


OttawaCarleton Institute of Mathematics and Statistics
Herzberg Building 4314
Telephone: 5202152
Fax: 5203536
Email: mathstat@carleton.ca
Web site: www.mathstat.carleton.ca
The Institute
Director of the Institute: Matthias Neufang
Associate Director: Vladimir Pestov
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.
The School of Mathematics and Statistics also offers a cooperative
master's program in statistics in collaboration with the federal
government, emphasizi ng practical training through work experience, along
with sound training in statistical inference and basic probability
theory.
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)
 Lucy Campbell, Geophysical fluid dynamics, partial differential
equations (C)
 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)
 Paul Mezo, Algebra and number theory (C)
 S.E. Mills, Applied statistics, statistical methods, inference,
data mining (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 alge bras (UO)
 Matthias Neufang, Analysis (C)
 Mohamedou Ould Haye, Statistics (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)
 Natalia Stepanova, Statistics (C)
 Brett Stevens, Combinatorics (C)
 I. Stojmenovic, Discrete mathematics, combinatorial algorithms,
multiplevalue logic, theoretical computer science (UO)
 Barbara Szyszkowicz, Probability(C)
 Remě 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 o f 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 m ust 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 Desi gn 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 20042005 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 envelop ing 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.
 Prerequ isite: 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 permiss ion 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.
 Prerequisite: undergraduate honours algebra, including group theory
and finite fields.
 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.
 Prerequisit e: 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 haza rd 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 5702 [0.5 cre dit] (MAT 5182)
 Modern Applied and Computational Statistics
 Resampling and computer intensive methods: bootstrap, jackknife
with applications to bias estimation, variance estimation, confidence
intervals, and regression analysis. Smoothing methods in curve
estimation; statistical classification and pattern recognition: error
counting methods, optimal classifiers, bootstrap estimates of the bias
of the misclassification error.
 Prerequisite: permission of the instructor.
 STAT 5703 [0.5 credit] (MAT 5181)
 Data Mining
 Visualization and knowledge discovery in massive datasets;
unsupervised learning: clustering algorithms; dimension reduction;
supervised learning: pattern recognition, smoothing techniques,
classification. Computer software will be used.
 Prerequisite: permission of the instructor.
 STAT 5704 [0.5 credit] (MAT 5174)
 Network Performance
 Advanced techniques in performance evaluation of large complex
networks. Topics may include classical queueing theory and simulation
analysis; models of packet networks; loss and delay systems; blocking
probabilities.
 Prerequisite: some familiarity with probability and stochastic
processes and queueing, or permission of the instructor.
 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, conditio nal 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)
 Topics in Analysis
 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

