Mathematics and Statistics
Staff
Department Head: A. Herman, Ph.D.
Professors: S. Fallat, Ph.D.; D.R. Farenick, Ph.D.; Ph.D.; B.C. Gilligan, Ph.D.; C. Guo, Ph.D.; S.J. Kirkland, Ph.D.; F. Labropulu, Ph.D.; R.J. McIntosh, Ph.D
Associate Professors: M. Argerami, Ph.D.; D. Deng, Ph.D.; J. Erlijman, Ph.D.; A. Herman, Ph.D.; A. Mare, Ph.D.; D. Stanley, Ph.D.; F. Szechtman, Ph.D.; A. Volodin, Ph.D.
Assistant Professors: T. Bae, Ph.D.; E. Doolittle, Ph.D.; R. Floricel, Ph.D.; I. Husain, Ph.D.; M. Kozdron, Ph.D.; K. Meagher, Ph.D.; Y. Zhao, Ph.D
Department Description
The Department is engaged in a broad range of research in pure and applied mathematics and statistics, and offers programs leading to the M.A., M.Sc., and Ph.D. degrees in mathematics or statistics. The M.A. and M.Sc. degrees normally require two years of study, and students may chose either a report option or a thesis option for the research component of the degree. The Ph.D. program is an advanced, research-oriented course of study for which an original contribution to knowledge in the form of a dissertation is to be written and defended. The Ph.D. program involves course work, comprehensive examinations, seminars, original research, and the defence of the dissertation.
The entrance requirement for the M.A. or M.Sc. program is a B.Sc. degree in mathematics or statistics, with a grade average of at least 75%. Applicants to the Ph.D. program should have an M.Sc. degree or its equivalent, and show strong evidence of research potential.
English Language Proficiency and Probationary Status
Applicants who have been accepted conditionally to a graduate
program in Mathematics or Statistics on the condition that they meet
the minimum English language requirement (80 internet Based TOFEL or
any of its equivalents) prior to registration, but who have scored
only in the range of 75 to 79 on the IBT (or the equivalent range on
other English proficiency tests) by the time of registration, will
be considered for enrolment of up to 6 credit hours of
graduate-level (800-level) courses for a period of one semester as a
probationary student.
Enrolment for a second semester of graduate study will be permitted
only if the student has by that time met the minimum English
language requirement (80 IBT or its equivalents) and has passed the
coursework taken in the first semester.
SPECIAL NOTES:
- Probationary students are not eligible for funding through the FGSR.
- The probationary category only applies at the master's level.
- Upon successful completion of the probationary condition,
a change in status to fully qualified will be automatic. If a
change in status to that of a PhD student also applies, this
too will be automatic, coupled to the concomitant program
requirements for a PhD program.
Degree Requirements
Master's Program
MA, M.Sc. in Mathematics Thesis Option
| Course work minimum (chosen from Mathematics graduate course offerings) * |
15 credit hours |
| Seminar (MATH 900) | 2 credit hours |
| Thesis research (MATH 901) | 14 credit hours |
| Research Methods (MATH 902) | 1 credit hour |
| Total | 32 credit hours |
MA, M.Sc. in Mathematics Report Option
| Course work minimum (chosen from Mathematics graduate course offerings)* |
24 credit hours |
| Report (MATH 801) | 6 credit hours |
| Seminar (MATH 900) | 1 credit hour |
| Research Methods (MATH 902) | 1 credit hour |
| Total | 32 credit hours |
MA, M.Sc. in Statistics Thesis Option
| Course work minimum (chosen from Statistics graduate course offerings)* |
15 credit hours |
| Seminar (MATH 900) | 2 credit hours |
| Thesis research (STAT 901) | 14 credit hours |
| Research Methods (STAT 902) | 1 credit hour |
| Total | 32 credit hours |
MA, M.Sc. in Statistics Report Option
| Course work minimum (chosen from Statistics graduate course offerings)* |
24 credit hours |
| Report (MATH 801) | 6 credit hours |
| Seminar (STAT 900) | 1 credit hour |
| Research Methods (STAT 902) | 1 credit hour |
| Total | 32 credit hours |
* Up to two courses may be from a related discipline.
Degree Requirements
Doctoral Program
After a Master's degree, the Ph.D. program in mathematics or statistics consists of course work with MATH 800 or STAT 800 being a required course, seminars, and original research resulting in the presentation of a thesis. All doctoral candidates are required to pass a comprehensive examination that is normally taken after the completion of the course work.
Ph.D. in Mathematics after MA/M.Sc.
| Course work minimum* | 15 credit hours |
| Seminar (MATH 900) | 2 credit hours |
| Research (MATH 901) | 44 credit hours |
| Research Methods (MATH 902) | 1 credit hour |
| Total | 62 credit hours |
Ph.D. in Statistics after MA/M.Sc.
| Course work minimum* | 15 credit hours |
| Seminar (MATH 900) | 2 credit hours |
| Research (MATH 901) | 44 credit hours |
| Research Methods (MATH 902) | 1 credit hour |
| Total | 62 credit hours |
* Up to two courses may be from a related discipline.
Course Descriptions
Please note that the frequency of the offering of any particular course in the list below depends on students' needs and the availability of suitable instructors.
MATH 800 Comprehensive Review of a Selected Topic in Mathematics
(3)
The student will conduct an in-depth literature review of a selected
area in Mathematics and prepare a report pertaining to the selected
topic. The topic will be chosen in consultation with the supervisor
and the Department Head. A final examination (written, oral or
both) will be conducted by a committee of the department.
MATH 801 Report (Variable credit 3-6)
Every Master's candidate, Report Option, will register in this
course either for 6 credit hours in one semester or for 3 credit
hours in each of two consecutive semesters. In this course the
student, with the supervisor, prepares an expository report on
some approved topic in mathematics. The candidate must present
the report and be examined on it by a departmental committee
chaired by the graduate program coordinator or by his or her
designate.
MATH 809 Foundations of Mathematics (3)
Development of the real numbers, axioms for set theory, Gödel’s
theorem.
MATH 810 (411) Real Analysis (3)
Integration and measure theory, spaces of continuous functions,
and LP spaces.
MATH 812 (412) Complex Analysis (3)
Riemann mapping theorem, analytic continuation, Riemann surfaces.
MATH 813 (485) Functional Analysis (3)
Banach spaces, Banach algebras, and operator theory.
MATH 814 Operator Algebras (3)
C*-algebras and von Neumann algebras.
MATH 819 Topics in Analysis (3)
Advanced study of selected areas of analysis.
MATH 821 Number Theory (3)
Topics from analytic and algebraic number theory.
MATH 822 (422) Linear Algebra (3)
Vector spaces, linear transformations and matrices, canonical forms,
multilinear algebra.
MATH 823 (423) Algebra (3)
Advanced study of group theory, Galois theory, and ring and module
theory.
MATH 824 Topics in Algebra (3)
Advanced study of selected areas of algebra.
MATH 825 Matrix Analysis (3)
Matrix canonical forms, norms, spectral theory, perturbation theory,
special classes of matrices.
MATH 826 Combinatorial Matrix Theory (3)
Matrices arising from directed and undirected graphs, and related
connections between matrix theory and combinatorial mathematics.
MATH 827 (427) Graph Theory (3)
Advanced study of selected areas of graph theory.
MATH 828 Combinatorics (3)
Advanced study of selected areas of combinatorics.
MATH 831 (431) Differential Geometry (3)
Differentiable manifolds, Lie groups, differential forms.
MATH 832 (432) Topics in Differential Geometry and Topology (3)
Advanced study of selected areas of differential geometry and topology.
MATH 839 Geometry (3)
Advanced study of selected areas of geometry.
MATH 841 (441) General Topology (3)
Separability of spaces, paracompactness, metrization theorems,
function spaces.
MATH 842 Algebraic Topology (3)
Introduction to homotopy groups, and to the homology and cohomology
of topological spaces.
MATH 849 Topics in Topology (3)
Advanced study of selected areas of topology.
MATH 869 (461) Numerical Analysis (3)
Advanced study of selected areas of numerical analysis.
MATH 881 (481) Partial Differential Equations (3)
The Cauchy problem, the Fredholm alternative in Banach spaces,
the potential equation, the Dirichlet problem, the heat equation,
Green’s functions, and the separation of variables.
MATH 882 (482) Topics in Applied Mathematics (3)
Advanced study of selected topics in applied mathematics.
MATH 890AA-ZZ Directed Readings (3)
Directed readings in various areas of Mathematics.
MATH 900 Seminar (1)
Preparation and presentation of a one-hour lecture to graduate
students and faculty.
MATH 901 Research (Variable credit 1-15)
Thesis research.
MATH 902 Research Tools in Mathematics (1)
Software tools (Maple, Mathematica, Matlab, GAP, LaTeX) and literature
databases (Math Sci Net, Zentralblatt Math, Euler, preprint archives).
STAT 800 Comprehensive Review of a Selected Topic in Statistics
(3)
The student will conduct an in-depth literature review of a selected
area in Statistics and prepare a report pertaining to the selected
topic. The topic will be chosen in consultation with the supervisor
and the Department Head. A final examination (written, oral or
both) will be conducted by a committee in the Department.
STAT 801 Report (Variable credit 3-6)
Every master’s candidate, Report Option, will register in
this course either for 6 credit hours in one semester or for 3
credit hours in each of two consecutive semesters. In this course
the student, with the supervisor, prepares an expository report
on some approved topic in Statistics. The candidate must present
the report and be examined on it by a departmental committee chaired
by the graduate program coordinator or by his or her designate.
STAT 826 (426) Advanced Survival Analysis (3)
Life table, survival distributions, types of censoring, estimation
of and inference for basic survival quantities, proportional
hazards regression model, goodness of fit tests.
STAT 851 (451) Probability (3)
Measure spaces, independence, expectations, convergence theorems,
distribution functions and characteristic functions.
STAT 852 (452) Statistical Inference (3)
Methods of estimation, properties of estimators, hypothesis testing,
properties of tests, relationship between confidence regions
and tests, large sample properties of tests and estimators.
STAT 853 Limit Theorems (3)
Probability inequalities, weak limit theorems (central limit theorem,
weak law of large numbers), strong limit theorems (strong law
of large numbers, law of iterated logarithm).
STAT 854 Regression Analysis (3)
Inferences in simple and multiple regression models, model fitting,
diagnostic checking and selection.
STAT 855 Generalized Linear Models (3)
Generalized linear models, exponential family, likelihood-based
inference, analysis of contingency tables, estimation procedures.
STAT 857 Sampling Theory (3)
Simple random sampling, systematic sampling, cluster sampling,
stratified sampling, sampling with unequal probabilities, multistage
and double sampling, ratio and regression estimators.
STAT 859 (485) Design of Experiments (3)
Completely randomized designs, randomized block designs, factorial
and fractional factorial designs, nested designs, fixed and random
effects models.
STAT 861 Applied Multivariate Analysis (3)
Sample geometry, random sampling from multivariate normal distribution,
inference about a mean vector, comparison of several mean vectors,
multivariate linear regression models, principal components,
factor analysis, discriminant analysis.
STAT 862 Stochastic Processes (3)
Poisson process, renewal processes, Markov processes, Brownian
motion, Gaussian processes, random walks and martingales.
STAT 871 (471) Time Series Analysis (3)
Stationarity, trend and seasonality, autoregressive and moving
average processes, nonstationary processes, Box-Jenkins modeling
method, spectrum and its estimation.
STAT 872 Large Sample Methods (3)
Asymptotic behavior of estimators and test statistics, asymptotic
relative efficiency, large sample theory for regression models.
STAT 881 Nonparametric Methods (3)
Order statistics, rank statistics, sign test, Mann-Whitney test,
Wilcoxon signed rank test, distribution of linear rank statistics,
tests of randomness.
STAT 882 Categorical Data Analysis (3)
Univariate discrete responses, cross-classified responses, loglinear
models, logistical regression, bayesian methods.
STAT 890AA-ZZ Directed Readings (3)
Directed readings in various areas of Statistics.
STAT 900 Seminar (1)
Preparation and presentation of a one-hour lecture to graduate
students and faculty.
STAT 901 Research (Variable credit 1-15)
Thesis research.
STAT 902 Research Tools in Statistics (1)
Software tools (SAS, Maple, Mathematica, Matlab, LaTeX) and literature
databases (Math Sci Net, STM-Z, preprint archives).
