**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

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: 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 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.

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 |

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 the following areas are the most frequently offered:

6910. Topology

6930. Statistics

6940. Pure and Applied Analysis

6950. Algebra

Last modified on June 4, 2003 by R. Bruce

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