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.

Completion Requirements

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

  • 3.0 approved full-course equivalents (FCEs) and a supervised research project (MAT4000Y), 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.

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.

Completion 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 (MAT4000Y), 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.

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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.

Completion Requirements

• Students must complete the program full-time as follows:

  • 3.0 approved full-course equivalents (FCEs) and a supervised research project (MAT4000Y), 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.

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.

Completion 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:

  • 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.

• Comprehensive examination.

  • Students must pass a comprehensive examination in basic mathematics before beginning an area of research. This examination is scheduled at the start of the Fall session (usually September) and should be taken no later than the start of the third session.

  • Students have the option to write the final exam of any core course to obtain core credit. This requires approval of the Graduate Office.

  • 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.

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.

Completion 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):

    • 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 also complete 1.0 elective FCE.

• Students must complete MAT4000Y Supervised Research Project or its equivalent.

• Comprehensive examination.

  • Students must pass a comprehensive examination in basic mathematics before beginning an area of research. This examination is scheduled at the start of the Fall session (usually September) and should be taken no later than the start of the third session.

  • Students have the option to write the final exam of any core course to obtain core credit. This requires approval of the Graduate Office.

  • 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.