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MATH G5443: Introduction to Analysis II
4.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 4433. Integration of functions of a single variable. Series of real numbers. Series of functions. Differentiation of functions of more than one variable. No student may earn credit for both 4443 and 5443. (Sp)
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MATH G5443 - Introduction to Analysis II
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MATH G5453: Real Analysis I
5.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 4433 or permission of instructor. Lebesgue measure and integration theory, absolutely continuous functions, metric spaces. (F)
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MATH G5453 - Real Analysis I
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MATH G5463: Real Analysis II
6.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5453. General measure and integration theory, Banach spaces, topics from related areas. (Sp)
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MATH G5463 - Real Analysis II
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MATH G5483: Wavelets
8.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 3113 or 3413 and 3333. Fourier analysis on a finite cyclic group, the group of integers, and the real line. The matching pursuit algorithm. The Poisson summation formula and sampling. Multi-resolution analysis, various wavelet constructions (including those of Daubechies and Meyer) and filter banks. An introduction to the MATLAB wavelet toolbox. (F)
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MATH G5483 - Wavelets
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MATH G5623: Convexity Theory I
2.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 3333, 2513 or permission of instructor. An introduction to the theory of convex sets. Topics include basic definitions and properties, separating and supporting hyperplanes, and combinatorial theorems of Caratheodory, Radon and Helly. No student may earn credit for both 4623 and 5623. (F)
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MATH G5623 - Convexity Theory I
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MATH G5633: Convexity Theory II
3.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5623 or permission of instructor. A continuation of the study of convex sets. Topics include Helly-type theorems, the Blaschke selection theorem, alternate characterizations of convex sets, convex polytopes and Eveler's formula. (Sp)
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MATH G5633 - Convexity Theory II
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MATH G5653: Introduction to Differential Geometry I
5.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 2433 and 3333, or permission of instructor. Elementary theory of curves and surfaces in three-dimensional Euclidean space, differentiable manifolds, Riemannian geometry of two dimensions, Gauss Theorem Egregium. No student may earn credit for both 4653 and 5653. (F)
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MATH G5653 - Introduction to Differential Geometry I
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MATH G5663: Introduction to Differential Geometry II
6.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 4653 or 5653. Intermediate theory of surfaces, covariant differentiation, geodesics, Gauss-Bonnet Theorem. Further topics may include: rigidity theorems, minimal surfaces, the Hopf-Rinow Theorem, the Hadamard Theorem, index of vector fields. No student may earn credit for both 4663 and 5663. (Sp)
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MATH G5663 - Introduction to Differential Geometry II
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MATH G5673: Graph Theory I
7.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 2513 or permission of instructor. An introduction to the theory of graphs. Topics include basic definitions, cutpoints, blocks, trees, connectivity and Menger's theorem. No student may earn credit for both 4673 and 5673. (F)
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MATH G5673 - Graph Theory I
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MATH G5683: Graph Theory II
8.00 Credits
University of Oklahoma Norman Campus
Prerequisite: 5673 or permission of instructor. A continuation of the study of graphs. Topics include partitions, Eulerian and Hamiltonian graphs, planarity and colorability. (Sp)
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MATH G5683 - Graph Theory II
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