This is an introductory course in functional analysis, which is basically a blend of linear algebra and topology. Our main concern will be with infinite dimensional linear spaces and linear operators between them. We will see that such spaces and operators come up naturally in many areas of math and its applications (most notably PDEs, ODEs and quantum mechanics).

The prerequisites for the course is technically Math 6337, Real Analysis I, but a good understanding of linear algebra, metric space topology (as you would see in most undergraduate analysis course) and a willingness to work a little to fill in some gaps should be sufficient for the course. Some people might not be familiar with abstract topology. That is not a serious problem, but as we will use some terminology from topology you might want to review the following

• Review of basic point set topology.

Lectures: Tuesday and Thursday 9:35 to 10:55 in Skiles 171 (new room, we are no longer in 269).
Professor: John Etnyre
Office: Skiles 106
Phone: 404.385.6760
e-mail: etnyre "at" math .gatech.edu

Grading Policy

Grading for the class will be based on approximately six homework assignments (and class participation, that is showing up for most of the classes).

The assignments will be posted below and will be due in class on the day indicated on the assignment.  I encourage you to work on these assignments with other students in the class and to use whatever other resources you might have (like me and others in the department), but each problem must be written up in your own words by you. At some point everyone needs to learn TeX or LaTeX so I encourage you to write up your homework using one of these packages, but this is not a requirement. If you would like help getting started with TeX or LaTeX you are welcome to talk to me about it.

Textbook

There official text book for the class is:

• A Course in Functional Analysis by John B. Conway.

This is a very nice text, but there are other great text too. I will not follow any textbook too closely, so you might also want to consider the following books:

• Functional Analysis by Walter Rudin,
• Functional Analysis byPeter D. Lax
• Introductory Functional Analysis with Applications by Erwin Kreyszig, and
• Functional Analysis, Volume 1 by Michael Reed and Barry Simon.

Homework

Homework Assignment 1: Here is a pdf of this assignment. It is due September 9.

Homework Assignment 2: Here is a pdf of this assignment. It is due October 4.

Homework Assignment 3: Here is a pdf of this assignment. It is due November 3.

Homework Assignment 4: Here is a pdf of this assignment. It is due December 1.