Math 205B Homepage, Winter 2010-2011

Real Analysis

Instructor: András Vasy

Office: 383M

Phone: 723-2226

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

Tentative office hours: M10-11, T4:15-5:15, W10-11.

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

Extra lecture on Tuesday, March 1, at 9:30am in 383N!

Course assistant: Bob Hough. Office: 380N. E-mail: rdhough "at" math.stanford.edu

Office hours: T2:15-4:15, W1-3, F2-4.

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 3rd or 4th (to be decided). There is no final exam.

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 second, take home, midterm is avaliable now!

It is due on Friday, March 4, at noon.

A small typo: on Problem 5(7), Pu should be P(D)u in both places. This is fixed above.

The take-home midterm has been graded!

Out of a max score of 100, the mean was 73, the median 82. As before, there are no grades for the midterm, as the score counts towards the course grade. However, to give you a rough idea of your grade if you perform similarly relative to the expectations (which are higher for problem sets and for the take-home exam than for the in-class midterm) the rough ranges are:

The first midterm is in class, on Thursday, February 3.

It is closed book, notes, etc.

Solutions to the midterm are now available.

The midterm has been graded!

Out of a total of 100 points, the median was 70, the mean 65. There are no grades for the midterm, as the score counts towards the course grade. However, to give you a rough idea of your grade if you perform similarly relative to the expectations (which are higher for problem sets and for the take-home exam) the rough ranges are:

A practice midterm with solutions is available.

Recommendations for the midterm: please read through your class notes, the topics covered from the textbook (listed in the syllabus), and make sure you know how to solve the homework problems. In the exam, the instructions will state: "You may quote any theorem from the textbook, the lecture or the homework provided that you are not explicitly asked to prove it (Problem ... falls into this category). If you cannot solve part of a problem, you may quote its result in subsequent parts." Thus, you will greatly benefit from knowing what you have proved on your homework, as well as how you did it.

After you do all this, you may want to take the practice exam as a timed exam. This exam is an edited version of the exam from 2007 (the midterm is now earlier, so a problem was removed, and there was some rephrasing). Thus, it is a little shorter than what you should expect on the in-class midterm. So give yourself 60 minutes for the practice exam if you want to do it in exam conditions.

Recent Real Analysis Quals

Problem Sets