MATH202B

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MATH 202B - Introduction to Topology and Analysis

Mathematics Graduate CLS - College of Letters and Science

Subject

MATH

Course Number

202B

Department

Course Level

Graduate

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