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What will I learn?

The principal aim of the Ph.D. program is to enable students to attain levels of mastery in one of the Department's areas of specializaiton, commensurate with carrying on independent mathematical research at a high level. These areas are listed below. Our Department has over thirty faculty members who specialize in these areas, and every year visiting and research professors, post-doctoral fellows, and adjunct faculty join the Department to collaborate on research and sometimes teach specialized courses.

In addition to the courses offered at Concordia University, students can take advantage of the Institute des sciences mathematiques (ISM), an organization which facilitates students taking courses at any of its other member universities in Montreal and across Quebec.

Requirements for the Degree

Credits: Students must complete a program of 90 credits, consisting of the following components:

Comprehensive examinations (12 credits);

Six courses or seminars (18 credits);

Thesis (60 credits).

Academic Standing: The 18 credits associated with seminar and course work must be completed with a grade point average of at least 3.00. The specific program of courses and seminars, chosen from the list, will be determined by the Graduate Studies Committee in consultation with the student’s Advisory Committee.

Residence: The minimum period of residence is two years of full-time graduate study, beyond the MA/MSc, or the equivalent in part-time study. (A minimum of one year of full-time study is normally expected).

Comprehensive Examination: The comprehensive examination is composed of the following two parts:

Part A (6 credits)

This is a written examination, consisting of two parts. The first part of the Comprehensive A examination is to test the candidate’s general knowledge of fundamental mathematical concepts. It will normally be completed within one year (3 terms) of the candidate’s entry into the program or the equivalent of part-time study. The second part of the Comprehensive A examination tests the candidate’s knowledge of topics in his or her area of specialization. The material will be chosen from the list of course descriptions given by the Graduate Studies Committee in consultation with the candidate’s research supervisor and the student’s Advisory Committee. Candidates are allowed at most one failure in the Part A examination.

Part B (6 credits)

The Comprehensive B examination is an oral presentation of the candidate’s plan of his or her doctoral thesis in front of the student’s Advisory Committee. It is normally taken within two-three years of the candidate’s entry into the program (or the equivalent of part-time study) and at least one year before the expected completion of the thesis.

Thesis: Concurrently with the preparation for the Part B exam, the students will be engaging in their research work towards the dissertation. After submitting the doctoral thesis, the candidate is required to pass an oral defense of the thesis. The doctoral thesis must make an original contribution to mathematical knowledge, at a level suitable for publication in a reputable professional journal in the relevant area.

Average Time to Completion: Normally a student completes all requirements for the degree, except for the thesis, within two years of entering the program. The normal period for completion of the program, for a student already holding the equivalent of an MA/MSc degree, is three to four years.

Which department am I in?

Faculty of Arts and Science

Study options

Full Time (2 years)

Tuition fees
Tuition fee: CAN $56,702 - CAN $57,111 for 90 credits
Start date

Expected September 2022


Faculty of Arts and Science

Loyola Campus,

7141 Sherbrooke St. W.,


Quebec (QC),

H4B 1R6, Canada

Entry requirements

For students from United States

Applicants normally must hold a master’s degree or equivalent with high standing. Other English language requirements: TOEFL (paper-based) score 577 or higher; MELAB min. score: 85, 3 on speaking test; CAEL min. score: 70; CAE min. score: A; CPE (advanced qualification for proficient users only) min. score: C.

For international students

Candidates will be selected on the basis of their past academic record, letters of recommendation and the relevance of the proposed area of research to the areas of specialization of the Department. The normal requirement for admission to the program is a Master of Science degree, with high standing in Mathematics or an allied discipline from a recognized university. Exceptional candidates who have successfully completed one-year's study at the Master's level may, upon approval by the Graduate Studies Committee, be exempted from the required completion of the Master's degree and admitted directly into the Ph.D. program.