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MATH G6383: Algebraic Geometry
8.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 6373. Hilbert's Nullstellensatz, the correspondence between ideals and algebraic sets, Zariski topology, irreducible algebraic sets, ringed spaces, morphisms, affine varieties, algebraic varieties, regular maps, sub-varieties and products, bi-rational equivalence, local rings and tangent spaces, differentials, non-singular points. (Irreg.)
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MATH G6383 - Algebraic Geometry
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MATH G6393: Topics in Algebra
9.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5353 or permission of instructor. May be repeated with change of content; maximum credit 15 hours. Topics of modern research interest in algebra. (Irreg.)
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MATH G6393 - Topics in Algebra
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MATH G6443: Topics in Differential Equations
4.00 Credits
University of Oklahoma Norman Campus
Prerequisite: permission of instructor. May be repeated with change of content; maximum credit 12 hours. Topics include, but are not limited to, dynamical systems, nonlinear boundary value problems, parameter identification theory, wave theory, nonlinear functional analysis.(F, Sp)
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MATH G6443 - Topics in Differential Equations
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MATH G6473: Functional Analysis I
7.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5463 or permission of instructor. Vector spaces with topology or norm, dual space, theorems on linear operators, spectral theory in Hilbert space, spectral decomposition of operators, convex sets and weak topologies, fixed point theorems. (Alt. F)
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MATH G6473 - Functional Analysis I
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MATH G6483: Functional Analysis II
8.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 6473. Banach algebras and harmonic analysis, representations of symmetric rings, unitary representations of a group, rings of operators in Hilbert space, decomposition of ring operators. Introduction to the theory of distributions. (Alt. Sp)
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MATH G6483 - Functional Analysis II
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MATH G6493: Topics in Analysis
9.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5453 or permission of instructor. May be repeated with change of course content. Topics of modern research interest in analysis. (Irreg.)
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MATH G6493 - Topics in Analysis
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MATH G6673: Differential Geometry I
7.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5853 or permission of instructor. Multilinear algebra, differential manifolds, exterior differential forms, affine connections, Riemannian manifolds. (F)
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MATH G6673 - Differential Geometry I
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MATH G6683: Differential Geometry II
8.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 6673. Riemannian manifolds, theory of connections, bundles with classical groups as structure groups, curvature and Betti numbers, complex manifolds. (Sp)
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MATH G6683 - Differential Geometry II
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MATH G6813: Algebraic Topology I
1.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5863. Introduction to homology theory of spaces, fundamental group and covering spaces, higher homotopy groups, CW-complexes and cellular homology, Whitehead and Hurewicz theorems, Eilenberg-Steenrod axioms. (F)
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MATH G6813 - Algebraic Topology I
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MATH G6823: Algebraic Topology II
2.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 6813. Topics in cohomology and homology theory, universal coefficient theorems, orientation and duality on manifolds. Further topics may include: obstruction theory, cohomology operations, fibre bundles and characteristic classes, theory of sheaves, Eilenberg-MacLane spaces and Postnikov systems, spectral sequences. (Sp)
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MATH G6823 - Algebraic Topology II
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