# Graduate Course 22M:210

## Analysis

### Fall 2007

#### Some facts and observations:

Following a long tradition, we will use Rudin's Real and Complex.

Rudin's "Real and Complex Analysis" has served as a standard textbook in the first graduate course in analysis at lots of universities in the US, and around the world. I know that some Rudin exercises are hard, so we will supplement with warm-up exercises from other books, for example

Elementary Real and Complex Analysis (Dover Books on Mathematics)
by Georgi E. Shilov
which is also a good and cheap supplement:

include measure theory, Fourier series, Fourier integrals, function spaces, including Hilbert spaces. Examples and applications will be part of the syllabus.
#### Book Comparison:

Shilov vs Rudin: Rudin's 'Real and Complex' has become an institution, but conventional wisdom will have it that Shilov is a lot gentler on students, and easier to get started with: It stresses motivation a bit more, the exercises are easier, and finally Shilov gets to touch upon a few applications; fashionable these days (see also 22m313.) Rudin's book goes more in depth, and has stood the test of time.
There will be an organizational session in the first class meeting where we will discuss course requirements, but by tradition, they are flexible and can be tailored to your plans.

See also (will be updated)
http://www.math.uiowa.edu/grad/gradcourses200fa2004.html.

#### Course Meeting Schedule:

MWF 3:30 in MLH 205.

#### Course Books:

Rudin, Walter; Real and complex analysis. Third edition. McGraw-Hill Book Co., New York, 1987. xiv+416 pp. ISBN: 0-07-054234-1.

#### Relevant Seminars:

FYI: The two seminars, Operator Theory and Math Physics for fall 2006.

One organizational meeting Tuesday 8/22 at 1:30 in VAN 301 (that's the
Physics building!)

Two slots: 1:30, and 2:30.

PS.: There are links to all of Jorgensen's book lists, reviews and other amazon.com activities at this link:

Palle E.T. Jorgensen's amazon Profile.

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This page was last modified on June 29, 2007 by Myung-Sin Song.

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