Math 175 Homepage, Autumn 2020-2021

Elementary Functional Analysis

Instructor: András Vasy

Office: virtual

Phone: zoom

E-mail: andras "at"

Tentative office hours: after class: MW3:30-4pm, F3:30-4:30pm, as well as M4:30-5:30pm (starting week 2).

Course Assistant: Alexandra Stavrianidi

E-mail: alexst "at"

Office: virtual

Tentative office hours: M11:30am-12:30pm, T2-4pm, F9-10am.

Class location: MWF 2:30-3:30pm on zoom.

Textbook: Young: An introduction to Hilbert space (required), plus the instructor's lecture notes. The textbook is electronically available via Stanford Libraries; the link to the web page is

The running syllabus will change somewhat, but should give an indication of the scope and speed of the course.

This course is an introduction to functional analysis, concentrating on Hilbert spaces and operators on them. It covers a number of topics also covered by Math 205B, but Math 205B proceeds at a much faster pace, covering much more material.

It is the continuation of the analysis courses 115 or 171, emphasizing rigorous (i.e. logically careful) proofs.

The knowledge of measure theory, as presented in 172, is NOT a prerequisite of the class, though L^p spaces will be discussed as completions. Some Fourier analysis will be covered in the course as well.

Grading policy: The grade will be based on the weekly quiz (10%), the weekly homework (25%), on the shorter, 30-45 minutes long, midterms 1-3 (15% each, for a total of 45%), and on the longer, week-long, project (20%), which will be due in week 10.

The homework will be due on canvas on the designated day, usually Wednesdays. 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 weekly quizzes feature easier material than the homeworks with 3-5 short questions. According to general Stanford policies, they are open book (including internet access, etc), but you must not discuss the questions with anyone other than the instructor and the course assistant. One part of the quiz is a feedback question, which is expected to be 2-3 points out of 10. As long as you enter feedback, possibly just `Nothing to report', you will receive credit. The quizzes are planned to be untimed, but with a due date, most likely on Fridays, becoming available on Wednesdays.

Lecture Notes

Below are the lecture notes. Note that these are restricted to Stanford students, and they should not be more broadly circulated.

Problem Sets