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Distribution theory for experimental designs. Experimental designs: Completely randomized, complete and incomplete block designs, Latin squares, split-plot, fractional, factorial and response surface designs. Sample size and power determination. Simultaneous inference. Variance component models.

Time domain methods: detrending, autoregressive moving average ARMA models, non stationarity and seasonality, state space methodology. Frequency domain methods: lagged regression, deterministic input and random coefficient models.

Examples of financial time series. Time series data will be analyzed using software packages. Roots of nonlinear equations fixed point, Newton, secant, bisection. Condition number of linear systems. Interpolation and polynomial approximation, numerical differentiation and integration. Numerical methods for differential equations. Error analysis. Introduction to modelling and to mathematical techniques used in applications. Mathematical models will come from various areas of applied sciences and use techniques from calculus, differential equations, linear algebra and vector geometry.

Les applications contractantes. Nombres complexes. Fonctions analytiques. Applications conformes. Modules, sommes directes et annulateurs de modules, modules libres, classification de modules sur un anneau principal.

Fractions continues. Distribution des nombres premiers. Fonctions de Legendre et de Bessel. Normes de vecteurs et de matrices. Analyse en composantes principales. Analyse d'erreur. Introduction to Banach and with emphasis on Hilbert spaces. Fourier series and Fourier transforms. Linear operators on Hilbert spaces. Introduction to spectral theory. Selected topics among: Compact operators, unbounded operators, etc.

General measure and integral, Lebesgue measure and integration on R, Fubini's theorem, Lebesgue-Radon-Nikodym theorem, absolute continuity and differentiation, Lp-spaces.

Banach and Hilbert spaces, bounded linear operators, dual spaces, some additional topics. Modelling with partial differential equations PDEs , elementary PDEs and the method of separation of variables, classification of PDEs, linear first order PDEs and method of characteristics, maximum principles for elliptic equations and classical solution of the Laplace equation, Green's functions, variational methods.

Heat and wave equations. Noetherian and artinian modules and rings. Localization of rings and modules. Tensor product of modules and algebras. Short exact sequences, free modules, projective modules, injective modules, flat modules. Structure of solvable, nilpotent and semisimple finite dimensional Lie algebras.

Group actions, class equation, Sylow theorems, central, composition and derived series, Jordan-Holder theorem, field extensions and minimal polynomials, algebraic closure, separable extensions, integral ring extensions, Galois groups, fundamental theorem of Galois theory, finite fields, cyclotomic field extensions, fundamental theorem of algebra, transcendental extensions.

Linear groups: the exponential map, Lie correspondence. Homomorphisms and coverings. Closed subgroups. Classical groups: Cartan subgroups, fundamental groups.

Homogeneous spaces. General Lie groups. Topological spaces, product and identification topologies, countability and separation axioms, compactness, metrisation. Brief overview of commutative algebra, Hilbert's Nullstellensatz, algebraic sets, and Zariski topology. Affine and projective varieties over algebraically closed fields. Regular functions and rational maps. Manifolds, differentiable structures, tangent space, vector fields, differential forms, tensor fields, Riemannian metric.

Covering spaces, homology via the Eilenberg-Steenrod axioms, applications, construction of a homology functor. Selected topics, such as: model theory, non-standard analysis, the theory of recursive functions, advanced set theory, philosophy of mathematics.

Topics from analytic number theory, algebraic number theory, Diophantine approximation, modular forms or arithmetic geometry. Probability spaces, random variables, expected values as integrals, joint distributions, independence and product measures, cumulative distribution functions and extension of probability measures, Borel-Cantelli lemmas, convergence concepts, independent and identically distributed sequences of random variables. Laws of large numbers, characteristic functions, central limit theorem, conditional probability and expectation, some additional topics.

Limit theorems. Sampling distributions. Parametric estimation. Concepts of sufficiency and efficiency. Neyman-Pearson paradigm, likelihood ratio tests. Parametric and non-parametric methods for two- sample comparisons. Notions of experimental design, categorical data analysis, the general linear model, decision theory and Bayesian inference. Previously MAT Tensor analysis with applications to Riemannian geometry and relativity theory.

Prerequisite: 12 course units in mathematics MAT at the level or above. Additional prerequisites may be imposed depending on the topic.

Representation theory of groups and algebras: characters, irreducible representations, induced representations, intertwining operators. Paths and cycles, trees, connectivity, Euler tours and Hamilton cycles, edge colouring, independent sets and cliques, vertex colouring, planar graphs, directed graphs.

Principle of inclusion -- exclusion, generating functions and partitions of the integers, Polya's theory of counting, latin squares, Steiner triple systems, block designs, finite geometries, posets and lattices. An introduction to stochastic processes, with emphasis on Markov processes.

Review of basic probability, limit theorems and conditioning. The Poisson process. Limit theorems for regenerative processes. Discrete-time and continuous-time Markov processes. Hidden Markov processes on finite state spaces. Applications chosen from signal processing, queuing theory, economics, finance and actuarial sciences.

Review of conditional expectation and an introduction to martingales, stopping times and the Snell envelope. Interest rate and present value, discrete time option pricing. Review of the multivariate normal with applications to Markovitz portfolio theory. An introduction to Brownian motion and the Black-Scholes formula for European options.

Discriminant analysis, principal component analysis, support vector machines; reproducing kernel Hilbert spaces and kernel methods; neural networks; VC Theory; PAC learning. Additional topics may include: Bayesian modelling, manifold learning, boosting. Simulation including the rejection method and importance sampling; applications to Monte Carlo Markov chains. Resampling methods such as the bootstrap and jackknife, with applications. Smoothing methods in curve estimation. Multivariate normal distribution: properties, estimation, testing.

Topics chosen from multivariate regression, analysis of variance and covariance, linear discriminant analysis, component and factor analysis, canonical correlation. Prerequisite: MAT additional prerequisites may be added depending on the topic. Prerequisite: MAT additional prerequisites may be imposed depending on the topic. Multi-way contingency tables. Generalized linear models for binary and count data. Logistic regression; inference and model verification.

Log-linear and logit models for multiway frequency tables. Applications drawn from life sciences. Statistical computer packages will be used in the course. Optimization problems, nonlinear programming, unconstrained optimization, convexity and coercivity, existence theory, gradient and Newton methods constrained optimization, gradient method with projection, Kuhn-Tucker relations, duality, Uzawa method.

Linear programming, simplex method. Prerequisite: 24 units in MAT courses at level or above. Introduction aux espaces de Hilbert et Banach avec emphase sur les espaces de Hilbert. Suites exactes courtes, modules libres, modules projectifs, modules injectifs, modules plats.

Espaces de recouvrement, homologie via les axiomes de Eilenberg-Steenrod, applications, construction d'un foncteur homologique. Le processus de Poisson. This course is intended for students interested in pursuing graduate studies. Theory 3 units. Selected topics from one or more of the following areas: algebraic graph theory, topological theory, random graphs. Network flow theory and related material.

Topics will include shortest paths, minimum spanning trees, maximum flows, minimum cost flows. Optimal matching in bipartite graphs. Ordinary and exponential generating functions; product formulas; permutations; partitions; rooted trees; cycle index; WZ method. Lagrange Inversions; singularity analysis of generating functions and asymptotics. Selected topics from one or more of the following areas: random graphs, random combinatorial structures, hypergeometric functions.

General measure and integral, Lebesgue measure and integration on R, Fubini's theorem, Lebesgue-Radon-Nikodym theorem, absolute continuity and differentiation, Lp-Spaces.

Selected topics such as Daniell-Stone theory. Banach and Hilbert spaces, bounded linear operators, dual spaces. Topics selected from: weak- and weak-topologies, Alaoglu's theorem, compact operators, differential calculus in Banach spaces, Riesz representation theorems.

One or two specialized Linear systems, fundamental solution. Nonlinear systems, existence and uniqueness, flow. Equilibria, periodic solutions, stability.

Invariant manifolds and hyperbolic theory. First-order equations, characteristics method, classification of second-order equations, separation of variables, Green's functions. Lp and Soboloev spaces, distributions, variational formulation and weak solutions, Lax-Milgram theorem, Galerkin approximation. Parabolic PDes. Wave equations, hyperbolic systems, nonlinear PDes, reaction diffusion equations, infinite-dimensional dynamical systems, regularity.

Prime spectrum of a commutative ring as a topological space ; localization of rings and modules; tensor product of modules and algebras; Hilbert's Nullstellensatz and consequences for finitely generated algebras; Krull dimension of a ring; integral dependence, going-up, going-down; Noether Normalization Lemma and dimension theory for finitely generated algebras over a field; noetherian rings and Hilbert Basis Theorem; introduction to affine algebraic varieties and their morphisms.

Topological spaces, product and identification topologies, countability and separation axioms, compactness, connectedness, homotopy, fundamental group, net and filter convergence.

Analysis of cryptographic methods used in authentication and data protection, with particular attention to the underlying mathematics, e.

Topics in current research. Prerequisite: undergraduate honours algebra, including group theory and finite fields.

A basic graduate course in mathematical logic. Propositional and Predicate logic, Proof theory, Gentzen's Cut-Elimination, Completeness, Compactness, Henkin models, model theory, arithmetic and undecidability. Special Topics time permitting depending on interests of instructor and audience. Prerequisite: Honours undergraduate algebra, analysis and topology or permission of the instructor.

Foundations of functional languages, lambda calculi typed, polymorphically typed, untyped , Curry-Howard Isomorphism, proofs-as-programs, normalization and rewriting theory, operational semantics, type assignment, introduction to denotational semantics of programs, fixed-point programming. Topics chosen from: denotational semantics for lambda calculi, models of programming languages, complexity theory and logic of computation, models of concurrent and distributed systems, etc.

Prerequisite: Honours undergraduate algebra and either topology or analysis. Some acquaintance with Logic useful. Probability spaces, random variables, expected values as integrals, joint distributions, independence and product measures, cumulative distribution functions and extensions of probability measures, Borel- Cantelli lemmas, convergence concepts, independent identically distributed sequences of random variables.

Laws of large numbers, characteristic functions, central limit theorem, conditional probabilities and expectation, basic properties and convergence theorems for martingales, introduction to Brownian motion. Brownian motion, continuous martingales and stochastic integration. The course will focus on 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. Pure significance tests; uniformly most powerful unbiased and invariant tests; asymptotic comparison of tests; confidence intervals; large sample theory of likelihood ratio and chi-square tests; likelihood inference; Bayesian inference.

Topics such as empirical Bayes inference, fiducial and structural inference, resampling methods. Floating pointing arithmetic; numerical solution of ordinary differential equations; finite difference methods for partial differential equations; stability, consistency and convergence: von Neumann analysis, Courant-Friedrichs-Lewy condition, Lax theorem; finite element methods: boundary value problems and elliptic partial differential equations; spectral and Pseudo-spectral methods.

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. 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.

Asymptotic series: properties, matching, application to linear and nonlinear differential equations. Perturbation methods: regular and singular perturbation for differential equations, multiple scale analysis, boundary layer theory, WKB theory.

Statistical decision theory; likelihood functions; sufficiency; factorization theorem; exponential families; UMVU estimators; Fisher's information; Cramer-Rao lower bound; maximum likelihood and moment estimation; invariant and robust point estimation; asymptotic properties; Bayesian point estimation.

Confidence intervals and pivotals; Bayesian intervals; optimal tests and Neyman-Pearson theory; likelihood ratio and score tests; significance tests; goodness-of-fit tests; large sample theory and applications to maximum likelihood and robust estimation. Unequal probability sampling with and without replacement; unified theory of standard errors; prediction approach; ratio and regression estimation; stratification and optimal designs; multistage cluster sampling; double sampling; domains of study; post-stratification; non-response; measurement errors.

Related topics. Theory of non-full-rank linear models: estimable functions, best linear unbiased estimators, hypothesis testing, confidence regions; multi-way classification; analysis of covariance; variance component models: maximum likelihood estimation, MINQUE, ANOVA methods. Miscellaneous topics. 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.

Topics chosen from stochastic dynamic programming, Markov decision processes, search theory, optimal stopping. Markov systems, stochastic networks, queuing networks, spatial processes, approximation methods in stochastic processes and queuing theory. Applications to the modelling and analysis of computer-communications systems and other distributed networks. Analysis of one-way and two-way tables of nominal date; multi-dimensional contingency tables, log-linear 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; biological applications.

Space of quantum bits; entanglement. Observables in quantum mechanics. Density matrix and Schmidt decomposition. Quantum cryptography. Classical and quantum logic gates. Quantum Fourier transform. Shor's quantum algorithm for factorization of integers. Lossless compression methods. Discrete Fourier transform and Fourier-based compression methods. Wavelet analysis. Digital filters and discrete wavelet transform.

Daubechies wavelets. Wavelet compression. Limit theorems; sampling distributions; parametric estimation; concepts of sufficiency and efficiency; Neyman-Pearson paradigm, likelihood ratio tests; parametric and non-parametric methods for two-sample comparisons; notions of experimental design, categorical data analysis, the general linear model, decision theory and Bayesian inference. This course is essential for students in applied statistics.

Couplage optimal dans les graphes bipartis. Prerequisite for MAT Localisation des anneaux et des modules. MAT S M. 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.

Project work and seminars on related topics. Grade S Satisfactory or NS Not satisfactory to be assigned based upon the mathematical content as well as upon the oral and written presentation of results, and to be determined by the professor in charge of the course in consultation with the internship supervisor.

Graded S Satisfactory or NS Not satisfactory by the supervisor and by another professor appointed by the director of graduate studies in mathematics and statistics. The project will normally be completed in one session. Cet examen porte sur le contenu du cours MAT This exam is the final exam of the course and is graded by the professors who teach MAT and MAT in the academic year.

Graded S satisfactory or NS not satisfactory. Cet examen porte sur le contenu du cours MAT Cet examen porte sur le contenuu du cours MAT Cet examen porte sur le contenu du sours MAT The syllabus should be given to the student at least six months before the date of the examination. The syllabus must provide the form, contents and expectations for the advanced comprehensive examination. Graded S satisfactory or NS non satisfactory. For more information about undergraduate studies at the University of Ottawa, please refer to your faculty.

For more information about graduate studies at the University of Ottawa, please refer to your academic unit. Send Page to Printer. Search uOttawa. Search one of the following.

Entire site Library Employee directory. Programs and courses. Mathematics MAT. MAT Functions 3 units Polynomial and rational functions: factoring, the remainder theorem, families of polynomials with specified zeros, odd and even polynomial functions.

MAT Calculus I 3 units Intuitive definition of limits; continuity, statement of intermediate value theorem. MAT Intensive Calculus I 3 units Instantaneous rate of change and definition of limits; continuity, statement of intermediate value theorem. MAT Calculus II and an Introduction to Analysis 3 units A second course in calculus emphasizing geometric and physical intuition in which attention is also given to the conceptual foundations of calculus-analysis.

MAT Calculus for the Life Sciences I 3 units Derivatives: product and quotient rules, chain rule, derivative of exponential, logarithm and basic trigonometric functions, higher derivatives, curve sketching. MAT Introduction to Calculus and Vectors 3 units Instantaneous rate of change as a limit, derivatives of polynomials using limits, derivatives of sums, products, the chain rule, derivatives of rational, trigonometric, exponential, logarithmic, and radical functions.

MAT Mathematical Reasoning and Proofs 3 units Elements of logic, set theory, functions, equivalence relations and cardinality. MAT Descriptive Statistics 3 units Topics from descriptive statistics: histograms and boxplot; average and observed standard deviation; elementary probability; normal distribution; statistical estimation and hypothesis testing; correlation and regression. MAT Probability and Games of Chance: Poker 3 units An introduction to elementary probability theory, game theory, and the mathematical underpinning of games of chance, demonstrated through their applications to poker games such as Texas Hold'em.

Course Component: Lecture This course cannot count as a science elective for students in the Faculty of Science. Course Component: Lecture Prerequisite: This course cannot count as a science elective for students in the Faculty of Science.

MAT Honours Linear Algebra 3 units Vector spaces, direct sums and complement of subspaces, linear maps, representation of linear maps by matrices, dual spaces, transpose mappings, multilinear mappings, determinants, inner products, orthogonal projections, the Gram-Schmidt algorithm.

MAT Discrete Mathematics 3 units Quick review of: sets, functions, relations, induction, basic counting techniques. MAT Introduction to Geometry 3 units Euclidean and non-Euclidean geometries; affine geometry, projective geometry.

MAT Foundations of Mathematics 3 units Introduction to proofs, set theory and the foundations of mathematics. MAT Introduction to Statistics 3 units Theory of statistical inference; point and interval estimation, tests of hypotheses. MAT Probability and Statistics for Engineers 3 units A concise survey of: combinatorial analysis; probability and random variables; discrete and continuous densities and distribution functions; expectation and variance; normal Gaussian , binomial and Poisson distributions; statistical estimation and hypothesis testing; method of least squares, correlation and regression.

MAT History of Mathematics II 3 units Historical development of mathematics as seen through a few central themes such as counting, space, randomness, approximation, the infinitely small, or algebraic abstraction. MAT Rings and Modules 3 units Rings and ideals, homomorphisms and isomorphism theorems, principal ideal domains and factorial rings, polynomial rings and the construction of finite fields. MAT Introduction to Number Theory 3 units Topics chosen from: Farey sequence, Fermat-Euler-Wilson theorems, power residues and primitive roots, Diophantine equations, continued fractions, algebraic and transcendental numbers, arithmetic functions, distribution of primes.

MAT Foundations of Probability 3 units An overview of probability from a non-measure theoretic point of view. MAT Applied Discrete Mathematics 3 units Trees and applications, applications of graphs, networks and flows, matching theory, introduction to linear programming. MAT Methods of Machine Learning 3 units Multivariate linear and polynomial regression, logistic regression, k-nearest neighbours. MAT Regression Analysis 3 units Distribution theory, hypothesis testing and estimation for simple, multiple and non-linear regression.

MAT Introduction to Mathematical Models 3 units Introduction to modelling and to mathematical techniques used in applications. MAT Introduction to Partial Differential Equations 3 units Modelling with partial differential equations PDEs , elementary PDEs and the method of separation of variables, classification of PDEs, linear first order PDEs and method of characteristics, maximum principles for elliptic equations and classical solution of the Laplace equation, Green's functions, variational methods.

MAT Groups and Galois Theory 3 units Group actions, class equation, Sylow theorems, central, composition and derived series, Jordan-Holder theorem, field extensions and minimal polynomials, algebraic closure, separable extensions, integral ring extensions, Galois groups, fundamental theorem of Galois theory, finite fields, cyclotomic field extensions, fundamental theorem of algebra, transcendental extensions.

MAT General Topology 3 units Topological spaces, product and identification topologies, countability and separation axioms, compactness, metrisation. MAT Elementary Manifold Theory 3 units Manifolds, differentiable structures, tangent space, vector fields, differential forms, tensor fields, Riemannian metric. MAT Topics in Mathematical Logic 3 units Selected topics, such as: model theory, non-standard analysis, the theory of recursive functions, advanced set theory, philosophy of mathematics. MAT Topics in Number Theory 3 units Topics from analytic number theory, algebraic number theory, Diophantine approximation, modular forms or arithmetic geometry.

MAT Probability Theory I 3 units Probability spaces, random variables, expected values as integrals, joint distributions, independence and product measures, cumulative distribution functions and extension of probability measures, Borel-Cantelli lemmas, convergence concepts, independent and identically distributed sequences of random variables. MAT Probability Theory II 3 units Laws of large numbers, characteristic functions, central limit theorem, conditional probability and expectation, some additional topics.

MAT Representation Theory 3 units Representation theory of groups and algebras: characters, irreducible representations, induced representations, intertwining operators. MAT Graph Theory 3 units Paths and cycles, trees, connectivity, Euler tours and Hamilton cycles, edge colouring, independent sets and cliques, vertex colouring, planar graphs, directed graphs.

MAT Combinatorial Theory 3 units Principle of inclusion -- exclusion, generating functions and partitions of the integers, Polya's theory of counting, latin squares, Steiner triple systems, block designs, finite geometries, posets and lattices.

MAT Financial Mathematics 3 units Review of conditional expectation and an introduction to martingales, stopping times and the Snell envelope. MAT Optimization: Theory and Practice 3 units Optimization problems, nonlinear programming, unconstrained optimization, convexity and coercivity, existence theory, gradient and Newton methods constrained optimization, gradient method with projection, Kuhn-Tucker relations, duality, Uzawa method. Theory 3 units Paths and cycles, trees, connectivity, Euler tours and Hamilton cycles, edge colouring, independent sets and cliques, vertex colouring, planar graphs, directed graphs.

Course Component: Lecture. MAT Partial Differential Equations I 3 units First-order equations, characteristics method, classification of second-order equations, separation of variables, Green's functions. Course Component: Lecture Permission of the Department is required. MAT Algebra II: Groups and Galois Theory 3 units Group actions, class equation, Sylow theorems, central, composition and derived series, Jordan-Holder theorem, field extensions and minimal polynomials, algebraic closure, separable extensions, integral ring extensions, Galois groups, fundamental theorem of Galois theory, finite fields, cyclotomic field extensions, fundamental theorem of algebra, transcendental extensions.

MAT Commutative Algebra 3 units Prime spectrum of a commutative ring as a topological space ; localization of rings and modules; tensor product of modules and algebras; Hilbert's Nullstellensatz and consequences for finitely generated algebras; Krull dimension of a ring; integral dependence, going-up, going-down; Noether Normalization Lemma and dimension theory for finitely generated algebras over a field; noetherian rings and Hilbert Basis Theorem; introduction to affine algebraic varieties and their morphisms.

MAT Topology I 3 units Topological spaces, product and identification topologies, countability and separation axioms, compactness, connectedness, homotopy, fundamental group, net and filter convergence.

MAT Mathematical Cryptography 3 units Analysis of cryptographic methods used in authentication and data protection, with particular attention to the underlying mathematics, e. Course Component: Lecture Prerequisite: undergraduate honours algebra, including group theory and finite fields.

Course Component: Lecture Prerequisite: Honours undergraduate algebra, analysis and topology or permission of the instructor. MAT Mathematical Foundations of Computer Science 3 units Foundations of functional languages, lambda calculi typed, polymorphically typed, untyped , Curry-Howard Isomorphism, proofs-as-programs, normalization and rewriting theory, operational semantics, type assignment, introduction to denotational semantics of programs, fixed-point programming.

Course Component: Lecture Prerequisite: Honours undergraduate algebra and either topology or analysis. MAT Probability Theory I 3 units Probability spaces, random variables, expected values as integrals, joint distributions, independence and product measures, cumulative distribution functions and extensions of probability measures, Borel- Cantelli lemmas, convergence concepts, independent identically distributed sequences of random variables.

MAT Probability Theory II 3 units Laws of large numbers, characteristic functions, central limit theorem, conditional probabilities and expectation, basic properties and convergence theorems for martingales, introduction to Brownian motion. MAT Stochastic Analysis 3 units Brownian motion, continuous martingales and stochastic integration.

MAT Network Performance 3 units The course will focus on advanced techniques in performance evaluation of large complex networks. Course Component: Lecture Prerequisite: Some familiarity with probability and stochastic processes and queueing, or permission of the instructor. MAT Advanced Statistical Inference 3 units Pure significance tests; uniformly most powerful unbiased and invariant tests; asymptotic comparison of tests; confidence intervals; large sample theory of likelihood ratio and chi-square tests; likelihood inference; Bayesian inference.

MAT Numerical Analysis for Differential Equations 3 units Floating pointing arithmetic; numerical solution of ordinary differential equations; finite difference methods for partial differential equations; stability, consistency and convergence: von Neumann analysis, Courant-Friedrichs-Lewy condition, Lax theorem; finite element methods: boundary value problems and elliptic partial differential equations; spectral and Pseudo-spectral methods.

MAT Data Mining I 3 units Visualization and knowledge discovery in massive datasets; unsupervised learning: clustering algorithms; dimension reduction; supervised learning: pattern recognition, smoothing techniques, classification. MAT Modern Applied and Computational Statistics 3 units Resampling and computer intensive methods: bootstrap, jackknife with applications to bias estimation, variance estimation, confidence intervals, and regression analysis.

MAT Asymptotic Methods of Applied Mathematics 3 units Asymptotic series: properties, matching, application to linear and nonlinear differential equations.

MAT Mathematical Statistics I 3 units Statistical decision theory; likelihood functions; sufficiency; factorization theorem; exponential families; UMVU estimators; Fisher's information; Cramer-Rao lower bound; maximum likelihood and moment estimation; invariant and robust point estimation; asymptotic properties; Bayesian point estimation.

MAT Mathematical Statistics II 3 units Confidence intervals and pivotals; Bayesian intervals; optimal tests and Neyman-Pearson theory; likelihood ratio and score tests; significance tests; goodness-of-fit tests; large sample theory and applications to maximum likelihood and robust estimation. MAT Sampling Theory and Methods 3 units Unequal probability sampling with and without replacement; unified theory of standard errors; prediction approach; ratio and regression estimation; stratification and optimal designs; multistage cluster sampling; double sampling; domains of study; post-stratification; non-response; measurement errors.

MAT Linear Models 3 units Theory of non-full-rank linear models: estimable functions, best linear unbiased estimators, hypothesis testing, confidence regions; multi-way classification; analysis of covariance; variance component models: maximum likelihood estimation, MINQUE, ANOVA methods. MAT Design of Experiments 3 units 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.

MAT Stochastic Optimization 3 units Topics chosen from stochastic dynamic programming, Markov decision processes, search theory, optimal stopping. MAT Stochastic Models 3 units Markov systems, stochastic networks, queuing networks, spatial processes, approximation methods in stochastic processes and queuing theory.

MAT Analysis of Categorical Data 3 units Analysis of one-way and two-way tables of nominal date; multi-dimensional contingency tables, log-linear 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; biological applications.

MAT Introduction to Mathematical Statistics 3 units Limit theorems; sampling distributions; parametric estimation; concepts of sufficiency and efficiency; Neyman-Pearson paradigm, likelihood ratio tests; parametric and non-parametric methods for two-sample comparisons; notions of experimental design, categorical data analysis, the general linear model, decision theory and Bayesian inference. Volet : Cours magistral. Undergraduate Studies For more information about undergraduate studies at the University of Ottawa, please refer to your faculty.

Graduate and Postdoctoral Studies For more information about graduate studies at the University of Ottawa, please refer to your academic unit. Close this window Print Options. Send Page to Printer Print this page. TD 2 : Mesures. TD 3 : Fonctions mesurables. TD 6 : Espaces de Lebesgue. Quelques corrections. Laur et P. Gisquet et A. Section 1. Section 4. TD 1 : Nombres complexes. Bilan des notes.

Semaine 1 : Fonctions de plusieurs variables. Application aux EDP. Quelques corrections d'exercices. Formes hermitiennes - espaces hermitiens. TD 2 : Espaces euclidiens. TP 1 : Interpolation. TD 3 : Espaces de Sobolev. Le chapitre 12 est hors programme pour l'examen final. DM pour le mercredi 27 mars : Exercices 3.

TD 2 : Changements de variables. TD 4 : Inversion locale - Fonctions implicites. Examen final. Spectrum of a non-selfadjoint quantum star graph , with G. Csobo , F. Genoud , M.