Office of the Registrar
School of Graduate Studies (2006/2007)
25.17 Mathematics and Statistics
  • Head of the Department
  • C. Radford

The degrees of Master of Applied Statistics (see appropriate calendar entry), Master of Science and Doctor of Philosophy are offered in the Department of Mathematics and Statistics. The Masters' degrees are offered by full-time and part-time studies.

25.17.1 Doctor of Philosophy

The following regulations should be read in conjunction with the General Regulations.

Admission to the Ph.D. program is limited and competitive. Of all the requirements listed in the regulations, the writing of the doctoral thesis is the most important, and a candidate may complete all other requirements satisfactorily without qualifying for the degree.

The real test is to show ability to attack and solve a significant mathematical or statistical problem independently and in an original manner for the thesis. The doctoral thesis must definitely advance the subject which it treats.

25.17.2 Specific Regulations for the Ph.D. in Mathematics
  1. The Department requires applicants who do not already hold an appropriate Master's degree (or equivalent) to register for the M.Sc. rather than for the Ph.D. directly.

  2. The candidate normally shall satisfactorily complete at least 6 credit hours from the following list:

    • Algebra: 6320, 6321
    • Analysis: 6310, 6311, 6312
    • Applied Mathematics: 6201 or 6212, 6100
    • Combinatorics: 6340, 6341, 6342
    • Topology: 6300 or 6301, 6332
  3. The Comprehensive Examination shall consist of two parts, called hereafter "qualifying review" and "intermediate review", and is subject to the following regulations. (More detailed information concerning the content of these examinations may be obtained from the Department).

    1. The qualifying review consists of one or more examinations, written or oral or both, and is to take place as soon as the Supervisory Committee deems appropriate, but not later than at the end of the candidate's first year in the doctoral program. Its main purpose is to ensure that the candidate has a sufficiently broad general knowledge of Mathematics (especially Analysis, Algebra, and Topology) before beginning work on the thesis.

    2. At a time to be determined by the Supervisory Committee, but not later than at the end of the candidate's second year in the doctoral program, the candidate must take the intermediate review, also consisting of one or more examinations which may be written or oral or both. Its purpose is to ensure that the candidate has sufficient specialized knowledge in the area of the proposed research work and related areas.

    3. The examinations associated with both the qualifying review and the intermediate review are general, and are not based on any particular course.

    4. Successful completion of both the qualifying and intermediate reviews constitutes successful completion of the Comprehensive Examination in the sense of General Regulation Comprehensive Examinations.

25.17.3 Specific Regulations for the Ph.D. in Statistics
  1. Successful completion of a M.A.S. or M.Sc. program or the equivalent is a prerequisite for entry into a Ph.D. program.

  2. The candidate shall complete satisfactorily a minimum of 6 credit hours in graduate courses other than those courses required for a M.A.S./M.Sc. Candidates may be required by the Supervisory Committee to take additional program courses.

  3. The comprehensive examination shall consist of a written and an oral examination.

    1. The written examination shall take place as soon as the supervisory committee deems appropriate but not later than at the end of the candidate's first year in the doctoral program. The purpose of the written comprehensive examination is to ensure that the candidate has a broad general knowledge of statistics before beginning work on the thesis.

    2. At the time to be determined by the supervisory committee, but not later than at the end of the candidate's second year in the doctoral program, the candidate will be required to take the oral examination. The purpose of the oral examination is to ensure that the candidate is making sufficient progress and has sufficient specialized knowledge in the area of the proposed research work and related areas. The oral examination may also include questions of a general nature relating to the field of specialization.

  4. Each candidate will be required to present at least one paper at a graduate seminar on a topic to be approved by his or her Supervisor.

Table of Credit Restrictions for Present Mathematics Courses with Former Mathematics Courses

Credit may be obtained for only course from each of the pairs listed in this table.

Present Course

Former Course

Present Course

Former Course

6323

6030

6212

6080

6321

6032

6310

6130

6322

6035

6330

6200

6340

6040

6331

6210

6341

6041

6332

6350

6342

6042

6312

6500

Courses

A selection of the following graduate courses will be offered to meet the requirements of candidates, as far as the resources of the Department will allow:

  • Mathematics
  • 6100 Dynamical Systems
  • 6101 Modern Perturbation Theory
  • 6102-6109 Special Topics in Applied Mathematics
  • 6120 The Theoretical Fluid Dynamics
  • 6121 Functional Differential Equations
  • 6201 Numerical Methods for Partial Differential Equations
  • 6202-6209 Special Topics in Numerical Analysis
  • 6210 Numerical Solution of Differential Equations (for Computational Science students only - required core course)
  • 6212 Numerical Methods for Initial Value Problems
  • 6300 Algebraic Topology I (Homology Theory)
  • 6301 Algebraic Topology II (Homotopy Theory)
  • 6302 Algebraic Topology III (Theory of Fibre Bundles)
  • 6304-6309 Special Topics in Topology
  • 6310 Functional Analysis
  • 6311 Complex Analysis
  • 6312 Measure Theory
  • 6313-6319 Special Topics in Analysis
  • 6320 Group Theory
  • 6321 Ring Theory
  • 6322 Nonassociative Algebra
  • 6323 Homological Algebra
  • 6324-6329 Special Topics in Algebra
  • 6330 Analytic Number Theory
  • 6331 Algebraic Number Theory
  • 6332 Point Set Topology
  • 6340 Graph Theory
  • 6341 Combinatorial Design Theory
  • 6342 Advanced Enumeration
  • 6343-6349 Special Topics in Combinatorics
  • 6910 Topology Seminar
  • 6940 Analysis Seminar
  • 6950 Algebra Seminar
  • Statistics
  • 6503 Stochastic Processes
  • 6505 Survival Analysis
  • 6510 Mathematical Statistics
  • 6520 Linear Models
  • 6530 Generalized Linear Longitudinal Mixed Models
  • 6540 Time Series Analysis
  • 6545 Statistical Computing
  • 6550 Nonparametric Statistics
  • 6560 Continuous Multivariate Analysis
  • 6561 Categorical Data Analysis
  • 6570-6589 Selected Topics in Statistics and Probability
  • 6590 A Course in Statistical Consulting
  • 6930 Statistics Seminar