MATH202B
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MATH 202B - Introduction to Topology and Analysis
Course Title
Introduction to Topology and Analysis
Course Description
Measure and integration. Product measures and Fubini-type theorems. Signed measures; Hahn and Jordan decompositions. Radon-Nikodym theorem. Integration on the line and in Rn. Differentiation of the integral. Hausdorff measures. Fourier transform. Introduction to linear topological spaces, Banach spaces and Hilbert spaces. Banach-Steinhaus theorem; closed graph theorem. Hahn-Banach theorem. Duality; the dual of LP. Measures on locally compact spaces; the dual of C(X). Weak and weak-* topologies; Banach-Alaoglu theorem. Convexity and the Krein-Milman theorem. Additional topics chosen may include compact operators, spectral theory of compact operators, and applications to integral equations.
Minimum Units
4
Maximum Units
4
Grading Basis
Default Letter Grade; S/U Option
Prerequisites
202A and 110.
Repeat Rules
Course is not repeatable for credit.
Formats
Lecture
Term
Fall and Spring
Weeks
15 weeks
Weeks
15
Lecture Hours
3
Lecture Hours Min
3
Lecture Hours Max
3
Outside Work Hours
9
Outside Work Hours Min
9
Outside Work Hours Max
9