Note: The information below is extracted from, or supplemental to, the Graduate and Postdoctoral Studies Calendar and may not be up to date. 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 of Mathematics and Statistics offers programs with concentrations in applied mathematics, pure mathematics and statistics leading to the Master's degree (both M.A. and M.Sc.). Students must choose between the thesis option, which requires a thesis (24 credits) and 6 approved courses of 3 or more credits each for a total of at least 21 credits, and the project option, which requires a project (16 credits) and 8 approved courses of 3 or more credits each for a total of at least 29 credits.

There are also program options in Computational Science and Engineering as well as in Bioinformatics. Details can be found in the Calendar.

Normally students must declare which of these options they choose to follow after their first semester.

The originality of a Master's thesis may lie in organization, exposition and scholarly evaluation, rather than in the results. The thesis must be approved by both an internal and an external examiner. The project, smaller in scope than thesis, requires a written report, normally to be approved by two internal examiners.

A thesis for the Master's degree must show familiarity with previous work in the field and must demonstrate ability to carry out research and to organize results. The thesis must be expressed in good literate style. An exhaustive review of work in the particular field of study is not necessarily required, nor is original scholarship necessarily expected.

A Master’s project is similar in form and content to a Master’s thesis, but on a smaller scope. As in the case of a Master’s thesis, the project need not make an original contribution to knowledge, but should show familiarity with previous work in the field and must demonstrate the ability to carry out research and to organize results. It must be presented in good literate style. A Master’s project should not be judged as if it were a Master’s thesis or even a Doctoral thesis. It does not have to be suitable for publication.

Past Master’s projects and theses are available for perusal in the Rosenthall library (Burnside Hall, 11th floor). Further information is available at http://www.mcgill.ca/gps/current/programs/thesis/guidelines/.

* Residence requirements:* The minimum residence requirement for the Master’s degree is three terms, of which at most one may consist of a summer term. It is expected that the degree be completed in at most 4 terms.

## Planning Your Course of Studies

* 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.

*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. Course information can be reached from this page.

During the first year of the masters program students are expected to take at least four (4) courses from one of the following lists of core courses:

** Applied Mathematics: **MATH 550 (Combinatorics), MATH 552 (Combinatorial Optimization), MATH 560 (Optimization), MATH 578 (Numerical Analysis 1), MATH 579 (Numerical Differential Equations), MATH 580 (Applied Partial Differential Equations 1), MATH 581 (Applied Partial Differential Equations 2), MATH 587 (Advanced Probability Theory 1), MATH 589 (Advanced Probability Theory 2).

**Pure**** Mathematics:** MATH 564 (Advanced Real Analysis 1), MATH 565 (Advanced Real Analysis 2), MATH 570 (Higher Algebra 1), MATH 571 (Higher Algebra 2), MATH 576 (Geometry and Topology 1), MATH 577 (Geometry and Topology 2).

* Statistics:* MATH523 (Generalized Linear Models), MATH 533 (Honours Regression and Analysis of Variance), MATH 556 (Mathematical Statistics 1), MATH 557 (Mathematical Statistics 2).

Taking four (4) courses from one of these lists is particularly important for students who are considering moving to the doctoral program after completing their masters since these are the courses which are examined in the Comprehensive examinations which all Ph.D. students are required to pass.

Notwithstanding the courses that students in their respective programs are expected to take, students can, and often do, select their remaining courses from different lists. We encourage our students to develop a broad base of expertise

## Research Centers, Colloquia and Seminars

* 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.

*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.

## Miscellaneous

** 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.

* 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.