Degree Requirements

  • The Department of Mathematics offers several graduate programs designed to support advanced study and research in Mathematics and Applied Mathematics. See below for an overview of each program and its major requirements.

 

Programs Offered 

Mathematics & Applied Mathematics 

General Course Rules for All Degree Programs 

In the following, a "half-course" means an ordinary one-semester course that meets for approximately three hours per week.
  • In combined undergraduate/graduate courses, graduate students must complete more substantial work than required of undergraduate students. 
  • Students must maintain a cumulative term average of 70% and receive a passing grade (at least 60%) in every course. 
  • Following a written request from the supervisor, the graduate affairs committee may permit a graduate student to substitute certain graduate courses in other departments towards the course requirement in their degree program. 

 

Core Courses

  • Core courses include regular graded assignments (or equivalent) and examinations. 
  • In exceptional cases, core course requirements may be waived if a student already has acquired substantial background in the area; in which case, the candidate may substitute another course with regular graded assignments (or equivalent) and exams for one or more core courses. 

 

Course-based M.Sc. degree requirements

A 3-term (1 year) program focused on coursework. 

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

Requirements: 

  • A student shall complete satisfactorily a minimum of 8 half courses. 
  • Applied Mathematics degree: at least 4 Applied Math courses. 
  • Mathematics degree: all course work must be in Mathematics or Applied Mathematics; 
  • At least 5 core courses, including one course in each of:  
Algebra 
Analysis 
Geometry/Topology 

See also: General course rules for all degree programs 

Project-based M.Sc. degree requirements

A 3-term (1 year) program combining coursework with a research project. 

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

Requirements: 

  • A student shall complete satisfactorily a minimum of 6 half courses. 
  • Completion of a research project. 
  • Applied Mathematics degree: at least 3 Applied Math courses. 
  • Mathematics degree: all course work must be in Mathematics or Applied Mathematics;  
  • At least 5 core courses, including one course in each of:  
  • Algebra 
  • Analysis 
  • Geometry/Topology 
  • A student shall complete a research project.  

More detailed rules about the new research project option will be provided soon. 

See also: General course rules for all degree programs

Thesis-based M.Sc. degree requirements

A 6-term (2 year) program that includes coursework and a thesis. 

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

Requirements: 

  • A student shall complete satisfactorily a minimum of 4 half courses. 
  • Applied Mathematics degree: at least 2 Applied Math courses. 
  • Mathematics degree: all course work must be in Mathematics or Applied Mathematics; 
  • at least 3 core courses across at least two of the areas:  
Algebra 
Analysis  
Geometry/Topology 
  • Completion and defense of an M.Sc. thesis. 

See also: General course rules for all degree programs 

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.
  7. A candidate shall complete and defend a Ph.D. thesis in accordance with the School of Graduate and Postdoctoral Studies thesis regulations. A thesis template is available here.
  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 their assessment will impact the candidate's subsequent progression evaluation.

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.

Graduate Appeals

An appeal is a request for exemption from a Departmental, School of Graduate and Postdoctoral Studies or Senate regulation on compassionate or medical grounds or because of extenuating circumstances OR a request that a grade on a particular piece of work or a final standing in a course or program be changed.

Students should consult the Graduate Student Academic Appeals section of Academic Handbook.