Mathematics

Program Overview

The Department of Mathematics offers opportunities for research—leading to the Master of Science and Doctor of Philosophy degrees—in the fields of pure mathematics and applied mathematics. Faculty areas of research include, but are not limited to, real and complex analysis, ordinary and partial differential equations, harmonic analysis, nonlinear analysis, several complex variables, functional analysis, operator theory, C*-algebras, ergodic theory, group theory, analytic and algebraic number theory, Lie groups and Lie algebras, automorphic forms, commutative algebra, algebraic geometry, singularity theory, differential geometry, symplectic geometry, classical synthetic geometry, algebraic topology, set theory, set-theoretic topology, mathematical physics, fluid mechanics, probability (in co-operation with the Department of Statistics), combinatorics, optimization, control theory, dynamical systems, computer algebra, cryptography, and mathematical finance.

Quick Facts

Domestic International
Application payment deadline MSc, PhD:

4-Dec-2020

MSc, PhD:

4-Dec-2020

Supporting documents deadline MSc, PhD:

11-Dec-2020

MSc, PhD:

11-Dec-2020

Minimum admission average MSc:

a final-year average of at least mid-B

PhD:

B+

Direct-entry PhD: GPA of 3.7

MSc:

a final-year average of at least mid-B

PhD:

B+

Direct-entry 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 (full-time only) MSc:

3 sessions full-time (typical registration sequence: F/W/S);

4 sessions full-time (typical registration sequence: F/W/S/F)

PhD:

4 years; 5 years for direct-entry PhD

MSc:

3 sessions full-time (typical registration sequence: F/W/S);

4 sessions full-time (typical registration sequence: F/W/S/F)

PhD:

4 years; 5 years for direct-entry PhD


Master of Science​

Program Description

The MSc is a research-oriented 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 full-time

    • 24 months part-time

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

    • 16 months full-time

    • 24 months full-time

Provisional admission to the PhD program may be granted at the time of admission to the master's program.

 

MSc Program (12-Month Full-Time and 24-Month Part-Time)

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 full-course equivalents (FCEs) and a supervised research project (MAT 4000Y), or its equivalent, or

    • 2.0 approved FCEs and an acceptable thesis. Two approved half-year courses are considered the equivalent of a full-year 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 part-time must, at a minimum, satisfy the requirements of the 12-month 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 full-time (typical registration sequence: F/W/S);
6 sessions part-time

Time Limit

3 years full-time;
6 years part-time

 

MSc Program (16-Month Full-Time)

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 16-month 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 full-time in one of two ways:

    • 3.0 approved full-course equivalents (FCEs) and a supervised research project (MAT 4000Y), or its equivalent, or

    • 2.0 approved FCEs and an acceptable thesis. Two approved half-year courses are considered the equivalent of a full-year 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 full-time (typical registration sequence: F/W/S/F)

Time Limit

3 years full-time

 

MSc Program (24-Month Full-Time)

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 24-month 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 full-time in one of two ways:

    • 3.0 approved full-course equivalents (FCEs) and a supervised research project (MAT 4000Y), or its equivalent, or

    • 2.0 approved FCEs and an acceptable thesis. Two approved half-year courses are considered the equivalent of a full-year 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 full-time (typical registration sequence: F/W/S/F/W/S)

Time Limit

3 years full-time

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​​

  • 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 full-course 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 (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
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

Yongshan He

“The faculty members I’ve met at U of T are all very friendly, so don’t be shy.”

Yongshan He
PhD Candidate, East Asian Studies
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