Degree Requirements

The Graduate Program in Mathematics offers the following degrees:

In the following, a "half-course" means an ordinary one-semester course that meets for approximately three hours per week. A list of Graduate Courses.

Course-based M.Sc. degree requirements

Our course-based M.Sc. degree is a 3-term (1-year) degree.

The requirements below are in addition to the requirements available from the website of the School of Graduate and Postdoctoral Studies.

  1. A candidate shall complete satisfactorily a minimum of eight half-courses numbered 9000 or above.
    For students in Mathematics, all coursework is in Mathematics or Applied Mathematics, and is subject to the core course requirement: at least five half-courses should be core courses, with at least one half-course in each of Algebra, Analysis, and Geometry/Topology.
    For students in Applied Mathematics, at least four of the courses must be in Applied Mathematics.
  2. A candidate may be permitted to substitute a project for one of the half-courses.
  3. In combined undergraduate-graduate courses, graduate students must do more substantial work than is required of undergraduate students. 
  4. Students are required to maintain an average grade of 70%, and to receive a passing grade (at least 60%) in every course. 

At the discretion of the graduate affairs committee, a candidate for the M.Sc. degree may be permitted to substitute certain graduate courses in other departments towards their course requirement.

Mathematics core courses

The list of core courses can be found here.

  1. Core courses have regular graded homework assignments (or equivalent) and exams.
  2. The core course requirement can be waived in exceptional cases when a candidate has already acquired substantial background in the area. In that case, the candidate may substitute another course with regular graded assignments (or equivalent) and exams for one or more core courses.

Thesis-based M.Sc. degree requirements

Our thesis-based M.Sc. degree is a 6-term (2-year) degree, comprising course-work and independent research components. This option is intended for students whose field of research is Applied Mathematics; students in Mathematics should apply instead for the course-based M.Sc. degree.

The requirements below are in addition to the requirements available from the website of the School of Graduate and Postdoctoral Studies.

  1. A candidate shall complete satisfactorily a minimum of four half-courses. In combined undergraduate-graduate courses, graduate students must do more substantial work than is required of undergraduate students. 
    Students in Applied Mathematics must complete at least two courses in Applied Mathematics.
    Students in Mathematics must complete all of their coursework in Mathematics or Applied Mathematics. At least three of their courses must be core courses in at least two of the areas: Algebra, Analysis, and Geometry/Topology.
  2. A candidate shall complete and defend an M.Sc. thesis.
  3. Students are required to maintain an average grade of 70%, and to receive a passing grade (at least 60%) in every course.

Ph.D. degree requirements

Our Ph.D. degree generally takes 4 years, although some students finish earlier or later than this. We provide 12 terms (4 years) of funding to all applicants unless they have external funding.

The requirements below are in addition to the requirements available from the website of the School of Graduate and Postdoctoral Studies.

  1. A candidate holding an approved Master's degree shall satisfactorily complete a minimum of 5 half-courses. A candidate without an approved Master's degree shall satisfactorily complete a minimum of 9 half-courses.  In combined undergraduate-graduate courses, graduate students must do more substantial work than is required of undergraduate students.
    For students in Mathematics, all coursework must be either in Mathematics or Applied Mathematics. In addition, at least three courses must be at the 9100-level or higher.
    Students in Applied Mathematics must complete two core courses: AM 9505 Partial Differential Equations and AM 9561 Introduction to Numerical Analysis.
  2. Students are required to maintain an average grade of 70%, and to receive a passing grade (at least 60%) in every course.
  3. A candidate is required to pass a comprehensive examination ascertaining the candidate's familiarity with the undergraduate and M.Sc.-level coursework.
  4. A candidate is required to pass a candidacy examination, which is a project and presentation related to the candidate's intended specialty.
  5. A candidate shall deliver a departmental presentation, which summarizes the candidate's progress towards their thesis since the completion of the candidacy exam.
  6. A candidate shall complete a departmental oral examination before final submission of the thesis. More information is available here.
  7. A candidate shall complete and defend a Ph.D. thesis in accordance with the School of Graduate and Postdoctoral Studies thesis regulations.
  8. Students are required to maintain satisfactory progress towards their degree, ascertained within the annual progression evaluations.

Ph.D. milestones

Comprehensive Exams

The student must complete the Comprehensive Exams. See this page for more information.

Candidacy Exam

The Candidacy Exam consists of completion of a written paper and oral presentation assigned by the candidate's supervisory committee. The objective here is to ascertain that the candidate has the potential to undertake research and to write down results. This is to test their familiarity with the background of the intended field of study. This project is assigned within two months of completing the comprehensive exams and is to be completed by the end of the second year in the program. The project is judged on a pass/fail basis by a three-person examining committee including the student's supervisor. 

The submitted paper shall typically be between 10 and 15 pages in length and compile results from several different sources together with the methodologies and proofs as appropriate for the student's research area. The presentation of the material shall be coherent and sufficiently detailed so that the members of the examining committee can evaluate its correctness without consulting specialized literature.

The examining committee will contain three faculty members appointed by the Graduate Affairs Committee and usually includes of the supervisory committee. A final version of the paper will be submitted to the examining committee at least two weeks before the presentation.

After the presentation and audience questions, the audience is asked to leave and the examining committee meets privately with the candidate to ask additional questions. Then the examining committee meets without the candidate, decides separately whether the paper and the presentation have been satisfactorily completed, and reports its decision to the candidate and the Graduate Affairs Committee. In the event that one or both of the paper and presentation is not deemed satisfactory by a majority of the committee, the candidate may attempt the failed portion(s) a second time, within two months of the first attempt. If the candidate fails again, they are withdrawn from the program.

Departmental Presentation

A candidate shall deliver a Departmental Presentation ("third-year talk") which summarizes the candidate's research progress since the completion of the candidacy exam. This 25 minute public talk will typically be given during the month of March of the candidate's third year in the PhD program. The candidate's supervisory committee members shall attend the talk, and shall determine whether the milestone was successfully completed.

Departmental Oral Examination

At least one week prior to submitting their thesis to SGPS, the student must complete the Departmental Oral Examination. The details can be found here.

Progression evaluation

At the end of each academic year, the supervisor is required to complete a Ph.D. Progression Report on the student's progress towards their degree. As part of the report, the supervisor will need to select a description of their overall assessment from a list of choices, including "unsatisfactory".

In the case that a progression report is returned as "unsatisfactory", the graduate chair will arrange a confidential meeting with the student to discuss the details of the situation. Subsequently, a "Probationary Meeting" will be arranged between the student, their supervisory committee, the graduate chair, and at the discretion of the student, a third-party faculty member who will serve as an advocate for the student.

During the Probationary Meeting, those present will mutually agree upon goals to be accomplished over the next six months. These goals will be outlined in a Probationary Letter delivered to the student by the graduate chair after the Probationary Meeting. Within six months, a second meeting must be convened among the student, their supervisory committee, and the graduate chair to assess the student's progress towards the goals. If the supervisory committee decides that the student failed to achieve them, the student will be withdrawn from the program.