Degree Requirements

The Department of Mathematics offers programs leading to the following degrees:

  • M.Sc. in Mathematics
  • M.Sc. in Applied Mathematics
  • Ph.D. in Mathematics
  • Ph.D. in Applied Mathematics

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.

M.Sc. in Mathematics

Our M.Sc. in Mathematics is a 3-term (1 year) course-work degree that is intended to provide a solid foundation in mathematics. A student completing this degree will be in an excellent position to dive into research in a PhD program.

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

M.Sc. Degree Requirements

  1. A candidate shall complete satisfactorily a minimum of eight half-courses in mathematics numbered 9000 or above. Of those eight half courses, at least five half-courses should be core courses, with at least one half-course in each of Algebra, Analysis, and Geometry/Topology. Core courses have regular graded homework assignments and exams. The core courses requirement can be waived in the exceptional cases when a candidate has already acquired substantial background in the area.
  2. A candidate may be permitted to substitute a thesis for at most four half-courses, in which case a student is required to pass three core half-courses in at least two of the three areas.  (The thesis option is rarely used and requires approval of the program.)
  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.

Note: At the discretion of the student's advisory committee, a candidate for the M.Sc. degree may be permitted to substitute certain graduate courses in other departments for mathematics courses.

List of Core Courses  (.pdf)

M.Sc. in Applied Mathematics

We offer two kinds of M.Sc. degrees in Applied Mathematics: a two-year thesis-based degree and a one-year course-based degree.

Thesis-based M.Sc. in Applied Mathematics

Our thesis-based M.Sc. in Applied Mathematics is a 6-term (2-year) degree, comprising course-work and independent research components.

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

Thesis-base M.Sc. in Applied Mathematics Degree Requirements 

  1. A candidate shall complete satisfactorily a minimum of four half-courses. (At the discretion of the student's advisory committee, a candidate for the M.Sc. degree may be permitted to substitute certain graduate courses in other departments for mathematics courses.)
  2. A candidate shall complete and defend an M.Sc. thesis.
  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 78%, and to receive a passing grade (at least 60%) in every course.

 

Course-based M.Sc. in Applied Mathematics

Our course-based M.Sc. in Applied Mathematics is a 3-term (1-year) degree, comprising course-work and independent research components.

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

Course-based M.Sc. in Applied Mathematics Degree Requirements

  1. A candidate shall complete satisfactorily a minimum of seven half-courses, up to two of which may be at the senior undergraduate level (third or fourth year).  (At the discretion of the student's advisory committee, a candidate for the M.Sc. degree may be permitted to substitute certain courses in other departments for applied mathematics courses.)
  2. A candidate shall complete a substantial independent research project.
  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 78%, and to receive a passing grade (at least 60%) in every course.

Ph.D. in Mathematics and Applied Mathematics

Our Ph.D. in Mathematics 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. Ph.D. students should in particular take note of the thesis regulations.

Ph.D. in Mathematics Degree Requirements

  1. A candidate holding an approved Master's degree shall satisfactorily complete a minimum of 6 half-courses in mathematics numbered 9000 or above, of which at least three must be numbered 9100 or above. A candidate without an approved Master's degree shall complete a minimum of 14 half-courses in mathematics numbered 9000 or above, of which at least three must be numbered 9100 or above. In combined undergraduate-graduate courses, graduate students must do more substantial work than is required of undergraduate students.
  2. A candidate will be required to pass a comprehensive examination. This examination is in two parts. The first part, a written exam, will cover certain undergraduate and MSc-level material. The second part will be a project and presentation related to the candidate's intended specialty. More information is available here.
  3. A candidate will be required to pass a departmental oral examination just before final submission of the thesis; this examination will be primarily concerned with the contents of his or her thesis, but may include questions of a general nature relating to his or her field of specialization.  More information is available here (.pdf).
  4. Students are required to maintain an average grade of 70%, and to receive a passing grade (at least 60%) in every course.

Note: At the discretion of the student's advisory committee, a candidate for the Ph.D. degree may be permitted to substitute certain graduate courses in other departments for mathematics courses.

Ph.D. in Applied Mathematics Degree Requirements

  1. A candidate holding an approved Master's degree shall satisfactorily complete a minimum of 4 half-courses in applied mathematics numbered 9000 or higher. These must include the two core courses: AM 9561 Introduction to Numerical Analysis and AM 9505 Partial Differential Equations.
  2. A candidate will be required to pass a comprehensive examination. This examination is in two parts: the first covers undergraduate material (calculus, linear algebra, ordinary differential equations, and numerical methods), the second covers the contents of the two core courses (AM 9561 Introduction to Numerical Analysis and AM 9505 Partial Differential Equations) and includes questions related to the candidate's research area.
  3. Students are required to maintain an average grade of 78%, and to receive a passing grade (at least 60%) in every course.