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2014-2015 Academic Year
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Graduate Studies Courses of Instruction Mathematics and Statistics


Mathematics and Statistics
COURSES IN MATHEMATICS
The department usually around 30 of the following courses each academic year.
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MATH-800* Seminar
Students are expected to participate in a weekly seminar in which they are required to present material on a topic that relates to their research.
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MATH-801* Graph Theory
An introduction to graph theory, one of the central disciplines of discrete mathematics. Topics include: graphs and subgraphs, trees, bond and cycle spaces, connectivity, Euler tours and Hamiltonian cycles, matchings, independent sets, cliques and networks (if time permits). (Offered jointly with MATH-401*.)
Three term-hours, fall; lectures.
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MATH-802* Combinatorics: Enumeration and Designs
An introduction to two subjects which together with MATH-801* provide an entry into discrete mathematics and its applications. Among the enumeration techniques covered are inclusion-exclusion, recurrence relations, and generating functions. The study of designs includes finite geometries and Latin squares. (Offered jointly with MATH-402*.) Three term-hours, winter; lectures.
EXCLUSIONS: MATH-803*, MATH-804*.
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MATH-805* Applications of Matrix Algebra
Among the topics covered are: similarity and canonical forms; non-negative matrices and Perron-Frobenius theory (with applications to probability theory and Markov chains); matrix differential equations and stability theory; estimation of eigenvalues using Gersgorin's theorem and related inequalities. (Offered jointly with MATH-405*.) Three term-hours, fall or winter; lectures. 
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MATH-806* Introduction to Coding Theory
Construction and properties of finite fields. Polynomials, vector spaces, block codes over finite fields. Hamming distance and other code parameters. Bounds relating code parameters. Cyclic codes and their structure as ideals. Weight distribution. Special codes and their relation to designs and projective planes. Decoding algorithms. (Offered jointly with MATH/MTHE 406*.) Three term-hours, fall or winter; lectures.
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MATH-812* Topics in Number Theory
Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.
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MATH-813* Computational Commutative Algebra
Algorithms for solving systems of nonlinear equations, applications in geometry, algebra, and other areas; Gröbner basis methods. Labs use software such as CoCoA or Macaulay 2. (Offered jointly with MATH-413). Three term-hours, fall or winter; lectures.
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MATH-818* Number Theory and Cryptography
Time estimates for arithmetic and elementary number theory algorithms (division algorithm, Euclidean algorithm, congruences), modular arithmetic, finite fields, quadratic residues. Design of simple cryptographic systems; public key, RSA systems. Primality and factoring: pseudoprimes, Pollard's rho-method, index calculus. Elliptic curve cryptography. Offered jointly with MATH/MTHE-418. Three term hours, fall or winter; lectures.
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MATH-825* Theory of Linear Operators
General properties of operators on Banach spaces: adjoints, closed graph theorem, spectrum and spectral radius, and the holomorphic functional calculus. The main part of the course will deal with operators on Hilbert spaces and will include: classification and examples of spectra, examples of operators, and the spectral theorem and its applications. Three term-hours, fall; lectures.
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MATH-827* Introduction to Deterministic Dynamical Systems
Topics include: global properties of flows and diffeomorphisms; invariant sets and dynamics; bifurcations of fixed and periodic points; stability and chaos. (Offered jointly with MATH-427*.) Three term-hours, fall or winter; lectures.
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MATH-830* Modern Control Theory
This course covers core topics in modern control theory: Linearization, existence and uniqueness of trajectories for nonlinear and linear systems, the transition matrix,controllability, observability, minimal realizations, feedback stabilization, linear state observers, optimal control theory, the linear quadratic regulator, dynamic programming. (Offered jointly with MTHE 430*.) Three term-hours, fall; lectures.
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MATH-832* Variational Methods
The classical calculus of variations: the Gateaux variation, necessary conditions, transversality, corner conditions, Euler-Lagrange multiplier theorem; applications to Hamiltonian mechanics and the Maximum Principle. (Offered jointly with MATH-432*.) Three term-hours, winter; lectures.
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MATH-834* Linear and Nonlinear Optimization
Problems of maximization and minimization of functions of many variables when the variables are restricted by inequality constraints, with applications to resource allocation, technology, estimation theory, etc.; convex sets and their properties, convex functions; Lagrange multipliers and the Kuhn-Tucker theorem. (Offered jointly with MATH-434*.) Three term-hours, fall; lectures.
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MATH-836* Lagrangian Mechanics, Dynamics, and Control
Geometric modelling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. The last part of the course develops one of the following three applications: mechanical systems with nonholonomic constraints; control theory for mechanical systems; equilibria and stability. (Offered jointly with MATH/MTHE 439) Three term-hours, winter; lectures.   
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MATH-837* Topics in Applied Mathematics
Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.
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MATH-838* Topics in Mathematical Biology
Subject matter may vary from year to year. Three term-hours, fall or winter; lectures.
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MATH-843* Algebraic Topology
Topological equivalence and topological invariants; homotopy and the fundamental group; covering spaces; homotopy type; Brower’s fixed point theorem; triangularization;  homology and cohomology groups.    (Offered jointly with MATH 443*.) Three term-hours, fall or winter; lectures.
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MATH-844* Differentiable Manifolds
Differentiable structures, smooth manifolds and submanifolds, immersions and submersions, vector fields and differential forms, orientation and integration, de Rham cohomology. Three term-hours, fall or winter; lectures.
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MATH 872* Control of Stochastic Systems
Optimal control of stochastic systems with applications to engineering systems and applied mathematics. Topics include Markov chains and stochastic stability, Martingales, dynamic programming, fully observed and partially observed models, non-linear filtering, Kalman Filtering, linear programming approach, team decision and information structures. (Offered jointly with MTHE 472.) Three term hours, fall or winter; lectures.
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MATH-874* Information Theory
An introduction to the fundamental principles of the theory of communication. Topics include:information measures, entropy, mutual information, divergence; modeling of information sources, discrete memoryless sources, Markov sources, entropy rate, source redundancy, fundamentals of lossless data compression, block encoding, variable-length encoding, Kraft inequality, design of Shannon-Fano and Huffman codes; fundamentals of channel coding, channel capacity, noisy channel coding theorem, channels with memory, lossless information transmission theorem; continuous-alphabet sources and channels, differential entropy, capacity of discrete-time and band-limited continuous-time Gaussian channels; rate-distortion theory, lossy data compression, rate-distortion theorem, lossy information transmission theorem. (Offered jointly with MATH/MTHE-474). Three term hours, fall; lectures.
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MATH-877* Data Compression and Source Coding
Fundamentals of the theoretical and practical (algorithmic) aspects of lossless and lossy data compression. Topics include: adaptive Huffman coding, arithmetic coding, the fundamental performance limits of universal lossless coding, Lempel-Ziv and related dictionary based methods, the Burrows-Wheeler transform, elements of Kolmogorov complexity theory, rate-distortion theory, scalar and vector quantization, applications to speech and image coding. (Offered jointly with MATH/MTHE-477*). PREREQUISITE:   MATH-874*
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MATH-884* Data Networks
This course covers performance models for data networking, delay models and loss models; analysis of multiple access systems, routing, and flow control; multiplexing; priority systems; satellite multiple access, wireless networking,  wireless sensor networks.  Knowledge of networking protocols is not required.  (Offered jointly with MATH/MTHE 484.) Three term hours, winter; lectures. PREREQUISITE:   STAT-855*
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MATH-890* Mathematics Modules
This course comprises three four-week modules on various topics in mathematics. The topics may vary from year to year. Three term-hours, fall or winter; lectures.
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MATH-891* Core Course in Analysis I
This course provides basic knowledge in real and complex analysis at the graduate level on the following topics: Lebesgue measure and integration theory; elementary Hilbert space theory; examples of Banach space techniques. Three term-hours, fall; lectures.
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MATH-892* Core Course in Analysis II
This course provides basic knowledge in real and complex analysis at the graduate level on the following topics: basic theory of Fourier transforms; basic elements of spectral theory and Banach algebras; complex analysis. Three term-hours, winter; lectures.
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MATH-893* Core Course in Algebra I
This course provides basic knowledge in algebra at the graduate level on the following topics: elementary theory of groups; elementary theory of rings and modules; Galois theory. Three term-hours, fall; lectures.
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MATH-894* Core Course in Algebra II
This course provides basic knowledge in algebra at the graduate level on the following topics: representation theory of finite groups through characters; advanced theory of modules; advanced theory of rings. Three term-hours, winter; lectures.
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MATH-895* Core Course in Probability Theory
This course provides basic knowledge in probability at the graduate level. Topics will include: basic notions and concepts of Probability Theory; characteristic functions; law of large numbers and central limit theorem; martingales; stochastic processes. Three term-hours, fall; lectures.
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MATH-896* Core Course in Mathematical Statistics
This course provides basic knowledge in mathematical statistics at the graduate level. Topics will include: Classical and Bayesian inference, Multivariate Gaussian distribution and its applications in Statistics; decision theory; basic techniques of non-parametric estimation. Three term-hours, winter; lectures.
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MATH-898 Master's Project
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MATH-899 Master's Thesis Research
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MATH-901* Fields or CRM Course
Research courses given at either the Fields Institute in Toronto, or the Centre de recherches mathématiques (CRM) in Montreal, can be used to discharge the course requirements for master's or doctoral degrees. Such credit must be applied for in advance with the Coordinator of Graduate Studies, with the agreement of the supervisor. Grades are assigned on a PASS - FAIL basis.
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MATH-902* Topics in Algebra
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-903* Topics in Algebra
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-905* Topics in Algebra
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-912* Topics in Number Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; seminar or reading course.
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MATH-913* Topics in Number Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-915* Topics in Number Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-922* Topics in Analysis
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-923* Topics in Analysis
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-925* Topics in Analysis
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-932* Topics in Applied Mathematics
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-933* Topics in Applied Mathematics
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-935* Topics in Applied Mathematics
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-936* Topics in Control Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-937* Topics in Control Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-939* Topics in Control Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-942* Topics in Topology and Geometry
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-943* Topics in Topology and Geometry
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-945* Topics in Topology and Geometry
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-972* Topics in Communication Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-973* Topics in Communication Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-975* Topics in Communication Theory
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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MATH-999 Ph.D. Thesis Research
 
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COURSES IN PROBABILITY AND STATISTICS
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STAT-853* Statistical Inference
Decision theory and Bayesian inference; principles of optimal statistical procedures; maximum likelihood principle; large sample theory for maximum likelihood estimates; principles of hypotheses testing and the Neyman-Pearson theory; generalized likelihood ratio tests; the chi-square, t, F and other distributions. (Offered jointly with STAT 463.) Three term hours, winter; lectures.
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STAT-854* Statistical Spectrum Estimation
Many systems evolve with an inherent amount of randomness in time and/or space. The focus of this course is on developing and analyzing methods for analyzing time series. Because most of the common time--domain methods are unreliable, the emphasis is on frequency--domain methods, i.e. methods that work and expose the bias that plagues most time--domain techniques.  Slepian sequences (discrete prolate spheroidal sequences) and multi--taper methods of spectrum estimation are covered in detail. (Offered jointly with MTHE 454*.)
Three term-hours, fall; lectures.
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STAT-855* Stochastic Processes and Applications
Markov chains, birth and death processes, random walk problems, elementary renewal theory, Markov processes, Brownian motion and Poisson processes, queuing theory, branching processes. (Offered jointly with MTHE/STAT 455.) Three term hours, fall or winter; lectures.
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STAT-856* Topics in Probability
This course treats probability topics not included in other courses and is offered occasionally.
Three term-hours, fall or winter; lectures.
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STAT-857*  Statistics in Life Sciences 
Subject matter may vary from year to year.  Possible topics include:  methodology for microarray data analysis, measurement error and misclassification in biostatistics, biodemography of laboratory and wild populations, inference in population genetics, probabilistic models for systems biology, Bayesian approaches in bioinformatics. Three term hours, fall or winter; lectures.
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STAT-862* Computational Data Analysis
An introduction to aspects of computer software consistent with modern professional practice of statistics. Particular attention is given to the use of the statistical packages SAS and S-Plus. (Offered jointly with STAT-462*.)
Three term-hours, fall; lectures.
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STAT-864* Discrete Time Series Analysis
Autocorrelation and autocovariance, stationarity; ARIMA models; model identification and forecasting; spectral analysis. Applications to biological, physical and economic data. (Offered jointly with STAT-464.) Three term-hours, fall; lectures.
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STAT-865* Quality Management
An overview of the statistical and lean manufacturing tools and techniques used in the measurement and improvement of quality in business, government and industry today. Topics include management and planning tools, Six Sigma approach, statistical process charting, process capability analysis, measurement system analysis. (Offered jointly with STAT 465.) Three term-hours, fall or winter; lectures.
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STAT-866* Applied Multivariate Analysis
Analysis of data consisting of measurements of several variables on a sample of individuals. Distribution theory, maximum-likelihood estimation and likelihood-ratio testing, Bayesian inference, discrimination, principal components, other topics. (Offered jointly with STAT-466*.) Three term-hours, winter; lectures.
PREREQUISITE:   STAT-870* and STAT-862*
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STAT-867* Survey Sampling
A course in applied statistics with topics to include: planning a survey, questionnaire design, concepts in sampling from a finite population, simple random sampling, stratified sampling, cluster and systematic sampling, introduction to multi-phase and multi-stage surveys, sampling with unequal probabilities, sampling with replacement, and design based estimation.  (Offered jointly with STAT-460*. ) Three term-hours, fall; lectures.  
 
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STAT-870* Regression Analysis
Topics include multivariate normal distribution theory, linear and nonlinear regression, generalized linear models, modern nonparametric regression. (Offered jointly with STAT-470*.)  Three term hours, fall; lectures. 
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STAT-871* Design and Analysis of Experiments
Analysis of variance for fixed, random and mixed models; analysis of covariance; distribution of mean squares; classical designs including fractional factorial experiments, Latin squares and split plot designs. Modern topics including Taguchi methods and designs for nonlinear models. (Offered jointly with STAT-471*.) Three term hours, fall or winter; lectures. 
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STAT-873* Generalized Linear Models
An introduction to advanced regression methods for binary, categorical, and count data. Major topics include maximum-likelihood method, binomial and Poisson regression, contingency tables, log linear models, and random effect models. The generalized linear models will be discussed both in theory and in applications to real data from a variety of sources.(Offered jointly with STAT-473*.)
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STAT-886* Survival Analysis
Introduces the theory and application of survival analysis: survival distributions and their applications, parametric and nonparametric methods, proportional hazards models, counting process and proportional hazards regression, planning and designing clinical trials. (Offered jointly with STAT-486*.) Three term-hours, winter; lectures.
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STAT-888 Master’s Practicum
Under the guidance of the supervisor, students will carry out a practicum project in a health research group/site and practise biostatistical methods and data analysis, or conduct methodology research in a biostatistical project. Students will summarize the results of the project in a written report that will be reviewed and orally defended.
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STAT-898 Master's Project
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STAT-899 Master's Thesis Research
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STAT-952* Topics in Probability
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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STAT-953* Topics in Probability
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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STAT-955* Topics in Probability
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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STAT-962* Topics in Statistics
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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STAT-963* Topics in Statistics
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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STAT-965* Topics in Statistics
Subject matter will vary from year to year. Three term-hours, Fall or winter; Seminar or reading course.
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STAT-999 Ph.D. Thesis Research
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Graduate Studies Courses of Instruction Mathematics and Statistics
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