The Doctoral Program

Note: The information below is extracted from, or supplemental to,  information and regulations contained in the Graduate and Postdoctoral Studies handbook entitled: General Information, Regulations and Research Guidelines.

Please note that it is the student's responsibility to read the Graduate and Postdoctoral Studies Handbook and to be aware of the regulations it contains.

The Department offers a course of studies leading to the Ph.D. degree. It differs substantially from the Master’s programs in that the student must write a thesis which makes an original contribution to knowledge. The thesis topic is chosen by the student in consultation with the research supervisor. The thesis must be examined and approved by an internal examiner (normally the research supervisor), an external examiner and the Oral Examination Committee. The student must make an oral defense of the thesis before that Committee. In addition, the student has to pass comprehensive examinations on which details are given below.

Entrance requirements: Students normally enter the Ph.D. program after completing a Master's degree program with high standing. Approval of the Department is needed even after successful completion of a Master's degree program at McGill.

A student in a Master’s program in the Department may apply to the Committee on Graduate Affairs to proceed directly to the Ph.D. program without completing the Master's degree provided that Part A of the comprehensive examinations (see below) has been passed with distinction by the end of the first year in the program.

In addition, students wishing to proceed directly to the Ph.D. degree, and willing to forego the Master’s, may, with the approval of the Department, register in Ph.D. 1 upon entering. Approval will be given only for students with a particularly strong undergraduate background. Students entering in Ph.D. 1 may have to register in M.Sc. 2 for their second year if they fail to maintain an “A–” average.

Residence requirements:
For a student entering with a Bachelor's degree, a minimum of three years of residence are required for the Ph.D. degree. A student with a recognized Master's degree is usually enrolled as a second year Ph.D. student and then only two years of residence are required. The Department may however, at its discretion, place the student into the first year of the Ph.D. program. This could happen, for example, if there is not sufficient overlap between the Master’s concentration and the proposed Ph.D. program.

A student proceeding directly to the Ph.D. program before completing a Master’s (as explained above) will be enrolled as Ph.D. 2 in the second year of studies.

Course requirements: The Doctoral program requires twelve one-semester courses or their equivalent beyond the Bachelor's level. During the first year, courses will be selected in consultation with the student’s advisor or research supervisor with due regard to the student’s area of concentration and possible areas in which prior preparation may be weak. The total program must be approved by the student's Advisory Committee (see “Planning Your Course of Studies).

Broad possible areas of concentration are applied mathematics, pure mathematics and statistics, and it is highly recommended that students complete fully, to the extent that they have not already done so, one of the course sequences outlined under “Guidelines for the choice of courses” in the description of the Master’s programs, during their first year in the Ph.D. program. The syllabus for Part A of the Ph.D. preliminary exams is largely based on these courses.

Comprehensive examinations:
The Comprehensive Examinations are given in two parts, traditionally labelled Part A and Part B.

Part A consists of two written papers which must be taken and passed together within the same examination period. Time limits and descriptions of these examinations are contained in a detailed document entitled: “Description of the Part ‘A’ Ph.D. Preliminary Examinations.” It is the student's responsibility to obtain and read the syllabus and regulations.

Part B is an oral examination on two advanced topics, selected in advance, and not covered by the Part A examinations. Part B must be taken not later than five semesters (not including summers) after the beginning of the Ph.D. Program.

Comprehensive Examinations passed at another university will not be accepted in place of the Part A and Part B examinations.


Advising: At the time of entering, each incoming graduate student, whether at the Master’s or Ph.D. level, will be assigned an Advisory Committee charged with monitoring the student's progress. This Committee consists of an advisor and at least one other staff member. During the first year of graduate study, the student should decide on a research topic and find a research supervisor to direct his or her Master’s thesis, Master’s project or Ph.D. thesis, as the case may be. The student's Advisory Committee will assist the student in these tasks. With the approval of the Department, the research supervisor may be chosen from outside the Department. A co-supervisor from the Department will be appointed in that case. The supervisor, once appointed, takes over the role of advisor in the Advisory Committee.

Research interests of staff: Information as to research interests of staff can be obtained from the included staff list. The web site of the Department provides additional information. Further inquiries should be addressed to the Department.

Course selection for new students is done at the beginning of September for the academic year in consultation with the advisor or research supervisor. A definitive list of graduate courses to be offered will be available during the summer. Advanced courses are coordinated on a Montreal-wide basis by the Institut des Sciences Mathématiques (ISM) and students are encouraged to take such courses at any of the four participating universities.

For preliminary course listings, usually available in the spring, students can consult the departmental and ISM web pages.




Institut des Sciences Mathématiques (ISM): The Institut des Sciences Mathématiques (ISM) is an inter‑university organization sponsored by six Quebec universities (Concordia, Laval, McGill, Montréal, Sherbrooke, UQAM) to offer graduate students a scientific environment complementing that of the university where they are enrolled. It allows them to profit from the presence of a pool of over 200 university mathematicians in Quebec. So that students can take maximum advantage of their stay in Montreal, the ISM has programs in a variety of subjects (10 at the moment) where students can work with and be advised by professors from any of the participating universities. In addition, ISM organizes colloquia and lectures as well as social activities to encourage a community spirit among Montreal mathematicians. The ISM is financed by the Ministère de l'Éducation supérieure et de la Science du Québec and by its member institutions. The ISM programs are continually in evolution. In conjunction with the participating institutions, the ISM also offers a limited number of postgraduate and postdoctoral fellowships.

2004-2005 programs:

  • Algebra and Number Theory
  • Analysis and Applications
  • Combinatorics, Algorythms and Algebraic Computing
  • Nonlinear Dynamics
  • Geometry and Topology
  • Computational Mathematics and Applications
  • Mathematical Physics
  • Probability: Theory and Applications
  • Mathematical and Applied Statistics
  • Category Theory and Applications

The Centre de Recherche en Mathématiques (CRM): The CRM, located at the Université de Montréal, is a mathematics research centre offering a wide variety of mathematical activities. Of particular interest to students in Montreal are theme years with lecture series and intensive workshops on varying subjects.

Centre de Recherche en Théorie des Catégories: The CRTC is a Research Centre consisting of researchers from the four universities in Montreal (McGill, Concordia, Montreal and UQAM), from two CEGEPs (Vanier and John Abbott), and from the University of Ottawa. The main activity is the organization of seminars.

CICMA (Centre Interuniversitaire en Calcul Mathématique Algébrique), a Research Centre in number theory, arithmetic geometry and computational algebra, comprising researchers at Concordia, Laval and McGill was established in 1990. The main goals of CICMA are the support of research in these areas, and the promotion of research interactions between these subjects.


CRM-ISM Colloqium and Colloque de Statistique de Montréal: These two colloquia meet at regular intervals and are held jointly with the other departments of mathematics and statistics in Montreal. They are addressed, in either French or English, by distinguished speakers.

Numerous city-wide seminars are held in various branches of mathematics and statistics with the participation of staff, students and invited speakers. Currently there are regular seminars in algebraic geometry, geometry and topology, integrable systems, number theory, analysis, applied mathematics, category theory, matrix theory, combinatorics, mathematical physics, statistics and logic. The Quebec-Vermont number theory seminar has participants from several universities in Montreal, and from Université de Laval in Quebec City and the University of Vermont. A weekly graduate student seminar (with graduate student speakers) is sponsored by the ISM.


Research Facilities: The Edward Rosenthall Mathematics and Statistics Library receives over 250 current research journals and other serials and has extensive back issues. The library also houses a departmental collection of mathematics and statistics books (approximately 10, 000), constantly enlarged by purchase of the most significant recent titles. In the university library system, there are well over 12,000 volumes on pure and applied mathematics. An excellent inter-library loans service is available, enhanced by a direct Telex link to the National Science Library in Ottawa and to other major research centres in Canada, the United States and Britain.

Excellent facilities available to students include a group of networked LINUX workstations located in labs and offices, a lab of X-terminals and NT workstations, a statistics lab of NT workstations and Linux workstations, and a teaching lab of networked LINUX workstations. Software such as Maple, Matlab, SAS and TeX are available to students for research and thesis preparation. Several laser printers are also available. The workstations are connected to a Department-wide Ethernet network to which students may attach their own terminals (with prior approval).

Language of Instruction: The language of instruction at McGill is English. However, students may write term papers, examinations and theses in French.

Student Body: There are currently over 30,000 registered students at McGill, of whom approximately 8,500 are graduate students. In the current year, more than half of the 79 graduate students in Mathematics and Statistics are working towards a Ph.D.

Cost of Living: Available fellowships and assistantships may be adequate for a single student, but a married student usually needs supplementary income. For the time being it is easy to rent apartments in Montreal. Look for "A LOUER" signs in apartment buildings or in the newspapers. Also, the McGill Housing centre maintains lists of vacant apartments and offers advice on housing. The University has on-campus room and board residences, however most of the graduate students in the Department live in their own (or shared) apartments.

The City: Montreal is a dynamic and cosmopolitan city. The population is over two million and approximately 80% have French as their mother tongue. In the summer, Montreal hosts several international festivals including the world-renowned Jazz Festival, the Just for Laughs Comedy Festival and the International Film Festival. Throughout the year, one can take advantage of Montreal's exciting theatre and dance productions, some of the best restaurants in North America and a lively night life. Montreal is also home of the Expos baseball team, and the famous Les Canadiens major league hockey team. Other major sports events include Grand Prix racing in the Villeneuve circuit, and the Montreal Marathon. The Laurentians, the Eastern Townships and New England are each about an hour's drive for skiing in winter, camping in summer and watching the magnificent change of colour in fall.

The University: Chartered over 175 years ago, McGill University is located in the downtown of Montreal. Besides its faculties of agriculture, arts, dentistry, education, engineering, graduate studies and research, law, management, medicine, music, religious studies and science, it has schools of architecture, computer science, food science, library science, nursing, physical and occupational therapy and social work - and a centre for continuing education.

Last edited by on Mon, 09/17/2007 - 11:46