Doctor of Philosophy
Program Description
The PhD is a researchoriented program consisting of coursework, comprehensive examinations, and a thesis embodying the results of original research. Opportunities for graduate study and research are available in most of the main areas of pure and applied mathematics.
Applicants may enter the PhD program via one of two routes: 1) following completion of an appropriate MA or 2) direct entry following completion of a bachelor’s degree.
PhD Program
Minimum Admission Requirements

Applicants are admitted under the General Regulations of the School of Graduate Studies. Applicants must also satisfy the Department of Mathematics' additional admission requirements stated below.

A master's degree from a recognized university. Students must satisfy the department of their ability to do independent research at an advanced level. They must show evidence of an excellent academic background and mathematical ability.
Program Requirements

Coursework. Students must complete at least 3.0 fullcourse equivalents (FCEs) (six half courses).

Students must pass a comprehensive examination in basic mathematics before beginning an area of research. This examination should be taken as soon as possible, and not later than the beginning of the third session of PhD study. The usual examination covers the three general areas of analysis, algebra, and topology, at the level of Year 1 graduate courses offered by the department in these subjects. Students planning to specialize in applied mathematics must take the analysis and/or algebra portion of the comprehensive examination, but may substitute from several areas of applied mathematics for the remaining portions.

Students must pass a qualifying oral examination or give a seminar presentation in their particular area of study before embarking on serious thesis research.

The main requirement of the degree is an acceptable thesis embodying original research of a standard that warrants publication in the research literature.
Program Length
4 years
Time Limit
6 years
PhD Program (DirectEntry)
Minimum Admission Requirements

Applicants are admitted under the General Regulations of the School of Graduate Studies. Applicants must also satisfy the Department of Mathematics' additional admission requirements stated below.

Exceptionally strong BSc students with a grade point average (GPA) of 3.7 or higher may apply for direct admission to the PhD program. Students must satisfy the department of their ability to do independent research at an advanced level. They must show evidence of an excellent academic background and mathematical ability.
Program Requirements

Coursework. Students must complete at least 4.0 fullcourse equivalents (FCEs) (eight half courses) and a supervised research project (MAT 4000Y) or its equivalent.

Students must pass a comprehensive examination in basic mathematics before beginning an area of research. This examination should be taken as soon as possible, and not later than the beginning of the third session of PhD study. The usual examination covers the three general areas of analysis, algebra, and topology, at the level of Year 1 graduate courses offered by the department in these subjects. Students planning to specialize in applied mathematics must take the analysis and/or algebra portion of the comprehensive examination, but may substitute from several areas of applied mathematics for the remaining portions.

Students must pass a qualifying oral examination or give a seminar presentation in their particular area of study before embarking on serious thesis research.

The main requirement of the degree is an acceptable thesis embodying original research of a standard that warrants publication in the research literature.
Program Length
5 years
Time Limit
7 years