PhD Comprehensive Examination Policy and Procedures
Students should be notified, in writing, of the dates and times of both their Qualifying Review and Intermediate Review at least three months in advance. Recent practice has been five months (March/April notification for August examinations).
The Qualifying Review
The Qualifying Review (QR), which consists of written examinations, must occur within one year of a student entering the PhD program. It is normally held in August. The main purpose of the QR is to ensure that the candidate has a reasonably broad general knowledge of the discipline at the honours undergraduate level before beginning work on a thesis.
The Examination Committee consists of the Head of Department or his delegate (usually the Graduate Officer) who serves as chair, the candidate's supervisor and three other persons, all of whom serve as voting members.
As soon as possible after the examinations have been graded, and normally within two weeks of writing, the Graduate Officer calls and chairs a meeting at which the performance of each student is assessed and recommendations are made. Recommendations are made in writing to the Head by the Graduate Officer who forwards the decision to the Dean of Graduate Studies, with copies to the student and the Examination Committee (including the supervisor).
All written examination scripts are kept on file by the Graduate Secretary for at least two years.
The Qualifying Review in Mathematics consists of three examinations chosen by the Supervisory Committee from the following list of subjects: algebra, analysis, combinatorics, differential equations, numerical analysis and methods, and topology. In addition to the Graduate Officer and Supervisor, the three other members of a student's Examination Committee have traditionally been those members of faculty who set the examinations which that student wrote. The outcome of each exam is pass (a grade of A or B), fail (F), or re-examination (a grade of C or D). Only one re-examination in at most two subjects is possible, and such re-examination(s) should occur no sooner than one month and no more than three months after the first examination. To pass the QR, a student must pass exams in all three subjects. In the case of failure, the student's program shall be terminated.
- Algebra: syllabus, sample exam
- Analysis: syllabus, sample exam
- Combinatorics: syllabus, sample exam 1, sample exam 2
- Differential Equations: syllabus, sample exam
- Numerical Analysis and Methods: syllabus, sample exam 1, sample exam 2
- Topology: syllabus, sample exam 1, sample exam 2
The Statistics Qualifying Review consists of two exams: theory and applications. The two possible outcomes for these exams are pass or fail. An exam is passed whenever the student obtains a grade of A. If the passing grade is not achieved in one or both exams but their average is B, the student will be given one last opportunity to rewrite the un-passed exam(s). In such a case, the exam(s) should be rewritten no sooner than one month and no more than two months (when both exams need to be rewritten) after the original date. To credit the QR, both exams must be passed; any other outcome shall result in termination of the student's program.
The Intermediate Review
The Intermediate Review (IR) is a public event that consists of a short presentation (30-45 minutes) by the candidate on a thesis topic followed by an oral examination. As the final stage of the PhD Comprehensive Exam, the IR must take place before the end of the candidate's seventh semester. It is normally held in August for students who entered the PhD program in September. The purpose of the IR is to ensure that the candidate has sufficient specialized knowledge in the area of the proposed thesis and related areas so as to make likely a high-quality PhD thesis. In the presentation, the candidate is expected to summarize work to date and to indicate directions for further research. The examination should consist of questions relevant to the presentation or related areas. Specifically, it is appropriate to ask questions not directly related to the thesis that probe the student's depth of knowledge in his/her chosen field. The candidate is expected to produce a short (2-3 pages) written synopsis of the presentation for distribution to the Examination Committee at least two weeks before the examination.
The Examination Committee is appointed by the Dean of Graduate Studies upon recommendation of the Department Head. It consists of the Head of Department or delegate (usually the Graduate Officer), the candidate's supervisor, the Dean of Graduate Studies (or delegate) and three other people. All members except the Dean of Graduate Studies are voting members. After the examiners have finished questioning the candidate, the floor is open to questions from the audience. After a reasonable period of questioning, everybody except the Examination Committee and supervisor leave the room. The Graduate Officer then chairs a meeting where a decision is made for transmission to the Head who in turn reports to the Dean of Graduate Studies. The possibilities are pass, fail, pass with distinction, or re-examination. Such re-examination must be held not less than one month and not more than six months after the first examination and at this point the only options are pass or fail and, in the event of fail, the candidate's program is immediately terminated. Only one re-examination is permitted.