Math 111a - Real Analysis

Class meets at: Goldsmith 116, MWTh 11:10 AM -12 noon
Lecturer: Dmitry Kleinbock
Office: Goldsmith 207, phone 6-3059
Office Hours: Th 3-4 PM or by appt.
E-mail address: kleinboc@brandeis.edu

Here are homework assignments 1, 2, 3, 4, 5, 6, 7, 8 in PDF format.

Suggested textbooks:

• Real and Functional Analysis, by S. Lang (Springer)


• Real and Complex Analysis, by W. Rudin (McGraw-Hill)


• Introductory Real Analysis, by A. Kolmogorov and S. Fomin (Dover)

This is a graduate course, and thus it assumes some background in undergraduate real analysis as a prerequisite. This includes basics on topological and metric spaces (compactness, completeness, etc), which will be reviewed at the beginning of the class.

Topics to be covered:

• Banach and Hilbert spaces, linear functionals, linear operators


• abstract measure theory and integration, Lebesgue integral on Rⁿ


• L^p spaces, duality (Radon-Nikodym)


• measures as functionals (Riesz representation)


• more analysis on Rⁿ: convolution, Fourier transform


• other topics -- if time permits

Homework will be assigned once every one or two weeks and will be due the following week. At the end of the course there will be a take-home final exam.