Math 205B Homepage, Winter 2020-2021

Real Analysis

Instructor: András Vasy

Office: virtual

E-mail: andras "at"

Tentative office hours: half an hour after every lecture (i.e. till 4pm), except Wednesday when until 4:30pm, and on Monday (starting week 2) an extra hour after half an hour break: 4:30-5:30pm.

Class location: Zoom, MWF 2:30-3:30.

Course assistant: Lie Qian

Office: virtual

E-mail: lqian "at"

Tentative office hours: Monday 9-11:30am (starting week 2) and Thursday 3:15-4:15pm and 5:45-6:45pm. On the weeks when Monday is a holiday, the Monday office hour will be instead replaced by a shorter one on Wednesday 9-10:30am -- please use the Monday link still.

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

On reserve at the library: Peter Lax: Functional Analysis.

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 (50%), on the two midterm exams (25% each). The first midterm will be in-class, while the second one will be take-home, most likely due towards the end of week 9.

The homework will be due on gradescope on the designated day, usually Fridays. 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.

Problem Sets