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MATH 5503: Theory of Functions of a Real Variable I
3.00 Credits
University of Arkansas
Real number system, Lebesque measure, Lebesque integral, convergence theorems, differentiation of monotone functions, absolute continuity and the fundamental theorem of calculus L^P spaces, Holder and Minkowski inequalities, and bounded linear functionals on the L^P spaces. Prerequisite: MATH 4523.
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MATH 5503 - Theory of Functions of a Real Variable I
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MATH 5513: Theory of Functions of a Real Variable II
3.00 Credits
University of Arkansas
Measure and integration on abstract measure spaces, signed measures, Hahn decomposition, Radon- Nikdoym theorem, Lebesque decomposition, measures on algebras and their extensions, product measures, and Fubini's theorem. Prerequisite: MATH 5503.
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MATH 5513 - Theory of Functions of a Real Variable II
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MATH 5523: Theory of Functions of a Complex Variable I
3.00 Credits
University of Arkansas
Complex numbers, analytic functions, power series, complex integration, Cauchy's Theorem and integral formula, maximum principle, singularities, Laurent series, and Mibius maps. Prerequisite: MATH 4513.
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MATH 5523 - Theory of Functions of a Complex Variable I
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MATH 5533: Theory of Functions of a Complex Variable II
3.00 Credits
University of Arkansas
Riemann Mapping Theorem, analytic continuation, harmonic functions, and entire functions. Prerequisite: MATH 5523.
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MATH 5703: Foundations of Topology
3.00 Credits
University of Arkansas
Metric and general topological spaces, separation axioms, Urysohn's lemma, Tietze extension theorem, connectedness, compactness, and the Tychonoff theorem. Prerequisite: MATH 4513.
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MATH 5703 - Foundations of Topology
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MATH 5713: Algebraic Topology
3.00 Credits
University of Arkansas
Homotopy, singular and relative homology, excision theorem, the Mayer- Vietoris sequence, Beti numbers, and the Euler characteristic. Prerequisite: MATH 5703.
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MATH 5713 - Algebraic Topology
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MATH 600V: Master's Thesis
3.00 Credits
University of Arkansas
Prerequisite: Graduate standing.
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MATH 600V - Master's Thesis
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MATH 610V: Directed Readings MATH619V Topics in Algebra(Irregular)(1-6)
3.00 Credits
University of Arkansas
Current research interests in algebra.
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MATH 610V - Directed Readings MATH619V Topics in Algebra(Irregular)(1-6)
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MATH 659V: Topics in Analysis
3.00 Credits
University of Arkansas
Current research interests in analysis.
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MATH 659V - Topics in Analysis
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MATH 679V: Topics in Topology
3.00 Credits
University of Arkansas
Current research interest in topology.
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MATH 679V - Topics in Topology
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