Admission Requirements
It is absolutely essential that the application for admission into the Doctor of Philosophy (PhD) program contain evidence of potential for performing original research. The minimum requirements for admission to the PhD program normally include:
- a Master's degree in a mathematics-related discipline;
- three letters of reference, normally from academic sources;
- completion of a Master's thesis;
- proof of competency in English (if applicable). A score of at least 600 (250 in the computerized version and 100 on the internet-based version) is required in the Test of English as a Foreign Language (TOEFL) and 4.0 on the TWE. See the English Language Proficiency page for other acceptable tests of English.
A student who is enrolled in the Master of Mathematics (MMath) program in this department and wishes to continue in the PhD program has to apply for admission into the program. The required evidence of research ability is typically of the kind provided by a MMath (Thesis) in which progress was made in solving a research problem; see below. In contrast, a MMath (Course Work) does not normally provide such evidence. In some circumstances a student enrolled in the MMath program may transfer to the PhD program without completing their MMath program. More information is provided below.
Degree Requirements
The requirements for the PhD degree are:
- four one-term (0.50 unit) graduate courses after the Master's degree, with a breadth requirement, or eight one-term (0.50 unit) graduate courses after the Bachelor's degree, with a breadth requirement,
- the successful completion of the PhD Comprehensive Examination,
- the PhD Lecturing Requirement,
- the presentation and defence of a PhD thesis which contains the results of original research.
PhD students are allowed to take at most one 600-level course (including similar cross-listed courses offered by other departments) for credit.
Breadth Requirement
All Doctoral students are required to take one Computation course, one Differential Equations course, and one Techniques course, from the following list:
If a PhD student has taken an equivalent course during a Master's program, this can be counted, upon approval from the graduate officer, towards completion of the breadth requirement but does not reduce the number of courses required.
The program of studies of a PhD student is directed by an Advisory Committee consisting of the research supervisor and two other faculty members who may be from outside the Applied Mathematics Department. The supervisor, who has the primary responsibility for directing a PhD student's research, must be an Approved Doctoral Dissertation Supervisor (ADDS). "ADDS" status is granted by the Mathematics Faculty Graduate Committee.
The course work of a PhD student's program is approved by the supervisor. In the spirit of the interdisciplinary nature of applied mathematics, students are encouraged to take a broad spectrum of courses which are not necessarily restricted to Applied Mathematics Departmental courses. For example, our students often take relevant courses from the Departments of Pure Mathematics, Physics, the School of Computer Science, and the various Departments in the Faculty of Engineering.
PhD Comprehensive Examination
The PhD Advisory Committee should be approved within 12 months of enrolment in the PhD program. It shall consist of the supervisor(s) and two others who will normally be in the department. This committee will ultimately be part of the PhD Examination Committee.
In the fourth term of enrolment in the program, the candidate will give a seminar of at most 30 - 45 minutes on the proposed area of research, emphasizing the background material. Shortly thereafter the Advisory Committee shall meet to decide on which areas relevant to the research the candidate will be examined and who will be responsible for each area. The candidate will be informed of the areas of examination 3 - 4 months prior to the Comprehensive Examination.
The candidate will submit a typed research proposal (normally 25 - 30 pages in length) to the Advisory Committee at least two weeks prior to the Comprehensive Examination, which will normally be taken in the fifth term of the PhD program. The proposal will contain a statement of the research problem, together with appropriate background information and motivation, references to related work in the literature, an indication of the methods that might be used to solve the problem, and any progress made to date. The examination will consist of a presentation by the candidate of the proposed resarch, 20 - 25 minutes in length, followed by two rounds of questions. The first will be on the background material and the second on the formulation of the research proposal and on the relevant research literature. Each examiner shall question the candidate for approximately 15 - 20 minutes in each round. If there is more than one supervisor, the candidate will normally be questioned by only one supervisor in each round in order not to diminish the time allotted to each questioner. The Comprehensive Examination should normally be completed in two hours.
If the Committee finds that the candidate's performance is unsatisfactory in some aspect, they will specify what further requirements the candidate has to fulfil, e.g., to resubmit the research proposal, suitably modified, to take an oral examination on a specific subject area at a later date.
The Comprehensive Examination is normally taken within the fifth term of admission to the PhD program. Students who have not satisfactorily completed this requirement by the end of the fifth term will have their progress reviewed by the Departmental Graduate Committee.
PhD Lecturing Requirement
Students normally satisfy this requirement 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 PhD 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 their field of research.
PhD Thesis Examination
It is required that a PhD thesis contain original results of a student that would warrant publication in the research literature. Indeed, candidates are encouraged to publish papers based on their research either before or after 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.
The candidate shall defend the thesis in an oral examination before an Examining Committee, which shall consist of the supervisor, two faculty members in the Department, one faculty member from outside the Department, and an external examiner familiar with the student's research field. The committee is approved by the Faculty Graduate Committee. Additional information is available on the Minimum Requirements for the PhD Degree page.
Transfer from MMath (Thesis) to PhD Program
Master's students who are excelling in their graduate work may transfer to the PhD program. To initiate a transfer the student's supervisor must submit a written request to the Graduate Officer. Names of two potential examiners should be included. The request should be accompanied by a statement of research progress to date, written by the student, approximately three pages in length. Normally transfers will be considered during the student's third or fourth term. For students who transfer in their fourth term, the transfer examination will count as their pre-comprehensive seminar, and they are expected to have their Comprehensive Examination in their fifth term. Students who transfer in their third term, can opt to have their transfer examination count as their pre-comprehensive seminar, in which case they are expected to have their Comprehensive Examination in their fourth term.
If the Graduate Officer agrees to consider the transfer, the student will be asked to give a departmental research seminar. The seminar will be attended by an examining committee, consisting of the supervisor(s), two other faculty members and the Graduate Officer. The examining committee would normally become the PhD Advisory Committee, should the requested transfer be approved. The research seminar should be approximately 40 minutes in length, with 20 minutes for questions by the examining committee and other members of the audience. For the transfer to be approved, the student must have excelled in his/her course work (normally four graduate courses) and must demonstrate outstanding research potential. In addition, the student should demonstrate good oral and written English skills. The transfer to the PhD program must be approved by both the examining committee and the Graduate Officer.
Applicants for the PhD program who hold a Master's degree from another university may, in some cases, be admitted initially into the MMath program. In such cases the Graduate Committee will decide, within three terms, whether to transfer the student into the PhD program.