Doctor of Philosophy (PhD) in Applied Mathematics

The program information below was valid for the spring 2017 term (May 1, 2017 - August 31, 2017). This is the archived version; the most up-to-date program information is available through the current Graduate Studies Academic Calendar.

The Graduate Studies Academic Calendar is updated 3 times per year, at the start of each academic term (January 1, May 1, September 1). Graduate Studies Academic Calendars from previous terms can be found in the archives.

• Admit term(s) 
  • Fall
  • Winter
  • Spring
• Delivery mode 
  • On-campus
• Program type 
  • Doctoral
  • Research
• Registration option(s) 
  • Full-time
  • Part-time
• Study option(s) 
  • Thesis

• Minimum requirements 
  • Minimum grade point average: 78% or its equivalent.
  • It is absolutely essential that the application for admission into the program contain evidence of potential for performing original research. This should be provided by successful completion of a Master’s thesis in a mathematics-related discipline.
  • In some circumstances a student enrolled in the MMath program (thesis) in Applied Mathematics may transfer to the PhD program without completing their MMath program.
• Application materials 
  • Résumé
  • Supplementary information form
  • Transcript(s)
• References 
  • Number of references:  3
  • Type of references: 

    normally from academic sources.

• English language proficiency (ELP) (if applicable)

Thesis option:

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 enrollment. At least one of the two other members should be from (or cross-appointed to) the Department, and one of the members should be from outside the research group of the supervisor(s).

Graduate Academic Integrity Module (Graduate AIM)

Courses 

• Students must complete 4 one-term (0.50 unit) graduate courses after the Master's degree, satisfying a breadth requirement, or 8 one-term (0.50 unit) graduate courses after the Bachelor's degree, satisfying a breadth requirement. Candidates for the PhD degree must maintain a grade point average of at least 70% in their coursework. Besides the breadth requirement, there are no other constraints on course selection.
• Breadth requirement: all PhD students are required to take 1 Computation course, 1 Differential Equations course, and 1 Techniques course, from the following lists:
  • Computation:
    • AMATH 740 Numerical Analysis
    • AMATH 741 Numerical Solution of Partial Differential Equations
  • Differential Equations:
    • AMATH 751 Advanced Ordinary Differential Equations
    • AMATH 753 Advanced Partial Differential Equations
    • AMATH 777 Stochastic Processes in the Physical Sciences
  • Techniques:
    • AMATH 731 Applied Functional Analysis
    • AMATH 732 Asymptotic Analysis and Perturbation Theory
• Students may not count more than 1 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 2 cross-listed courses.
• 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
• Courses are selected in consultation with the student's supervisor. Students are encouraged 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.

Link(s) to courses

• Applied Mathematics (AMATH) courses

PhD Comprehensive Examination

• 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. The student will be informed of the areas of examination 3-4 months prior to the 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 Lecturing Requirement

• 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.

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 Office website; additional departmental guidelines apply.
• The candidate shall defend the thesis in an oral examination before an Examining Committee, which shall consist of the Advisory Committee, one faculty member from outside the Department, and an external examiner familiar with the student's research field.