


OttawaCarleton Institute of Mathematics and
Statistics
Herzberg Building 4314
Telephone: (613) 5202152
Fax: (613) 5203536
Email: mathstat@carleton.ca
Web site: www.mathstat.carleton.ca
The Institute
Director of the Institute: Philip Scott
Associate Director: Sam Melkonian
Students pursuing studies in pure mathematics, applied
mathematics, probability and statistics at the graduate level
leading to a M.Sc. or a Ph.D. degree do so in a joint program
offered by the School of Mathematics and Statistics at Carleton
University and the Department of Mathematics and Statistics at
the University of Ottawa under the auspices of the
OttawaCarleton Institute of Mathematics and Statistics. The
Institute is responsible for supervising the programs,
regulations, and student admissions, as well as providing a
framework for interaction between the two departments at the
research level.
The list below of all members of the Institute along with
their research interests can be used as a guide to possible
supervisors.
In addition to the programs administered by the Institute,
the School of Mathematics and Statistics at Carleton University
offers several other programs.
In cooperation with the Department of Epidemiology and
Community Medicine at the University of Ottawa, students may
pursue a program leading to an M.Sc. with a Specialization in
Biostatistics. For information, see the OttawaCarleton
Collaborative Program in Biostatistic's section in this
Calendar.
In cooperation with the Department of Systems and Computer
Engineering and the School of Computer Science at Carleton
University, students may pursue a program leading to an M.Sc.
in Information and Systems Science. For information see the
Information and Systems Science section of this Calendar.
Requests for information and completed applications should
be sent to the Director or Associate Director of the
Institute.
Members of the Institute
The home department of each member of the Institute is
indicated by (C) for the School of Mathematics and Statistics,
Carleton University and (UO) for the Department of Mathematics
and Statistics, University of Ottawa.
 Mayer Alvo, Nonparametric statistics, sequential
analysis (UO)
 David Amundsen, Nonlinear wave equations, numerical
analysis (C)
 Nick Barrowman, Biostatistics, applied
statistics (C)
 Y. Billig, Algebra (C)
 R. Blute, Logic, Category theory (UO)
 Amitava Bose, Stochastic modeling, probability
theory (C)
 Y. Bourgault, Numerical methods, mathematical
modeling (UO)
 S. Boyd, Combinatorial optimization, algorithm
design and analysis, graph theory, polyhedral
combinatorics (UO)
 W.D. Burgess, Algebra, noncommutative rings
(UO)
 Charles Castonguay, Demography (UO)
 Miklós Csörgó, Probability and statistics
(C)
 A.R. Dabrowski, Invariance principles, weakly
dependent variables (UO)
 Daniel Daigle, Algebraic geometry, commutative
algebra (UO)
 D.A. Dawson, Stochastic processes and probability
theory (C)
 Benoit Dionne, Ordinary differential equations,
bifurcation theory (UO)
 J.D. Dixon, Group theory, algebra computation
(C)
 Vlastimil Dlab, Finite dimensional algebras,
representation theory (C)
 Kokou Dossou, Numerical solution of partial
differential equations of mathematical physics (C)
 P. Farrell, Sampling, discrete data, applied
statistics (C)
 P. Felty, Automated deduction, logic, formal methods
in software engineering (UO)
 CheKao Fong, Operator theory (C)
 Eric Freeman, Number theory (C)
 Zhicheng Gao, Graph theory (C)
 C.W.L. Garner, Foundations of geometry (C)
 Thierry Giordano, Operator algebras, ergodic
theory (UO)
 D.E. Handelman, Ktheory, operator algebras, ring
theory (UO)
 Roger HerzFischler, History and sociology of
mathematics (C)
 B.G. Ivanoff, Probability, point processes,
martingales (UO)
 W. Jaworski, Analysis, probability (C)
 Barry Jessup, Rational homotopy (UO)
 Alexander Kitaev, Isomonodromy deformations,
Painleve equations (C)
 Daniel Krewski, Applied statistics in medicine
(C)
 E.O. Kreyszig, Partial differential equations,
numerical analysis (C)
 V. LeBlanc, Dynamical systems, bifurcation theory,
mathematical cosmology (UO)
 J. Levy, Lie groups (UO)
 I.A. Manji, Homological methods in commutative
algebra and algebraic geometry, cryptography (C)
 D.R. McDonald, Applied probability (UO)
 Sam Melkonian, Nonlinear differential equations
(C)
 S.E. Mills, Applied statistics, statistical methods,
inference (C)
 A.B. Mingarelli, Ordinary differential equations,
difference equations (C)
 M. Mojirsheibani, Resampling, classification and
pattern recognition (C)
 B.C. Mortimer, Group theory, coding theory
(C)
 L. Moura, Combinatorial algorithms and optimization,
combinatorics, (UO)
 Erhard Neher, Jordan algebras (UO)
 Matthias Neufang, Analysis (C)
 D. Panario, Finite fields, combinatorics, analysis
of algorithms (C)
 J.N. Pandey, Generalized functions, partial
differential equations (C)
 Chul Gyu Park, Statistics (C)
 J.C. Poland, Group theory (C)
 I.S. Pressman, Optimization, algebra (C)
 Michel Racine, Jordan algebras (UO)
 Mizanur Rahman, Special functions (C)
 J.N.K. Rao, Sample surveys theory and methods
(C)
 P. Révész, Probability (CU)
 Luis Ribes, Group theory (C)
 R.B. Richter, Graph theory, combinatorics
(C)
 Ivan Rival, Combinatorics, algorithms (UO)
 Wulf Rossmann, Lie groups (UO)
 Damien Roy, Number theory (UO)
 A.K. Md. E. Saleh, Order statistics, mathematical
statistics (C)
 Matias SalibianBarrera, Robust inference,
resampling methods (C)
 P. Sawyer, Differential geometry (UO)
 P.J. Scott, Logic, Category theory (UO)
 A. Sebbar, Number theory, quantum groups
(UO)
 P. Selinger, Logic, category theory (UO)
 A. Singh, Statistics (C)
 Benjamin Steinberg, Algebra (C)
 Brett Stevens, Combinatorics (C)
 I. Stojmenovic, Discrete mathematics, combinatorial
algorithms, multiplevalue logic, theoretical computer
science (UO)
 Barbara Szyszkowicz, Probability(C)
 Rémi Vaillancourt, Partial differential
equations, numerical Methods (UO)
 G. Walsh, Number theory (UO)
 K. S. Williams, Number theory (C)
 M. Zarepour, Resampling and nonparametric Bayesian
inference, time series analysis (UO)
 Y. Zhao, Applied probability (C)
Master of Science
Admission Requirements
The normal requirement for admission to the master's program
is an Honours bachelor's degree in mathematics, or the
equivalent, with at least high honours standing. Applicants
holding a general (3year) degree with at least high honours
standing may be admitted to a qualifyingyear program.
Subsequent admission to the regular master's program depends
on performance during the qualifyingyear program and will be
decided no later than one year after admission to the
qualifyingyear program. Details are outlined in the General
Regulations section of this Calendar. Students with outstanding
academic performance and research promise while in the M.Sc.
program may be permitted to transfer to the Ph.D. program
without completing the M.Sc. program.
Special consideration may be given, for acceptance in the
hightechnology concentration, to graduates in computer science
or engineering with a strong mathematical background and work
experience in the hightechnology sector.
Program Requirements
The two options for the M.Sc. program are:
 2.5 credits and a thesis
 4.0 credits
The courses must be chosen from those at the graduate level
except that a student may take up to 1.0 credit of
undergraduate courses at the 4000level to satisfy these
requirements. Not all these courses may be taken in the same
field of mathematics; at least 1.0 credit must be in another
field. All master's students are required to participate
actively in a seminar or project under the guidance of their
adviser. A maximum of 1.0 credit taken outside of the School of
Mathematics and Statistics at Carleton University or the
Department of Mathematics and Statistics at the University of
Ottawa may be allowed for credit.
Students who plan to specialize in probability or statistics
are strongly advised that during their master's program they
include, where possible, the courses STAT 5600, STAT 5501 in
mathematical statistics, STAT 4502, STAT 5505 in applied
statistics, and STAT 4501, STAT 5701 in probability, together
with 1.0 credit further in the School of Mathematics and
Statistics. In addition, a graduate course in another field,
such as biology, biostatistics, economics, computer science,
systems analysis, and stochastic modeling, is highly
recommended.
HighTechnology Concentration in the M.Sc.
An M.Sc. with a hightechnology concentration is available.
This concentration is intended for mathematics graduates
interested in employment in the high technology area; it is
also intended for science or engineering graduates currently
employed in the hightechnology area who require a greater
understanding of mathematics for their work. The course
requirement for the hightechnology designation on a student's
transcript is completion of a minimum of five courses for the
thesis option and six courses for the nonthesis option,
selected from the list of hightechnology courses authorized by
the Director of the Institute. Each student will be assigned an
adviser who will be responsible for approving course
selection.
Doctor of Philosophy
Admission Requirements
The normal requirement for admission to the Ph.D. program is
a master's degree in mathematics, or the equivalent, with at
least high honours standing. Details are outlined in the
General Regulations section of this Calendar.
Program Requirements
Course requirements, which are determined at the time of
admission, include a minimum of 3.0 credits and a suitable
thesis. Not all of these courses may be taken in the same field
of mathematics; at least 1.0 credit must be in another
field.
All candidates must take comprehensive examinations, and
must satisfy a language requirement. The language requirement
is determined by the candidate's advisory committee and
normally requires the ability to read mathematical literature
in a language considered useful for his/her research or career,
and other than the candidate's principal language of study.
Students specializing in mathematics or probability
undertake a comprehensive examination in the following
areas:
 The candidate's general area of specialization at the
Ph.D. level
 Examinations on two topics chosen from algebra,
analysis, probability, topology, and statistics. (This
choice excludes the student's specialty.)
Students specializing in statistics must write an
examination in the following areas:
 Mathematical statistics which includes multivariate
analysis
 An examination in probability, and
 An examination in either (i) applied statistics, or
(ii) analysis
In all cases, the examination must be completed successfully
within twenty months of initial registration in the Ph.D.
program in the case of fulltime students, and within
thirtyeight months of initial registration in the case of
parttime students.
All Ph.D. candidates are also required to undertake a final
oral examination on the subject of their thesis.
Selection of Courses
The following undergraduate courses may, with the approval
of the School of Mathematics and Statistics, be selected by
master's candidates in partial fulfillment of their degree
requirements:
 Mathematics and Statistics
 MATH 4001 Vector Calculus
 MATH 4105 Rings and Modules
 MATH 4107 Commutative Algebra
 MATH 4207 Foundations of Geometry
 MATH 4208 Introduction to Differentiable Manifolds
 MATH 4405 Analytical Dynamics
 MATH 4406 Hydrodynamics and Elasticity
 MATH 4407 Tensor Analysis and Relativity Theory
 STAT 4501 Probability Theory
 STAT 4502 Sampling: Theory and Methods
 STAT 4503 Applied Multivariate Analysis
 STAT 4506 NonParametric Methods
 STAT 4508 Stochastic Models
 STAT 4509 Stochastic Optimization
 MATH 4702 Integral Transforms
 MATH 4703 Qualitative Theory of Ordinary Differential
Equations
 MATH 4802 Introduction to Mathematical Logic
 MATH 4803 Topics in Applied Logic
 MATH 4804 Design and Analysis of Algorithms
 MATH 4806 Numerical Analysis
 MATH 4808 Graph Theory and Algorithms
Graduate Courses
Not all of the following courses are offered in a given
year. For an uptodate statement of course offerings for
20032004 and to determine the term of offering, consult the
Registration Instructions and Class Schedule booklet, published
in the summer and also available online at
www.carleton.ca/cu/programs/sched_dates/
Course Designation System
Carleton's course designation system has been restructured.
The first entry of each course description below is the new
alphanumeric Carleton course code, followed by its credit value
in brackets. The old Carleton course number (in parentheses) is
included for reference, where applicable.
University of Ottawa course numbers (in parentheses) follow
the Carleton course number and credit information.
 MATH 5001 [0.5 credit] (formerly 70.501) (MAT
5120)
 Abstract Measure Theory
 Abstract measure and integral, Lspaces, complex
measures, product measures, differentiation theory, Fourier
transforms.
 Prerequisite: MATH 4007.
 MATH 5003 [0.5 credit] (formerly 70.503) (MAT
5122)
 Banach Algebras
 Commutative Banach algebras; the space of maximal
ideals; representation of Banach algebras as function
algebras and as operator algebras; the spectrum of an
element. Special types of Banach algebras: for example,
regular algebras with involution, applications.
 MATH 5004 [0.5 credit] (formerly 70.504) (MAT
5129)
 Integral Equations
 A survey of the main results in the theory of
nonsingular linear integral equations; Volterra and
Fredholm equations of first and second kind in the L2 case,
with special results for the continuous case; Hermitian
kernels; eigenfunction expansions; compact operators.
 Prerequisites: MATH 3002 and MATH 4003.
 MATH 5005 [0.5 credit] (formerly 70.505) (MAT
5127)
 Complex Analysis
 Complex differentiation and integration, harmonic
functions, maximum modulus principle, Runge's theorem,
conformal mapping, entire and meromorphic functions,
analytic continuation.
 MATH 5006 [0.5 credit] (formerly 70.506) (MAT
5316)
 Topological Vector Spaces
 Construction of new topological vector spaces out of
given ones; local convexity and the HahnBanach theorem;
compactness and the KreinMilman theorem; conjugate spaces,
polar sets.
 Prerequisite: MATH 4003.
 MATH 5007 [0.5 credit] (formerly 70.507) (MAT
5125)
 Real Analysis I (Measure Theory and
Integration)
 General measure and integral, Lebesgue measure and
integration on R, Fubini's theorem, LebesgueRadonNikodym
theorem, absolute continuity and differentiation,
LPspaces. Selected topics such as DaniellStone theory.
Also offered, with different requirements, as MATH 4007 for
which additional credit is precluded.
 Prerequisites: MATH 3001 and MATH 3002 (MAT 3125) or
permission of the Department.
 MATH 5008 [0.5 credit] (formerly 70.508) (MAT
5126)
 Real Analysis II (Functional Analysis)
 Banach and Hilbert spaces, bounded linear operators,
dual spaces. Topics selected from: weaktopologies,
Alaoglu's theorem, compact operators, differential calculus
in Banach spaces, Riesz representation theorems. Also
offered, with different requirements, as MATH 4003 for
which additional credit is precluded.
 Prerequisite: MATH 5007 (MAT 5125) or permission of the
Department.
 MATH 5009 [0.5 credit] (formerly 70.509) (MAT
5121)
 Introduction to Hilbert Space
 Geometry of Hilbert Space, spectral theory of linear
operators in Hilbert Space.
 Prerequisites: MATH 3001, MATH 3002, and MATH
4003.
 MATH 5102 [0.5 credit] (formerly 70.512) (MAT
5148)
 Group Representations and Applications
 An introduction to group representations and character
theory, with selected applications.
 MATH 5103 [0.5 credit] (formerly 70.513) (MAT
5146)
 Rings and Modules
 Generalizations of the WedderburnArtin theorem and
applications, homological algebra.
 MATH 5104 [0.5 credit] (formerly 70.514) (MAT
5143)
 Lie Algebras
 Basic concepts: ideals, homomorphisms, nilpotent,
solvable, semisimple. Representations, universal
enveloping algebra. Semisimple Lie algebras: structure
theory, classification, and representation theory.
 Prerequisites: MATH 5107 (MAT 5141) and MATH 5109 (MAT
5142) or permission of the Department.
 MATH 5106 [0.5 credit] (formerly 70.516) (MAT
5145)
 Group Theory
 Fundamental principles as applied to abelian,
nilpotent, solvable, free, and finite groups;
representations. Also offered, with different requirements,
as MATH 4106, for which additional credit is
precluded.
 Prerequisite: MATH 3100 or permission of the
Department.
 MATH 5107 [0.5 credit] (formerly 70.517) (MAT
5141)
 Algebra I
 Groups, Sylow subgroups, finitely generated abelian
groups. Rings, field of fractions, principal ideal domains,
modules. Polynomial algebra, Euclidean algorithm, unique
factorization.
 Prerequisite: permission of the Department.
 MATH 5108 [0.5 credit] (formerly 70.518) (MAT
5147)
 Homological Algebra and Category Theory
 Axioms of set theory, categories, functors, natural
transformations; free, projective, injective and flat
modules; tensor products and homology functors, derived
functors; dimension theory. Also offered, with different
requirements, as MATH 4108 for which additional credit is
precluded.
 Prerequisite: MATH 3100 or permission of the
Department.
 MATH 5109 [0.5 credit] (formerly 70.519) (MAT
5142)
 Algebra II
 Field theory, algebraic and transcendental extensions,
finite fields, Galois groups. Modules over principal ideal
domains, decomposition of a linear transformation, Jordan
normal form.
 Prerequisites: MATH 5107 (MAT 5141) and permission of
the Department.
 MATH 5201 [0.5 credit] (formerly 70.521) (MAT
5150)
 Topics in Geometry
 Various axiom systems of geometry. Detailed
examinations of at least one modern approach to
foundations, with emphasis upon the connections with group
theory.
 Prerequisite: permission of the Department.
 MATH 5202 [0.5 credit] (formerly 70.522) (MAT
5168)
 Homology Theory
 The EilenbergSteenrod axioms and their consequences,
singular homology theory, applications to topology and
algebra.
 Prerequisite: MATH 4205.
 MATH 5205 [0.5 credit] (formerly 70.525) (MAT
5151)
 Topology I
 Topological spaces, product and identification
topologies, countability and separation axioms,
compactness, connectedness, homotopy, fundamental group,
net and filter convergence. Also offered, with different
requirements, as MATH 4205 for which additional credit is
precluded.
 Prerequisite: MATH 3001 or permission of the
Department.
 MATH 5206 [0.5 credit] (formerly 70.526) (MAT
5152)
 Topology II
 Covering spaces, homology via the EilenbergSteenrod
Axioms, applications, construction of a homology functor.
Also offered, with different requirements, as MATH 4206 for
which additional credit is precluded.
 Prerequisites: MATH 3100 (MAT 3143) and MATH 5205 (MAT
5151) or permission of the Department.
 MATH 5207 [0.5 credit] (formerly 70.527) (MAT
5169)
 Foundations of Geometry
 A study of at least one modern axiom system of
Euclidean and nonEuclidean geometry, embedding of
hyperbolic and Euclidean geometries in the projective
plane, groups of motions, models of nonEuclidean
geometry.
 Prerequisite: MATH 3100 (may be taken concurrently) or
permission of the Department.
 MATH 5208 [0.5 credit] (formerly 70.528) (MAT
5155)
 Differentiable Manifolds
 A study of differentiable manifolds from the point of
view of either differential topology or differential
geometry. Topics such as smooth mappings, transversality,
intersection theory, vector fields on manifolds, Gaussian
curvature, Riemannian manifolds, differential forms,
tensors, and connections are included.
 Prerequisite: MATH 3001 or permission of the
Department.
 MATH 5300 [0.5 credit] (MAT 5160)
 Mathematical Cryptography
 Analysis of cryptographic methods used in
authentication and data protection, with particular
attention to the underlying mathematics, e.g. Algebraic
Geometry, Number Theory, and Finite Fields. Advanced topics
on PublicKey Cryptography: RSA and integer factorization,
DiffieHellman, discrete logarithms, elliptic curves.
Topics in current research.
 MATH 5301 [0.5 credit] (formerly 70.531) (MAT
5161)
 Mathematical Logic
 A basic graduate course in mathematical logic.
Propositional and predicate logic, proof theory, Gentzen's
CutElimination, completeness, compactness, Henkin models,
model theory, arithmetic and undecidability. Special topics
(time permitting) depending on interests of instructor and
audience.
 Prerequisites: Honours undergraduate algebra, analysis
and topology or permission of the instructor.
 MATH 5305 [0.5 credit] (formerly 70.535) (MAT
5163)
 Analytic Number Theory
 Dirichlet series, characters, Zetafunctions, prime
number theorem, Dirichlet's theorem on primes in arithmetic
progressions, binary quadratic forms. Also offered at the
undergraduate level, with different requirements, as MATH
4305, for which additional credit is precluded.
 Prerequisite: MATH 3007 or permission of the
Department.
 MATH 5306 [0.5 credit] (formerly 70.536) (MAT
5164)
 Algebraic Number Theory
 Algebraic number fields, bases, algebraic integers,
integral bases, arithmetic in algebraic number fields,
ideal theory, class number. Also offered, with different
requirements, as MATH 4306 for which additional credit is
precluded.
 Prerequisite: MATH 3100 or permission of the
Department.
 MATH 5403 (formerly 70.543) (MAT 5187)
 Topics in Applied Mathematics
 MATH 5405 [0.5 credit] (formerly 70.545) (MAT
5131)
 Ordinary Differential Equations
 Existence and uniqueness theorems, boundary value
problems, qualitative theory.
 Prerequisite: MATH 3008 or permission of the
Department.
 MATH 5406 [0.5 credit] (formerly 70.546) (MAT
5133)
 Introduction to Partial Differential
Equations
 First order linear, quasilinear, and nonlinear
equations; second order equations in two or more variables;
systems of equations; the wave equation; Laplace and
Poisson equations; Dirichlet and Neumann problems; Green's
functions. Also offered, with different requirements, as
MATH 4700 for which additional credit is precluded.
 Prerequisites: MATH 3002, or MATH 3007 and MATH 3008,
or permission of the Department.
 MATH 5407 [0.5 credit] (formerly 70.547) (MAT
5134)
 Topics in Partial Differential Equations
 Theory of distributions, initialvalue problems based
on twodimensional wave equations, Laplace transform,
Fourier integral transform, diffusion problems, Helmholtz
equation with application to boundary and initialvalue
problems in cylindrical and spherical coordinates. Also
offered, with different requirements, as MATH 4701 for
which additional credit is precluded.
 Prerequisite: MATH 5406 or permission of the
Department.
 STAT 5500 [0.5 credit] (formerly 70.550) (MAT
5177)
 Multivariate Normal Theory
 Multivariate normal distribution properties,
characterization, estimation of means, and covariance
matrix. Regression approach to distribution theory of
statistics; multivariate tests; correlations;
classification of observations; Wilks' criteria.
 Prerequisite: MATH 3500.
 STAT 5501 [0.5 credit] (formerly 70.551) (MAT
5191)
 Mathematical Statistics II
 Confidence intervals and pivotals; Bayesian intervals;
optimal tests and NeymanPearson theory; likelihood ratio
and score tests; significance tests; goodnessoffittests;
large sample theory and applications to maximum likelihood
and robust estimation. Also offered, with different
requirements, as MATH 4507 for which additional credit is
precluded.
 Prerequisite: MATH 4500 or STAT 5600 or permission of
the Department.
 STAT 5502 [0.5 credit] (formerly 70.552) (MAT
5192)
 Sampling Theory and Methods
 Unequal probability sampling with and without
replacement; unified theory for standard errors; prediction
approach; ratio and regression estimation; stratification
and optimal designs; multistage cluster sampling; double
sampling; domains of study; poststratification;
nonresponse; measurement errors; related topics.
 Prerequisite: MATH 4502 or permission of the
Department.
 STAT 5503 [0.5 credit] (formerly 70.553) (MAT
5193)
 Linear Models
 Theory of non full rank linear models; estimable
functions, best linear unbiased estimators, hypotheses
testing, confidence regions; multiway classifications;
analysis of covariance; variance component models; maximum
likelihood estimation, Minque, Anova methods; miscellaneous
topics.
 Prerequisite: MATH 4500 or STAT 5600 or permission of
the Department.
 STAT 5504 [0.5 credit] (formerly 70.554) (MAT
5194)
 Stochastic Processes and Time Series
Analysis
 Stationary stochastic processes, inference for
stochastic processes, applications to time series and
spatial series analysis.
 Prerequisite: MATH 4501 or permission of the
Department.
 STAT 5505 [0.5 credit] (formerly 70.555) (MAT
5195)
 Design of Experiments
 Overview of linear model theory; orthogonality;
randomized block and split plot designs; latin square
designs; randomization theory; incomplete block designs;
factorial experiments: confounding and fractional
replication; response surface methodology. Miscellaneous
topics.
 Prerequisite: STAT 3505 or STAT 4500 or STAT 5600 or
permission of the Department.
 STAT 5506 [0.5 credit] (formerly 70.556) (MAT
5175)
 Robust Statistical Inference
 Nonparametric tests for location, scale, and regression
parameters; derivation of rank tests; distribution theory
of linear rank statistics and their efficiency. Robust
estimation of location, scale and regression parameters;
Huber's Mestimators, Rankmethods, Lestimators. Influence
function. Adaptive procedures. Also offered, with different
requirements, as MATH 4506 for which additional credit is
precluded.
 Prerequisite: MATH 4500 or STAT 5600 or permission of
the Department.
 STAT 5507 [0.5 credit] (formerly 70.557) (MAT
5176)
 Advanced Statistical Inference
 Pure significance test; uniformly most powerful
unbiased and invariant tests; asymptotic comparison of
tests; confidence intervals; largesample theory of
likelihood ratio and chisquare tests; likelihood
inference; Bayesian inference; fiducial and structural
methods; resampling methods.
 Prerequisite: MATH 4507 or STAT 5501 or permission of
the Department.
 STAT 5508 [0.5 credit] (formerly 70.558) (MAT
5172)
 Topics in Stochastic Processes
 Course contents will vary, but will include topics
drawn from Markov processes. Brownian motion, stochastic
differential equations, martingales, Markov random fields,
random measures, and infinite particle systems, advanced
topics in modeling, population models, etc.
 Prerequisites: STAT 3506 or STAT 4501, or permission of
the Department.
 STAT 5509 [0.5 credit] (formerly 70.559) (MAT
5196)
 Multivariate Analysis
 Multivariate methods of data analysis, including
principal components, cluster analysis, factor analysis,
canonical correlation, MANOVA, profile analysis,
discriminant analysis, path analysis. Also offered at the
undergraduate level, with different requirements, as MATH
4503, for which additional credit is precluded.
 Prerequisite: MATH 4500 or STAT 5600 or permission of
the Department.
 STAT 5600 [0.5 credit] (formerly 70.560) (MAT
5190)
 Mathematical Statistics I
 Statistical decision theory; likelihood functions;
sufficiency; factorization theorem; exponential families;
UMVU estimators; Fisher's information; CramerRao lower
bound; maximum likelihood, moment estimation; invariant and
robust point estimation; asymptotic properties; Bayesian
point estimation. Also offered, with different
requirements, as MATH 4500 for which additional credit is
precluded.
 Prerequisite: MATH 3500 or permission of the
Department.
 STAT 5601 [0.5 credit] (formerly 70.561) (MAT
5197)
 Stochastic Optimization
 Topics chosen from stochastic dynamic programming,
Markov decision processes, search theory, optimal stopping.
Also offered at the undergraduate level, with different
requirements, as MATH 4509, for which additional credit is
precluded.
 Prerequisite: STAT 3506 or permission of the
Department.
 STAT 5602 [0.5 credit] (formerly 70.562) (MAT
5317)
 Analysis of Categorical Data
 Analysis of oneway and twoway tables of nominal data;
multidimensional contingency tables, loglinear models;
tests of symmetry, marginal homogeneity in square tables;
incomplete tables; tables with ordered categories; fixed
margins, logistic models with binary response; measures of
association and agreement; applications biological
 Prerequisites: MATH 4500 or STAT 5600, MATH 4507 or
STAT 5501, or permission of the Department.
 STAT 5603 [0.5 credit] (formerly 70.563) (MAT
5318)
 Reliability and Survival Analysis
 Types of censored data; nonparametric estimation of
survival function; graphical procedures for model
identification; parametric models and maximum likelihood
estimation; exponential and Weibull regression models;
nonparametric hazard function models and associate
statistical inference; rank tests with censored data
applications.
 Prerequisites: MATH 4500 or STAT 5600, MATH 4507 or
STAT 5501 or permission of the Department.
 STAT 5604 [0.5 credit] (formerly 70.564) (MAT
5173)
 Stochastic Analysis
 Brownian motion, continuous martingales, and stochastic
integration.
 Prerequisites: MATH 4501 or STAT 5708 or permission of
the Department.
 MATH 5605 [0.5 credit] (formerly 70.565) (MAT
5165)
 Theory of Automata
 Algebraic structure of sequential machines,
decomposition of machines; finite automata, formal
languages; complexity. Also offered, with different
requirements, as MATH 4805/COMP 4805 for which additional
credit is precluded.
 Prerequisite: MATH 2100 or permission of the
Department.
 MATH 5607 [0.5 credit] (formerly 70.567) (MAT
5324)
 Game Theory
 Twoperson zerosum games; infinite games; multistage
games; differential games; utility theory; twoperson
generalsum games; bargaining problem; nperson games;
games with a continuum of players. Also offered, with
different requirements, as MATH 4807 for which additional
credit is precluded.
 Prerequisite: MATH 3001 or permission of the
Department.
 MATH 5609 [0.5 credit] (formerly 70.569) (MAT
5301)
 Topics in Combinatorial Mathematics
 Prerequisite: permission of the Department.
 STAT 5701 [0.5 credit] (formerly 70.571) (MAT
5198)
 Stochastic Models
 Markov systems, stochastic networks, queuing networks,
spatial processes, approximation methods in stochastic
processes and queuing theory. Applications to the modeling
and analysis of computercommunications systems and other
distributed networks. Also offered, with different
requirements, as MATH 4508 for which additional credit is
precluded.
 Prerequisite: STAT 3506 or permission of the
Department.
 STAT 5708 [0.5 credit] (formerly 70.578) (MAT
5170)
 Probability Theory I
 Probability spaces, random variables, expected values
as integrals, joint distributions, independence and product
measures, cumulative distribution functions and extensions
of probability measures, BorelCantelli lemmas, convergence
concepts, independent identically distributed sequences of
random variables.
 Prerequisites: MATH 3001, MATH 3002, and MATH 3500, or
permission of the Department.
 STAT 5709 [0.5 credit] (formerly 70.579) (MAT
5171)
 Probability Theory II
 Laws of large numbers, characteristic functions,
central limit theorem, conditional probabilities and
expectations, basic properties and convergence theorems for
martingales, introduction to Brownian motion.
 Prerequisite: STAT 5708 (MAT 5170) or permission of the
Department.
 MATH 5801 [0.5 credit] (formerly 70.581) (MAT
5303)
 Linear Optimization
 Linear programming problems; simplex method, upper
bounded variables, free variables; duality; postoptimality
analysis; linear programs having special structures;
integer programming problems; unimodularity; knapsack
problem.
 Prerequisite: course in linear algebra and permission
of the Department.
 MATH 5802 [0.5 credit] (formerly 70.582) (MAT
5325)
 Introduction to Information and Systems
Science
 Introduction to the process of applying computers in
problem solving. Emphasis on the design and analysis of
efficient computer algorithms for large, complex problems.
Applications: data manipulation, databases, computer
networks, queuing systems, optimization. (Also listed as
SYSC 5802, COMP 5802 and ISYS 5802.)
 MATH 5803 [0.5 credit] (formerly 70.583) (MAT
5304)
 Nonlinear Optimization
 Methods for unconstrained and constrained optimization
problems; KuhnTucker conditions; penalty functions;
duality; quadratic programming; geometric programming;
separable programming; integer nonlinear programming;
pseudoBoolean programming; dynamic programming.
 Prerequisite: permission of the Department.
 MATH 5804 [0.5 credit] (formerly 70.584) (MAT
5307)
 Topics in Operations Research
 MATH 5805 [0.5 credit] (formerly 70.585) (MAT
5308)
 Topics in Algorithm Design
 MATH 5806 [0.5 credit] (formerly 70.586) (MAT
5180)
 Numerical Analysis
 Error analysis for fixed and floating point arithmetic;
systems of linear equations; eigenvalue problems; sparse
matrices; interpolation and approximation, including
Fourier approximation; numerical solution of ordinary and
partial differential equations.
 Prerequisite: permission of the Department.
 MATH/COMP 5807 [0.5 credit] (formerly 70.587) (MAT
5167)
 Formal Language and Syntax Analysis
 Computability, unsolvable and NPhard problems. Formal
languages, classes of language automata. Principles of
compiler design, syntax analysis, parsing (topdown,
bottomup), ambiguity, operator precedence, automatic
construction of efficient parsers, LR, LR(O), LR(k), SLR,
LL(k). Syntax directed translation.
 Prerequisites: MATH 5605 or MATH 4805 or COMP 3002, or
permission of the Department.
 MATH 5808 [0.5 credit] (formerly 70.588) (MAT
5305)
 Combinatorial Optimization I
 Network flow theory and related material. Topics will
include shortest paths, minimum spanning trees, maximum
flows, minimum cost flows. Optimal matching in bipartite
graphs.
 Prerequisite: permission of the Department.
 MATH 5809 [0.5 credit] (formerly 70.589) (MAT
5306)
 Combinatorial Optimization II
 Topics include optimal matching in nonbipartite
graphs, Euler tours and the Chinese Postman problem. Other
extensions of network flows: dynamic flows, multicommodity
flows, and flows with gains, Bottleneck problems. Matroid
optimization. Enumerative and heuristic algorithms for the
Traveling Salesman and other "hard" problems.
 Prerequisite: MATH 5808.
 MATH 5900 [0.5 credit] (formerly 70.590) (MAT
5990)
 Seminar
 MATH 5901 [0.5 credit] (formerly 70.591) (MAT
5991)
 Directed Studies
 STAT 5902 [0.5 credit] (formerly 70.592) (MAT
5992)
 Seminar in Biostatistics
 Students work in teams on the analysis of experimental
data or experimental plans. The participation of
experimenters in these teams is encouraged. Student teams
present their results in the seminar, and prepare a brief
written report on their work.
 MATH 5903 [0.5 credit] (formerly 70.593)
 Project
 Intended for students registered in Information and
Systems Science and M.C.S. programs. Students pursuing the
nonthesis option will conduct a study, analysis, and/or
design project. Results will be given in the form of a
typewritten report and oral presentation.
 STAT 5904 [0.5 credit] (formerly 70.594)
 Statistical Internship
 This projectoriented course allows students to
undertake statistical research and data analysis projects
as a cooperative project with governmental or industrial
sponsors. Practical data analysis and consulting skills
will be emphasized. The grade will be based upon oral and
written presentation of results.
 Prerequisite: permission of the Institute.
 MATH/SYSC/COMP 5905 [2.0 credits] (formerly
70/94/95.595)
 M.C.S. Thesis
 MATH 5906 (formerly 70.596) (MAT 5993)
 Research Internship
 This course affords students the opportunity to
undertake research in mathematics as a cooperative project
with governmental or industrial sponsors. The grade will be
based upon the mathematical content as well as upon oral
and written presentation of results.
 Prerequisite: permission of the Institute.
 MATH/ISYS/SYSC/COMP 5908 [1.5 credits] (formerly
70/93/94/95.598)
 M.Sc. Thesis in Information and Systems
Science
 MATH 5909 [1.5 credits] (formerly 70.599)
 M.Sc. Thesis
 MATH 6002 [0.5 credit] (formerly 70.602) (MAT
5309)
 Harmonic Analysis on Groups
 Transformation groups; Haar measure; unitary
representations of locally compact groups; completeness and
compact groups; character theory; decomposition.
 MATH 6008 [0.5 credit] (formerly 70.608) (MAT
5326)
 MATH 6009 [0.5 credit] (formerly 70.609) (MAT
5329)
 Topics in Analysis
 MATH 6101 [0.5 credit] (formerly 70.611) (MAT
5327)
 Topics in Algebra
 MATH 6102 [0.5 credit] (formerly 70.612) (MAT
5330)
 Topics in Algebra
 MATH 6103 [0.5 credit] (formerly 70.613) (MAT
5331)
 Topics in Algebra
 MATH 6104 [0.5 credit] (formerly 70.614) (MAT
5158)
 Lie Groups
 Matrix groups: oneparameter groups, exponential map,
CampbellHausdorff formula, Lie algebra of a matrix group,
integration on matrix groups. Abstract Lie groups.
 Prerequisites: MATH 5007 and PADM 5107 or permission of
the Department.
 MATH 6201 [0.5 credit] (formerly 70.621) (MAT
5312)
 Topics in Topology
 MATH 6507 [0.5 credit] (formerly 70.657) (MAT
5313)
 Topics in Probability and Statistics
 MATH 6508 [0.5 credit] (formerly 70.658) (MAT
5314)
 Topics in Probability and Statistics
 MATH 6806 [0.5 credit] (formerly 70.686) (MAT
5361)
 Topics in Mathematical Logic
 MATH 6807 [0.5 credit] (formerly 70.687) (MAT
5162)
 Mathematical Foundations of Computer
Science
 Foundations of functional languages, lambda calculi
(typed, polymorphically typed, untyped), CurryHoward
Isomorphism, proofsasprograms, normalization and
rewriting theory, operational semantics, type assignment,
introduction to denotational semantics of programs,
fixedpoint programming.
 Prerequisites: honours undergraduate algebra and either
topology or analysis, permission of the instructor or some
acquaintance with logic.
 MATH 6900 [0.5 credit] (formerly 70.690) (MAT
6990)
 Seminar
 MATH 6901 [0.5 credit] (formerly 70.691) (MAT
6991)
 Directed Studies
 MATH 6909 (formerly 70.699)
 Ph.D. Thesis

