RESEARCH

Research interests cover a wide range of topics. Our primary research groups are:

Pure Math

Applied Mathematics and Scientific Computation

Relativity

Statistics

We have an active Center for Research in Noncommutative Geometry and Topology that hosts workshops and conferences.

Supervision of MSc reports is available in the areas of Algebra, Analysis, Combinatorics and Graph Theory, Differential Equations, Fluid Mechanics, General Relativity, Geometry, Index Theory, Multivariate Statistics, Number Theory, Numerical Analysis, Operator Algebras, Optimization Techniques, Quantum Gravity and Cosmology, Queueing Theory, Reliability Theory, Sampling Theory, Statistical Computations, Statistical Inference and Wave Propagation.

Supervision of PhD theses is available in several areas. Potential PhD candidates should make clear their research interests and name potential advisors at the time of application.

Departmental computer facilities include 3 SPARC servers with numerous X-terminals and Linux workstations linked to the university's high-speed network backbone. The university has a large number of computer labs providing access to its UNIX and NOVELL servers and an IBM/SP Supercomputer in the Advanced Computing Research Lab. Several PC labs and Unix terminals are available at UNBSJ.

Faculty Members of the Graduate Academic Unit (GAU)

^*TIM ALDERSON, BSc, MA, PhD (W Ontario)
Combinatorics, Finite Geometries, Coding and Information Theory

DAVID BARCLAY, BSc (Carleton), MMath (Waterloo), PhD (W Ontario)
Wave Propagation

^* KEITH DE'BELL, BSc, MSc, PhD (London)
Mathematical Modelling of Physical Systems

DONGLEI DU, BSc (Fudan), MSc (Shandong), PhD (Chinese Acad of Sci), PhD (Texas)
Operations Research; Combinatorial Optimization

^*LAWRENCE E. GAREY, BSc (St. Francis Xavier), MA, PhD (Dalhousie)
Numerical Analysis, Integral Equations

JACK D. GEGENBERG, BA (Colorado), MSc (British Columbia), PhD (Simon Fraser)
General Relativity; Quantum Field Theory

^*R.D. GUPTA, BSc, MSc (Meerut), MA, PhD (Dalhousie)
Multivariate Analysis; Distribution Theory; Statistical Inference; Reliability Theory

^*M.H. HAMDAN, BSc, MSc, PhD (Windsor)
Computational Fluid Dynamics; Flow Through Porous Media; Environmental Flows

M. TARIQ HASAN, BSc, MSc (Dhaka), MSc, PhD (Memorial)
Biostatistics, Statistical Computing, Statistical Teaching, Sequential Analysis, Longitudinal Data Analysis

VIQAR HUSAIN, BSc (Manchester), MPhil, PhD (Yale)
General Relativity, Quantum Gravity, Mathematical Finance and Scientific Computation

COLIN INGALLS, BSc (Dalhousie), PhD (MIT)
Noncommutative Algebra, Algebraic Geometry

S.N. KABADI, BS, MTech (Indian Institute of Technology), PhD (University of Texas at Dallas)
Quantitative Methods

^*MERZIK T. KAMEL, BSc (Assiut), MSc, PhD (Windsor)
Fluid Mechanics and Differential Equations

DAN KUCEROVSKY, BSc (UWO), MSc, DPhil (Magdalen College, Oxford)
C*-algebras and Noncommutative Topology, Mechanics and Differential Equations

RENJUN MA, BSc, MSc, PhD (UBC)
Generalized Linear Models, Survival Analysis, Random Effects Modelling

R.J. MCKELLAR, BMath, MMath (Waterloo), PhD (Arizona)
Relativity; Differential Geometry

BARRY MONSON, BSc (Saskatchewan), MSc, PhD (Toronto)
Discrete and Classical Geometry

ROMAN MUREIKA, BA, MA, PhD (Catholic University of America)
Characteristic Functions; Information; Sampling Theory

JEFFREY D. PICKA, BASc, BSc, MSc (Toronto), PhD (Chicago)
Spatial Statistics, Random Sphere Packings, Properties of Composite Materials

^*GEORGE STOICA, MSc (Bucharest), PhD (Paris)
Probability Theory, Stochastic Processes, Financial Mathematics

VLADIMIR TASIC, BSc (Novi Sad), PhD (Manitoba)
Group Theory; Lie Algebras and Lie Rings; Geometry

HUGH THOMAS, BSc (Toronto), MS, PhD (Chicago)
Algebraic Combinatoris; Algebraic Geometry

JON THOMPSON, BSc (UNB), MA, PhD (Toronto)
Differential Equations

DARYL TINGLEY, BSc, MA (Dalhousie), MSc, PhD (Michigan State)
Functional Analysis; Geometry

MAUREEN TINGLEY, BA (Adelaide), MAT, MSc (Michigan State), MA, PhD (Dalhousie)
Robust Statistics; Information

LIN WANG, BSc, MSc, PhD (Memorial)
Mathematical Biology, Applied Dynamical Systems

JAMES WATMOUGH, BASc, MSc, PhD (UBC)
Mathematical Biology, Mathematical Ecology

^*UNB Saint John

Professors Emeriti

GORDON MASON, BSc (Bishop's), MSc, PhD (McGill)
Ring Theory

BRIAN TUPPER, BSc, PhD, DSc, (London)
General Relativity and Cosmology

Adjunct Professors

^*NABIL BELACEL, BSc (Algiers), PhD (ULB, Brussels)
Research Officer, National Research Council of Canada (NRC)
Operations Research, Data Mining, Multicriteria Classification, Metaheuristics, Machine Learning, e-Health, Bioinformatics

ÉRIC P. MARCHAND, BSc, MSc, PhD (Montréal)
Professor, Université de Sherbrooke
Statistical Decision Theory; Multivariate Analysis

^*ABRAHAM PUNNEN, BSC (Kerala), MSc (Kanpur), PhD (Indian Institute of Technology, Kanpur)
Professor, Simon Fraser University
Operations Research, Combinatorial Optimization, Algorithms & Complexity

T. ROLF TURNER, BA, (Victoria), MSc (Queen's), PhD (Michigan), MStat (New South Wales)
Time Series; Analysis of Unbalanced Designed Experiments

ADMISSION AND DEGREE REQUIREMENTS

Interested persons should also read the Graduate Calendar.

MSc

Candidates for an MSc in Pure or Applied Mathematics should hold a Bachelor's degree with first or second class honours in mathematics from a recognized university. The normal time required for completion of the requirements for the MSc is at least one year. Students with high standings in a Majors program may be admitted to a two-year MSc program.

Candidates for an MSc in Statistics should hold a Bachelor's degree with first or second class honours in mathematics or statistics or equivalent from a recognized university. A candidate with a sufficient background in both mathematics and statistics can complete the MSc in Statistics in one year.

Students who have difficulty with spoken English may have to defer MATH/STAT 6392, and the program will then take at least 16 months.

A student's progress is monitored by a three-member Committee, including the student's supervisor and two other members of the Graduate Academic Unit. Choice of courses, of seminar, report and thesis topics, and of comprehensive examination topics is subject to the Committee's approval.

Candidates for the MSc in Mathematics or Statistics may, with the consent of the Committee, choose one of two options for the degree program, viz., the report or the thesis option. For either option, candidates may be required to take any undergraduate courses deemed necessary to make up for deficiencies in the candidate's background. Further requirements:

Report Option:

1. Seven graduate courses, including at least three from Group A and the remainder from Group B.
2. A written report on an assigned topic and a passing grade in an oral examination on the report.

Thesis Option:

1. Five graduate courses, including at least two from Group A and the remainder from Group B.
2. A written thesis, which must contain original work embodying the results of the candidate's research on an approved topic, and a passing grade in an oral examination on the thesis.

Rules for selection of courses are as follows:

PhD

Candidates for a PhD should hold a Masters degree from a recognized university. Promising students may transfer from the MSc program to the PhD program.

The requirements for the PhD:

1. Any undergraduate or graduate courses required to make up deficiencies in the candidate's background.
2. Four graduate courses, at least three from Group A and the remainder from Group B.
3. A passing grade on each of three comprehensive examinations, to be completed within 18 months of starting the program.
4. A thesis and passing grade on an oral examination on the thesis.

Rules for selection of Group A courses are the same as for the MSc programs, with MATH/STAT 6392 replaced by MATH/STAT 6492. A candidate for PhD, holding an MSc from this Graduate Academic Unit, is not exempt from MATH/STAT 6492.

Each comprehensive examination is a three hour written paper. One examination must be in the candidate's field of specialization. The other two must be chosen from these fields: algebra, analysis, combined algebra and analysis, applied mathematics, topology, differential geometry, combined topology and differential geometry, statistics. The combined algebra and analysis examination is intended for students specializing in applied mathematics or statistics.

Choice of examinations must be approved by the student's Committee. Reading lists for comprehensive examinations are updated periodically, and are available to registered students upon request.

PROGRAM IN APPLIED MATHEMATICS AND THEORETICAL PHYSICS

Applicants who have a suitable background in Applied Mathematics and Theoretical Physics, may be admitted to an MSc program in these areas which is offered jointly by the GAU of Mathematics and Statistics and the GAU of Physics.

In order to enter the program, prospective students will require the approval of both Departments. Students will be attached to one of the Departments, but their course of studies will require the approval of both Departments. Completion of this program will be officially noted on the student's transcript.

1. A minimum of nine one-term graduate courses selected from appropriate courses offered by both GAUs. A maximum of four of these courses may be replaced by undergraduate 4000 level courses selected from the GAU other than the one in which the student is registered. A student may replace two of these 4000 level courses from a GAU other than Mathematics and Statistics or Physics. All course selections require the approval of both the GAU of Mathematics and Statistics and the GAU of Physics.
2. A report on an assigned topic.
3. Any undergraduate courses required to make up deficiencies in the candidate's background (apart from those mentioned in 1 above).

The examining committee for the report shall normally consist of at least three faculty members drawn from the two GAUs, one of whom is the supervisor and the majority of whom are members of the Department in which the candidate is registered.

COURSES OFFERED

A selection of the following courses will be offered in any given year depending upon student enrolment. Reading courses may be taken for graduate credit subject to GAU approval. Mathematics and Statistics students may not take courses marked with an asterisk (^*) for credit. All courses, unless otherwise noted, are for three credit hours (3ch).

Group A

Mathematics
MATH 6001. Real Analysis
MATH 6021. Group Representation Theory
MATH 6022. Group Theory
MATH 6032. Ring Theory
MATH 6053. Topics in Advanced Algebra II
MATH 6131. Qualitative Theory of Differential Equations
MATH 6132. Theory of Partial Differential Equations
MATH 6151. Advanced Topology
MATH 6201. Graph Theory
MATH 6222. Topics in Optimization
MATH 6231. Topics in Differential Equations
MATH 6321. Principles of Combinatorics
MATH 6331. Rational Mechanics
MATH 6332. Mathematical Theory of Relativity
MATH 6392. Seminar in Pure and Applied Mathematics (cr.)
MATH 6492. Advanced Seminar in Pure and Applied Mathematics (cr.)
MATH 6501. Advanced Topics in Mathematics I
MATH 6512. Advanced Topics in Mathematics II
MATH 6615. Linear Programming
MATH 6625. Network Flows
MATH 6635. Approximation Algorithms
MATH 6991. Reading Course
MATH 6992. Reading Course

Statistics
STAT 6211. Mathematical Statistics
STAT 6212. Sample Survey Theory II
STAT 6221. Sequential Analysis
STAT 6222. Linear Models
STAT 6251. Stochastic Process II
STAT 6262. Stochastic Models in Reliability
STAT 6291. Statistical Inference
STAT 6372. Non-Parametric Statistics II
STAT 6392. Seminar in Statistics and Operations Research (cr.)
STAT 6402. Multivariate Statistical Analysis
STAT 6492. Advanced Seminar in Statistics (cr.)
STAT 6801. Advanced Topics in Statistics I
STAT 6812. Advanced Topics in Statistics II
STAT 6891. Reading Course
STAT 6892. Reading Course

Group B

Mathematics
MATH 6013. Topics in Complex Analysis
MATH 6023. Functional Analysis with Applications
MATH 6043. Topics in Advanced Algebra I
MATH 6102. Graph Theory and Programing
MATH 6103. Measure Theory
MATH 6142. Advanced Ordinary Differential Equations
MATH 6153. Topology
MATH 6313. Combinatorial Optimization
MATH 6363. Enumeration Theory
MATH 6413. Fluid Mechanics
MATH 6423. Mathematical Theory of Control
MATH 6433. Calculus of Variations
MATH 6443. Quantum Field Theory
MATH 6453. Special Functions
MATH 6463. Integral Equations
MATH 6473. Introduction to Differential Geometry
MATH 6483. Introduction to General Relativity
MATH 6503. Numerical Methods for Differential Equations
MATH 6633^*. Calculus Revisited
MATH 6634^*. Fundamental Principles of School Mathematics
MATH 6853. Mathematics of Financial Derivatives
MATH 6903. Independent Study in Mathematics

Statistics
STAT 5293^*. Applied Statistics
STAT 5473^*. Experimental Design and Data Analysis in Biology and Forestry
STAT 6043. Sample Survey Theory I
STAT 6053. Regression Analysis
STAT 6073. Non-Parametric Statistics I
STAT 6083. Introduction to Multivariate Statistics
STAT 6323. Dynamic Programing
STAT 6333. Queueing Theory
STAT 6383. Introduction to Stochastic Processes
STAT 6433. Statistical Computing
STAT 6443. Time Series Analysis and Applications
STAT 6473. Experimental Design
STAT 6903. Independent Study in Statistics

Report/Thesis
MATH/STAT 6996. Master's Report (cr.)
MATH/STAT 6997. Master's Thesis (cr.)
MATH/STAT 6998. PhD Thesis