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Mathematics (MATH) Graduate Courses Listing

Mathematics 5110 Measure Theory View Details
Measure spaces, measurable functions, measures, the integral, integrable functions, the Lebesgue dominated convergence theorem, modes of convergence, Egoroff's theorem, the Hahn and Jordan decomposition theorems, the Radon-Nikodym theorem, Lebesgue spaces, and the Reisz representation theorem for Lebesgue spaces.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5111 Topology View Details
Topological spaces; neighbourhoods, bases, and sub-bases; product spaces and weak topologies; nets and filters; convergence; separation axioms, including Urysohn's lemma and Tietze's extension theorem; compact and locally compact spaces, including Tychonoff's theorem and compactifications; metrizability; and connectedness.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5112 Functional Analysis I View Details
The course content covers normed vector spaces, bounded operators, Baire category, the Banach-Steinhaus theorem, the open mapping theorem, the closed graph theorem, the Hahn-Banach theorems, Hilbert spaces, the Riesz representation theorem, and compact operators.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5113 Functional Analysis II View Details
Banach algebras, the spectrum and spectral radius, the Gelfand transform, function algebras, involution in Banach algebras, C*-algebras, continuous functional calculus, Borel functional calculus, spectral measures, spectral projections, and eigenvalues.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5114 Fourier Analysis View Details
Fourier analysis on the circle, Dirichlet kernel, Fejer's theorem, convergence of Fourier series.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5115 Harmonic Analysis View Details
An introduction to abelian locally compact groups, Haar measure convolutions, dual group, the Fourier transform, Fourier Stieltjes transform, Plancherel theorem, Pontryagin duality theorem, basic representation theory.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5116 Introduction to Banach Space Theory View Details
Schauder basis, Mazur's theorem, unconditional basis, approximation property, the spaces c_0 and I_p.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5117 Introductory Algebraic Topology View Details
Categories and functors, the fundamental group, free groups and free products of groups, the Siefert and v. Kampen theorem, covering spaces, applications of the fundamental group to group theory, CW complexes and the fundamental group of higher dimensional spaces.      
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5118 Introduction to Operator Algebras View Details
An introduction to C*-algebras. Topics will include: axioms; homomorphisms, ideals, and quotients; positivity; states, representations, and the GNS construction; weak topologies; von Neumann algebras; and density theorems. Additional topics may include: K-theory, applications to group representations and harmonic analysis, and applications in physics.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5119 Abstract Algebra View Details
Groups, isomorphism theorems, the Sylow theorems, direct and semidirect products, finitely generated abelian groups, simple groups, symmetric groups, free groups, nilpotent and solvable groups, generators and relations, rings, ideals, Euclidean domains, principal ideal domains, and unique factorization domains, and modules.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5131 Commutative Algebra View Details
An introduction to commutative algebra: rings and ideals, modules, local rings, primary decomposition, chain conditions, Noetherian rings, Hilbert functions and dimension theory, Stanley-Reisner rings.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5132 Algebraic Geometry View Details
Affine and projective varieties over algebraically closed fields: coordinate rings, function fields, singularities, morphisms and birational isomorphisms; Bezout's theorem.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5133 Group Rings View Details
An introdution to group rings. Topics include: units, idempotents, polynomial identities, group identities, prime and semiprime group rings.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5211 Reading Course View Details
Directed studies in some area of Mathematical Sciences.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Special Topic: Yes
Offering: 3-0; 0-0

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Mathematics 5213 Reading Course View Details
Directed studies in some area of Mathematical Sciences.
Credit Weight: 0.5
Prerequisite(s): Permiossion of the Chair of the Department
Special Topic: Yes
Offering: 0-0; 3-0

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Mathematics 5301 Graduate Seminar View Details
Seminars are normally presented by the instructor(s), and by students who are asked to prepare and present a number of papers. There may be separate course sections for students studying mathematics, statistics, or applied mathematics.
Credit Weight: 1.0
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; 3-0

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Mathematics 5331 Advanced Topics in Statistics View Details
Topics in statistics.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Special Topic: Yes
Offering: 3-0; or 3-0

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Mathematics 5332 Estimation and Hypothesis Testing View Details
Statistics and sampling distributions, point estimation, sufficiency and completeness, interval estimation, tests of hypothesis, contingency tables and goodness-of-fit, nonparametric methods, regression and linear models, reliability and distributions.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5333 Advanced Topics in Probability View Details
Topics in probability.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Special Topic: Yes
Offering: 3-0; or 3-0

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Mathematics 5335 Statistical Consulting View Details
Students will review recent research articles pertaining to the role of the statistical consultant and to the operation of a statistical consulting laboratory, and will present short seminars on the content of these articles. Students will also be expected to engage in statistical consulting (under supervision) and to provide a written summary of their activities.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 1-3; or 1-3

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Mathematics 5351 Advanced Numerical Analysis I View Details
Advanced topics in numerical analysis may include: computational linear algebra, solution of ordinary and partial differential equations, approximation of functions, optimization, iterative methods, numerical methods of statistics, numerical methods of finance and problems of current research interest. Topics will be picked to complement those in Mathematics 5371.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5352 Partial Differential Equations View Details
The analysis of partial differential equations arising from Physics, Geometry and Optimization. Topics include well-posedness; fundamental solutions; non-homogeneous PDEs, Sobolev spaces and inequalities; linear evolution equations; Calculus of Variations; Conservation Laws and symmetry; fixed point theorems; nonlinear PDEs.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5353 Continuous Optimization View Details
Convexity. Mathematical programming including linear and nonlinear programming. Necessary conditions of the first and second orders. Optimization methods including descent methods, Newton and Quasi-Newton methods, feasible direction methods, penalty methods, and Lagrange methods.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5354 Operations Research - Probabilistic Models View Details
An introduction to probabilistic optimization models in various industries, management sciences, and finance.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5355 Operations Research - Deterministic Models View Details
An introduction to deterministic optimization models in various industries and management sciences.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5371 Advanced Numerical Analysis II View Details
Advanced topics in numerical analysis may include: computational linear algebra, solution of ordinary and partial differential equations, approximation of functions, optimization, iterative methods, numerical methods of statistics, numerical methods of finance and problems of current research interest. Topics will be picked to complement those in Mathematics 5351.
Credit Weight: 0.5
Prerequisite(s): Permission of the Chair of the Department
Offering: 3-0; or 3-0

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Mathematics 5801 (9801) Project View Details
Credit Weight: 1.0

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Mathematics 5901 (9901) Master's Thesis View Details
Credit Weight: 2.0

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