Mathematics
Program Overview
Quick Facts
Domestic  International  

Application payment deadline  MSc, PhD: 4Dec2020  MSc, PhD: 4Dec2020 
Supporting documents deadline  MSc, PhD: 11Dec2020  MSc, PhD: 11Dec2020 
Minimum admission average  MSc: a finalyear average of at least midB PhD:B+ Directentry PhD: GPA of 3.7  MSc: a finalyear average of at least midB PhD:B+ Directentry PhD: GPA of 3.7 
Direct entry option from bachelor's to PhD?  PhD: Yes  PhD: Yes 
Is a supervisor identified before or after admission?  MSc, PhD: After  MSc, PhD: After 
If a supervisor is identified after admission (as per question above), is admission conditional upon securing a supervisor?  MSc, PhD: No  MSc, PhD: No 
Is a supervisor assigned by the graduate unit or secured by the applicant?  MSc, PhD: Applicant  MSc, PhD: Applicant 
Program length (fulltime only)  MSc: 4 years; 5 years for directentry PhD  PhD: MSc: 4 years; 5 years for directentry PhD  PhD:
Master of Science
Program Description
The MSc is a researchoriented program. Opportunities for graduate study and research are available in most of the main areas of pure and applied mathematics. There is a large selection of graduate courses and seminars, a diverse student body of domestic and international students, and yet classes are small and the ratio of graduate students to faculty is low.
Many recent graduates are engaged in university teaching, and a significant number hold administrative positions in universities or in the professional communities. Others are pursuing careers in industry (technological or financial) or in government.
The MSc program is offered:

for students with a complete undergraduate background in mathematics:

12 months fulltime

24 months parttime


for students who do not have a complete undergraduate background in mathematics. This option is not available on a parttime basis:

16 months fulltime

24 months fulltime

Provisional admission to the PhD program may be granted at the time of admission to the master's program.
MSc Program (12Month FullTime and 24Month PartTime)
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.

Evidence of an excellent academic background and mathematical ability.
Program Requirements

Students must complete the program in one of two ways:

3.0 approved fullcourse equivalents (FCEs) and a supervised research project (MAT 4000Y), or its equivalent, or

2.0 approved FCEs and an acceptable thesis. Two approved halfyear courses are considered the equivalent of a fullyear course.


With approval, two prerequisite undergraduate half courses can be substituted for 0.5 graduate FCE.

Students may, with approval, take courses outside the department as part of a coherent program.

Students who undertake the MSc parttime must, at a minimum, satisfy the requirements of the 12month program.

Students who plan to continue to the PhD program may select 2.0 FCEs in core courses from the approved list in the PhD program requirements section. Students who obtain a grade of A– or higher in each of the corresponding core courses may count coursework towards the PhD comprehensive examination requirement in the particular subject areas.
Program Length
3 sessions fulltime (typical registration sequence: F/W/S);
6 sessions parttime
Time Limit
3 years fulltime;
6 years parttime
MSc Program (16Month FullTime)
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.

Evidence of an excellent academic background and mathematical ability.

Students who do not have a complete undergraduate background in mathematics may be accepted into the 16month program. This possibility may interest students who have some background in a subject in which mathematics is applied and/or who are interested in industrial applications of mathematics.
Program Requirements

Students must complete the program fulltime in one of two ways:

3.0 approved fullcourse equivalents (FCEs) and a supervised research project (MAT 4000Y), or its equivalent, or

2.0 approved FCEs and an acceptable thesis. Two approved halfyear courses are considered the equivalent of a fullyear course.


Students must also complete an approved selection of prerequisites and other courses: an additional 2.0 FCEs in Year 2, 3, or 4 undergraduate courses in any of the following subjects: algebra, analysis, partial differential equations, probability, and topology.

With approval, two prerequisite undergraduate half courses can be substituted for 0.5 graduate FCE.

Students may, with approval, take courses outside the department as part of a coherent program.

Students who plan to continue to the PhD program may select 2.0 FCEs in core courses from the approved list in the PhD program requirements section. Students who obtain a grade of A– or higher in each of the corresponding core courses may count coursework towards the PhD comprehensive examination requirement in the particular subject areas.
Program Length
4 sessions fulltime (typical registration sequence: F/W/S/F)
Time Limit
3 years fulltime
MSc Program (24Month FullTime)
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.

Evidence of an excellent academic background and mathematical ability.

Students who do not have a complete undergraduate background in mathematics may be accepted into the 24month program. This possibility may interest students who have some background in a subject in which mathematics is applied and/or who are interested in industrial applications of mathematics.
Program Requirements

Students must complete the program fulltime in one of two ways:

3.0 approved fullcourse equivalents (FCEs) and a supervised research project (MAT 4000Y), or its equivalent, or

2.0 approved FCEs and an acceptable thesis. Two approved halfyear courses are considered the equivalent of a fullyear course.


Students must also complete an approved selection of prerequisites and other courses: an additional 3.0 FCEs in Year 2, 3, or 4 undergraduate courses in any of the following subjects: algebra, analysis, partial differential equations, probability, and topology.

With approval, two prerequisite undergraduate half courses can be substituted for 0.5 graduate FCE.

Students may, with approval, take courses outside the department as part of a coherent program.

Students who plan to continue to the PhD program may select 2.0 FCEs in core courses from the approved list in the PhD program requirements section. Students who obtain a grade of A– or higher in each of the corresponding core courses may count coursework towards the PhD comprehensive examination requirement in the particular subject areas.
Program Length
6 sessions fulltime (typical registration sequence: F/W/S/F/W/S)
Time Limit
3 years fulltime
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 successfully complete at least 3.0 fullcourse equivalents (FCEs). Out of the following 12 core courses, students must complete 6 courses.
Core Courses
MAT 1000H

Real Analysis I

MAT 1001H

Real Analysis II

MAT 1002H

Complex Analysis

MAT 1060H

Partial Differential Equations I

MAT 1061H

Partial Differential Equations II

MAT 1100H

Algebra I

MAT 1101H

Algebra II

MAT 1300H

Topology I

MAT 1301H

Topology II

MAT 1600H

Mathematical Probability I

MAT 1601H

Mathematical Probability II

MAT 1850H

Linear Algebra and Optimization


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 (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). 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
MAT 1000H  Real Analysis I 
MAT 1001H  Real Analysis II 
MAT 1002H  Complex Analysis 
MAT 1060H  Partial Differential Equations I 
MAT 1061H  Partial Differential Equations II 
MAT 1100H  Algebra I 
MAT 1101H  Algebra II 
MAT 1300H  Topology I 
MAT 1301H  Topology II 
MAT 1600H  Mathematical Probability I 
MAT 1601H  Mathematical Probability II 
MAT 1850H  Linear Algebra and Optimization 

Students must complete MAT 4000Y^{+} 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
“Toronto has become one of the major research centres for AI in North America.”
 Cedric Beaulac
 PhD Candidate, Statistical Sciences