Program Requirements

The PhD Program normally takes four years of full-time study beyond the Master's level to complete. A Master's degree is a prerequisite. Expected progress is outlined in the following table:

1) Coursework for PhD (4-year program): 

Completion of at least 6 half-courses (or the equivalent combination of half and full-year courses). Normally, 6 half-courses are taken in the first year of study (3 half courses in the fall term and 3 in the spring term). It is strongly recommended that student take some additional courses in later years. 

2) Comprehensive Examination: 

The student is required to pass six core courses with an A- grade before beginning an area of specialization. A single "pass/fail" examination in the six general areas (analysis (real and complex), algebra, topology, partial differential equations, linear algebra & optimization and probability) is offered over a 2-day period in early or late September. Passing the comprehensive exam will fulfill the core course requirement. Students have the option to write the final exam of any core course and obtain core credit.

3) Thesis 

The main requirement of the degree is an acceptable thesis. This will embody an individual contribution to original research of a stand that warrants publication in the research literature. It must be written under the supervision of one or more members of the department. 

For more information on Thesis requirements, please see our2023-24 Graduate Studies in Mathematics Handbook.

4) Departmental Academia / Student Advancement 

Students are expected to become extensively involved in departmental life (seminars, colloquia, and related activities).

The following is a list and description of the core courses offered to graduate students during the academic year. These are the basic beginning graduate courses. They are designed to help the student broaden and strengthen his/ her general background in mathematics prior to specializing towards a thesis. A student with a strong background in the area of any of the core courses should not take that particular course: 

The PhD Direct-Entry program normally takes five years of full-time study to complete. Expected progress in the program is outlined in the following table: 

1) Coursework for PhD (Direct-Entry program): 

Completion of at least 8 half courses (or the equivalent combination of half- and full-year courses). Normally 6 half courses are taken in the first year of study (3 half-courses in the fall term and 3 in the spring term) and 2 half-courses in the second year. It is strongly recommended that the student do a Supervised Reading Project (MAT1900Y, MAT1950Y) in the summer between Year 1 and 2 and take some additional courses in other years. Students must achieve an A- grade in each core course.

2) Comprehensive Examination: 

The student is required to pass six core courses with an A- grade before beginning an area of specialization. A single "pass/fail" examination in the six general areas (analysis (real and complex), algebra, topology, partial differential equations, linear algebra & optimization and probability) is offered over a 2-day period in early or late September. Passing the comprehensive exam will fulfill the core course requirement. Students have the option to write the final exam of any core course and obtain core credit.

3) Thesis 

The main requirement of the degree is an acceptable thesis. This will embody an individual contribution to original research of a stand that warrants publication in the research literature. It must be written under the supervision of one or more members of the department. 

For more information on Thesis requirements, please see our 2023-24 Graduate Studies in Mathematics Handbook.

4) Departmental Academia / Student Advancement 

Students are expected to become extensively involved in departmental life (seminars, colloquia, and related activities).

The following is a list and description of the core courses offered to graduate students during the academic year. These are the basic beginning graduate courses. They are designed to help the student broaden and strengthen his/ her general background in mathematics prior to specializing towards a thesis. A student with a strong background in the area of any of the core courses should not take that particular course: