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Prelim Courses - Pure Mathematics
 
This is not necessarily the official description for the courses. For the official descriptions, consult the 2008 - 2009 graduate catalog.

MATH 5111 (303) : Measure and Integration Link: More Info
Description: Lebesgue measure and integration, differentiation, Lp-spaces. Banach spaces, general theory of measure and integration.
Prerequisites: MATH 5110
Offered: Spring
Credits: 3

MATH 5120 (340) : Complex Function Theory I Link: More Info
Description: This class is an introduction to complex analysis at the graduate level. A practical purpose of the class is to prepare students to take the qualifying exams. Highlights of the course will be (not an exclusive list) analytic functions, meromorphic functions, the Cauchy Integral Formula, residues, maximum principle and the Schwartz Lemma.
For prelims, check out the Complex Analysis Study Guide.
Prerequisites: MATH 5110
Credits: 3

MATH 5210 (315) : Abstract Algebra I Link: More Info
Description: Group theory, ring theory and modules, and universal mapping properties.
Offered: Fall
Credits: 3

MATH 5310 (307) : Introduction to Geometry and Topology I Link: More Info
Description: Topological spaces, connectedness, compactness, separation axioms, Tychonoff theorem, compact-open topology, fundamental group, covering spaces, simplicial complexes, differentiable manifolds, homology theory and the De Rham theory, intrinsic Riemannian geometry of surfaces.
Offered: Fall
Credits: 3