From big data to corporate finance, intelligence analysis to operational research, mathematics researchers tackle complex problems in an array of fast-evolving fields. Investigate research questions and become a well-trained scholar in some of the discipline’s most vibrant areas of study. By pursuing a PhD in Mathematics at Concordia, you will play a critical role in shaping and advancing the field of mathematics among leading faculty members.
Benefit from Concordia’s association with the ISM (Institut des sciences mathématiques) and the CRM (Centre de recherches mathématiques), by choosing to take courses at any of the four universities in Montreal, register to workshops and participate in collaborative projects throughout your studies.
With a PhD in mathematics, you will be ready to pursue a career in academia or apply your cutting-edge research expertise to fast-evolving fields, including finance, big data, risk management and computer science.
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 MSc 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 PhD program.
Proficiency in English. Applicants whose primary language is not English must demonstrate that their knowledge of English is sufficient to pursue graduate studies in their chosen field. Please refer to the Graduate Admission page for further information on the Language Proficiency requirements and exemptions.
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).
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 defence 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.
The department offers financial support to approximately 25-30 full-time M.A/M.Sc. and Ph.D. students per year. It also awards internal scholarships through organized competitions and allocates research and teaching assistantships. Some scholarships and bursaries are also available through ISM.
Faculty of Arts and Science Fellowships
The Faculty of Arts and Science supports graduate students by awarding one-year Masters fellowships ($7,000). Other awards available through the faculty include:
Concordia Merit Scholarship
Concordia University Graduate Fellowship
Harriet and Abe Gold Endowment
Hydro-Quebec Graduate Award
Concordia International Tuition Award of Excellence
John W. O'Brien Graduate Fellowship
Clara Strozyk Scholarship
Out-of-Province Fee Remission Awards
Consideration for Entrance Awards is automatically part of the admissions process for all new students. We also encourage students seeking admission to our program to apply for funding from external sources (e.g. NSERC, FRQNT). An important part of these applications is writing a research project proposal which candidates may discuss with their potential supervisors.
The Department is part of the Institut des sciences mathématiques (ISM), a unique centre of excellence for graduate training in Mathematics, combining the resources and expertise of the mathematics departments at the four Montreal-area universities, as well as Université de Sherbrooke and Université Laval.
The Department is also associated with the Centre de recherches mathématiques (CRM), a NSERC National Research Centre whose mission is to provide leadership in the development of mathematical sciences in Canada.
To foster interdisciplinary research and cross-specialty collaborations, we maintain close ties with the Department of Computer Science, as well as other departments and universities. A wide range of research seminars and lectures are held regularly throughout the year, many of them being organized in conjunction with other Montreal universities, the ISM and the CRM.