REGULATIONS GOVERNING THE DEGREE OF DOCTOR OF PHILOSOPHY

MATHEMATICS AND STATISTICS

Professor and Head of the Department H. Gaskill

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.

DOCTOR OF PHILOSOPHY

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

SPECIFIC REGULATIONS FOR THE PH.D. IN MATHEMATICS

SPECIFIC REGULATIONS FOR THE PH.D. IN STATISTICS

TABLE OF CREDIT RESTRICTIONS

COURSES


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 six credit hours from the following list:

ALGEBRA: M6320 (Group Theory), M6321 (Ring Theory)

ANALYSIS: M6310 (Functional Analysis), M6311 (Complex Analysis), M6312 (Measure Theory)

APPLIED MATHEMATICS: M6201 or M6212 (Numerical Differential Equations), M6100 (Dynamical Systems)

COMBINATORICS: M6340 (Graph Theory), M6341 (Combinatorial Design Theory), M6342 (Advanced Enumeration)

TOPOLOGY: M6300 or M6301 (Algebraic Topology), M6332 (Point Set Topology)

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).

a) 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.

b) 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.

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

d) Successful completion of both the qualifying and intermediate reviews constitutes successful completion of the Comprehensive Examination in the sense of General Regulation H.

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 six 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.

a) 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.

b) 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 ONE 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:

6100. Dynamical Systems
6101. Modern Perturbation Theory
6102-6109. Special Topics in Applied Mathematics
6212. Numerical Methods for Initial Value Problems
6201. Numerical Methods for Partial Differential Equations
6202-6209. Special Topics in Numerical Analysis
6300. Algebraic Topology I (Homology Theory)
6301. Algebraic Topology II (Homotopy Theory)
6302. Algebraic Topology III (Theory of Fibre Bundles)
6332. Point Set Topology
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
6340. Graph Theory
6341. Combinatorial Design Theory
6342. Advanced Enumeration
6343-6349. Special Topics in Combinatorics
6503. Stochastic Processes
6510. Mathematical Statistics
6520. Linear Models
6560. Continuous Multivariate Analysis
6561. Discrete Multivariate Analysis
6580-6589. Selected Topics in Statistics and Probability
6590. A Course in Statistical Consulting

SEMINAR COURSES IN MATHEMATICS AND STATISTICS

Seminar courses in the following areas are the most frequently offered:

6910. Topology
6930. Statistics
6940. Pure and Applied Analysis
6950. Algebra


Last modified on May 21, 2002 by MaryJane Puxley

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