Doctor of Philosophy
Program Description
The PhD is a research-oriented 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
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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.
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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
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Coursework. Students must successfully complete at least 3.0 full-course equivalents (FCEs). Out of the following 12 core courses, students must complete 6 courses.
Core Courses
| Course Code | Course Title |
|---|---|
|
MAT1000H
|
Real Analysis I
|
|
MAT1001H
|
Real Analysis II
|
|
MAT1002H
|
Complex Analysis
|
|
MAT1060H
|
Partial Differential Equations I
|
|
MAT1061H
|
Partial Differential Equations II
|
|
MAT1100H
|
Algebra I
|
|
MAT1101H
|
Algebra II
|
|
MAT1300H
|
Topology I
|
|
MAT1301H
|
Topology II
|
|
MAT1600H
|
Mathematical Probability I
|
|
MAT1601H
|
Mathematical Probability II
|
|
MAT1850H
|
Linear Algebra and Optimization
|
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Comprehensive examinations.
-
Students must pass comprehensive examinations in basic mathematics before beginning an area of research. These examinations are scheduled at the start of the Fall session (usually September) and should be taken no later than the start of the third session.
-
Students who obtain a grade of A– or higher in each of the corresponding core courses for the general areas of mathematics will be exempted from the comprehensive examination requirement in the specific area of study.
-
-
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 (Direct-Entry)
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 full-course equivalents (FCEs). Out of the following 12 core courses, students must complete 6 courses (3.0 FCEs). Students must also complete 1.0 elective FCE.
Core Courses
| Course Code | Course Title |
|---|---|
| MAT1000H | Real Analysis I |
| MAT1001H | Real Analysis II |
| MAT1002H | Complex Analysis |
| MAT1060H | Partial Differential Equations I |
| MAT1061H | Partial Differential Equations II |
| MAT1100H | Algebra I |
| MAT1101H | Algebra II |
| MAT1300H | Topology I |
| MAT1301H | Topology II |
| MAT1600H | Mathematical Probability I |
| MAT1601H | Mathematical Probability II |
| MAT1850H | Linear Algebra and Optimization |
-
Students must complete MAT4000Y+ Supervised Research Project (1.0 FCE) or its equivalent.
-
Comprehensive examinations.
-
Students must pass comprehensive examinations in basic mathematics before beginning an area of research. These examinations are scheduled at the start of the Fall session (usually September) and should be taken no later than the start of the third session.
-
Students who obtain a grade of A– or higher in each of the corresponding core courses for the general areas of mathematics will be exempted from the comprehensive examination requirement in the specific area of study.
-
-
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