Office: 383M

Phone: 723-2226

E-mail: andras "at" math.stanford.edu

Tentative office hours: TW 10:30-11:30, Th 2-3.

Class location: MWF 12-12:50pm, Room 380-380W.

Course assistant: Gergely Szűcs

Office: 381B

E-mail: gergelys "at" math.stanford.edu

Tentative office hours: M 2-3:30, T5-8, W 1:30-3

Textbook: Reed and Simon: Functional Analysis (volume 1 of `Methods of Mathematical Physics')

On reserve at the library: Peter Lax: Functional Analysis and Royden: Real Analysis (Royden's book is on permanent reserve).The syllabus will be posted here.

The second quarter of the graduate real analysis sequence covers functional analysis. We will use Reed and Simon's Functional Analysis (volume 1 of `Methods of Mathematical Physics'), quickly covering Chapter 1 as background (except the measure theory part, which was covered in 205A), and start with Chapter 2 (Hilbert spaces). We cover Banach spaces, topological spaces, locally convex vector spaces, bounded operators and the spectral theorem.Grading policy: The grade will be based on the weekly homework (30%), on the two midterm exams (35% each). The first midterm will be in-class, while the second one will be take-home, due around March 5th (to be decided).There is no final exam.

The midterm covers chapters I-III of the text, i.e. through the Banach space results.

A practice midterm with solutions is available.The homework will be due either in class or by 9pm in the instructor's mailbox on the designated day. You are allowed to discuss the homework with others in the class, but you must write up your homework solution by yourself. Thus, you should understand the solution, and be able to reproduce it yourself. This ensures that, apart from satisfying a requirement for this class, you can solve the similar problems that are likely to arise on the exams.

- Fall 2007. Recommended qual preparation problems: Part I: 1,2,3,5, Part II:1,2,3,4,5. Solutions of the functional analysis problems, thanks to Dean Baskin (course CA from a while back)!
- Spring 2007. Recommended qual preparation problems: Part I: 1,2,3,4,5, Part II:1,4. Solutions of the functional analysis problems, thanks to Dean Baskin (course CA from a while back)!
- Fall 2006. Recommended qual preparation problems: Part I: 1,2,3,4, Part II:1,4. Solutions of the functional analysis problems, thanks to Dean Baskin (course CA from a while back)!
- Spring 2006. Recommended qual preparation problems: Part I:1,2,3,5, Part II:1,2,3,5. Solutions of the functional analysis problems, thanks to Dean Baskin (course CA from a while back)!
- Fall 2005. Recommended qual preparation problems: Part I:1b,3,4, Part II:1,2,3,4,5. Solutions of the functional analysis problems, thanks to Dean Baskin (course CA from a while back)!
- Spring 2005. Recommended qual preparation problems: Part I:2,3,4, Part II:6,7,10. Solutions of the functional analysis problems, thanks to Dean Baskin (course CA from a while back)!

- Problem Set 1, due Thursday, January 15. Solutions, thanks to many CA's over the years!
- Problem Set 2, due Thursday, January 22. Solutions, thanks to many CA's over the years!
- Problem Set 3, due Thursday, January 29. Solutions, thanks to many CA's over the years!
- Problem Set 4, due Thursday, February 5. Solutions, thanks to many CA's over the years!
- Problem Set 5, due Thursday, February 12. Solutions, thanks to many CA's over the years!
- Problem Set 6, due Thursday, February 19. Solutions, thanks to many CA's over the years!
- Problem Set 7, due Thursday, February 26.
- Problem Set 8, due Friday, March 13, noon (in class).