20 MATHEMATICS AND STATISTICS

20.1.1 GRADUATE FACULTY

Professors

Tracy, Derrick Shannon; B.Sc., M.Sc. (Lucknow), M.S., Sc.D. (Michigan)—1965.

McDonald, James F.; B.S., Ph.D. (Wayne State)—1967.

Chandna, Om Parkash; B.A. (Panjab), M.A. (Delhi), M.Sc., Ph.D. (Windsor)—1968.

Kaloni, Purna N.; M.Sc. (Allahabad), M. Tech., Ph.D. (Indian Inst. of Tech.)—1970.

Lemire, Francis William; B.Sc. (Windsor), M.Sc., Ph.D. (Queen's)—1970.

Britten, Daniel J.; B.A. (Merrimack College), M.S., Ph.D. (Iowa)—1971.

Wong, Chi Song; B.S. (National Taiwan), M.S. (Oregon), M.S., Ph.D. (Illinois-Urbana)—1971.

Barron, Ronald Michael; B.A., M.Sc. (Windsor), M.S. (Stanford), Ph.D. (Carleton)—1975.

Fung, Karen Yuen; B.A., M.S., Ph.D. (U.C.L.A.)—1976.

Paul, Sudhir R.; B.Sc., M.Sc. (Dacca), Ph.D. (Wales)—1982.

Caron, Richard J.; B.M., M.M., Ph.D. (Waterloo)—1983. (Head of the Department)

Zamani, Nader G.; B.Sc. (Case Western), M.Sc., Ph.D. (Brown)—1986.

Associate Professors

Traynor, Tim Eden; B.A., M.A. (Saskatchewan), Ph.D. (British Columbia)—1971.

Hlynka, Myron; B.Sc. (Manitoba), M.A., Ph.D. (Pennsylvania State)—1986.

Assistant Professor

Hu, Zhiguo; B.Sc., M.Sc. (Northeast China), Ph.D. (Alberta)—1993

Cross-appointments

Brill, Percy; B.Sc. (Carleton), M.A. (Columbia), Ph.D. (Toronto)—1984

Fan, Yanqin; B.Sc. (Jilin), M.A., Ph.D. (Western Ontario)—1989.

Gencay, Ramazan; B.Sc. (Middle East Tech. U., Ankara), M.A. (Guelph), Ph.D. (Houston)—1991.

20.2 Programs of Study

20.2.1THE DOCTOR OF PHILOSOPHY DEGREE

Admission Requirements

For admission requirements and period of study, the general regulations of the Faculty of Graduate Studies and Research should be consulted (see 1.5). Qualifying examinations will not normally be required.

Candidacy

Students will be recommended for candidacy (see 1.5.1) only after successful completion of the Comprehensive Examinations and course work.

Program Requirements for the Ph.D. (Mathematics)

1) Course Work: Students admitted with an M.Sc. or equivalent must successfully complete at least four graduate courses numbered with the prefix 62-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed. In addition, graduate courses completed at this institution must include two of the following: Real Analysis (62-510), Functional Analysis (62-512), or Partial Differential Equations (62-561).

Students admitted with an Honours B.Sc., or equivalent, which is done only in exceptional cases, must successfully complete at least twelve graduate courses, eight of which must be numbered with the prefix 62-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed.

2) Doctoral Committee: Within the student's first term of study at the doctoral level, a doctoral committee will be appointed by the Head of the Department upon the advice of the Graduate Studies Committee. The doctoral committee must be approved by the Executive Committee of the Faculty of Graduate Studies and Research. The doctoral committee shall include the student's advisor as chairperson, at least two other members of the Department, one faculty member from outside the Department, and an external examiner, who shall not be involved in the preparation of the dissertation. The selection of the external examiner is subject to the approval of the Dean of Graduate Studies and Research. Members of other departments may also be invited to join the committee (see also 1.5.2).

3) Dissertation: The dissertation shall be defended at an oral examination (see also 1.5.2).

4) Comprehensive Examinations: Each student will be required to pass a series of three written comprehensive examinations. These will test the student's background knowledge and preparedness for research in a particular area of mathematics. If a student fails an examination, it may be repeated once, but if the examination is failed a second time, the student must withdraw from the program (see also 1.5.3). In any case, these examinations must be successfully completed within twenty-five months of registration in the doctoral program. If this deadline is not met, the student must withdraw from the program.

Program Requirements for the Ph.D. (Statistics)

1) Course Work: Students admitted with an M.Sc. or equivalent must successfully complete at least four graduate courses numbered with the prefix 65-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed. (Up to two courses prefixed 65- may be replaced by 62-510 and/or 62-511.)

Students admitted with an Honours B.Sc., or equivalent, which is done only in exceptional cases, must successfully complete at least twelve graduate courses, eight of which must be numbered with the prefix 65-; further graduate courses may be assigned by the Graduate Studies Committee in consultation with the advisor. Transfer credits will not be allowed.

It is strongly recommended that all Ph.D. students in Statistics take a measure theoretic probability course.

2) Doctoral Committee: within the student's first term of study at the doctoral level, a doctoral committee will be appointed by the Head of the Department upon the advice of the Graduate Studies Committee. The doctoral committee must be approved by the Executive Committee of the Faculty of Graduate Studies and Research. The doctoral committee shall include the student's advisor as chairperson, at least two other members of the Department, one faculty member from outside the Department, and an external examiner, who shall not be involved in the preparation of the dissertation. The selection of the external examiner is subject to the approval of the Dean of Graduate Studies and Research. Members of other departments may also be invited to join the committee (see also 1.5.2).

3) Dissertation: The dissertation shall be defended at an oral examination (see also 1.5.2).

4) Comprehensive Examinations: A student must pass a series of three written comprehensive examinations as follows:

(i) Paper I—Mathematical Statistics and Probability

(ii) Paper II—Statistics OR Probability

(iii) Paper III—Topics (two topics mutually agreed upon by the advisor and student).

If a student fails an examination, it may be repeated once, but if the examination is failed a second time, the student must withdraw from the program (see also 1.5.3). In any case, these examinations must be successfully completed within twenty-five months of registration in the doctoral program. If this deadline is not met, the student must withdraw from the program.

20.2.2THE MASTER OF SCIENCE DEGREE

Program Requirements for the M.Sc. (Mathematics)

The candidate must complete six graduate courses, and a thesis, where the originality of a Master's thesis may lie in the organization, exhibition, and scholarly evaluation, rather than in the result.

In addition, graduate courses completed at this institution must include two of the following: Real Analysis (62-510), Functional Analysis (62-512), or Partial Differential Equations (62-561).

Program Requirements for the M.Sc. (Statistics)

The candidate must complete six graduate courses, of which at least four must be numbered with the prefix 65-, and a thesis, where the originality of a Master's thesis may lie in the organization, exhibition, and scholarly evaluation, rather than in the result.

Master's Committee

A Master's committee must be appointed within the student's first term of study at the II Master's (Candidate) level. The Master's committee must be approved by the Executive Committee of the Faculty of Graduate Studies and Research. The Master's committee shall include the student's supervisor as chairperson, one other member of the Department, and one faculty member from outside the Department.

20.3.1COURSE DESCRIPTIONS

All courses listed will not necessarily be offered in any given year.

MATHEMATICS

62-500.Mathematical Logic

62-501.Axiomatic Set Theory

62-510.Functions of a Real Variable I

62-511.Functions of a Real Variable II

62-512.Functional Analysis I

62-513.Functional Analysis II

62-520.Abstract Algebra I

62-521.Abstract Algebra II

62-523.Lie Algebras

62-524.Representation Theory

62-525.Matrix Algebra and Analysis

62-530.General Topology

62-533.Differential Geometry

62-536.Riemannian Geometry

62-561.Partial Differential Equations

62-568.Numerical Analysis I

62-569.Numerical Analysis II

62-570.Continuum Mechanics

62-572.Fluid Dynamics I

62-573.Perturbation Methods in Fluid Mechanics

62-575.Compressible Flow I

62-577.Numerical Techniques in Fluid Dynamics I

62-579.Visco-elasticity and Plasticity

62-582.Fluid Dynamics II

62-585.Compressible Flow II

62-587.Numerical Techniques in Fluid Dynamics II

62-590.General Relativity

62-592.Relativistic Fluid Dynamics

62-593.Introduction to Finite Element Method

62-595.Mathematical Programming

62-598.Special Topics

62-796.Major Paper

62-797.Thesis (M.Sc.)

62-798.Dissertation (Ph.D.)

STATISTICS

65-540.Theory of Probability

65-541.Stochastic Processes

65-542.Advanced Mathematical Statistics I

65-543.Advanced Mathematical Statistics II

65-544.Multivariate Analysis I

65-545.Multivariate Analysis II

65-546.Statistical Data Analysis

65-548.Non-parametric Statistics

65-549.Discrete Multivariate Analysis

65-550.Linear Models

65-552.Experimental Design

65-554.Theory of Sampling and Surveys

65-555.Regression Analysis

65-556.Decision Theory

65-559.Topics in Statistics

Topics offered may include queueing theory, generalized multivariate analysis, bioassy, generalized linear models, optimal design, and Bayesian analysis.

65-796.Major Paper

65-797.Thesis (M.Sc.)

65-798.Dissertation (Ph.D.)

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