Math 205B Homepage, Winter 2007-2008

Real Analysis

Instructor: András Vasy

Office: 383M

Phone: 723-2226

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

Office hours: T 1-2pm, W 10-11am, F 10-11am.

Office hour on Friday, January 25, is moved to Thursday, January 24, 2-3pm.

Class location: TTh 11am-12:15pm, Room 381U.


Course assistant: Dean Baskin. Office: 380-N. E-mail: dbaskin "at" math.stanford.edu

Office hours: M 10-11am, W 2:15-3:15pm, T 9:30-11am.


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 is 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, the spectral theorem, and hopefully unbounded operators.

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 7th or 8th (to be decided).

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.


The first midterm has been graded!

The mean score was 67.5/100, the median was 72/100. There are no grades for the exam, as grades are decided based on performance in the whole course, and it is the score that counts. But to give you a rough idea, scores above 70 or so would be A's, in the 60-70 range (again, roughly) would be A-'s, in the 40-60 range B's, in the 30-40 range B-'s. Students with weaker scores should definitely talk to me about their performance in the course.

As practice, here is the midterm from 2007 with solutions.

The actual first midterm and the solutions are also available.


The second midterm is due on Friday, March 7, at noon.

Midterm 2 due date has been extended to 1pm on Saturday, March 8, due to popular demand.

Solutions to the midterm, thanks to Dean.

The second midterm has been graded!

The mean is 77/100, the median is 83. Again, there are no grades for the exam, but the following gives a rough idea: scores above 80: A, 70s: A-, 60s: B+, 50ish, B-, below 40:C.

Recent Real Analysis Quals


Answer to a question in class, concerning whether if the unit ball in the dual of a Banach space is weakly compact, the space is reflexive.


Problem Sets