CS 880 - Advanced Complexity Theory Spring 2008

Course Description

The main topic for the Spring 2008 edition of CS 880 is harmonic analysis of Boolean functions. Just like in the case of real functions, the Fourier transform turns out to be a very powerful tool in the analysis of Boolean functions. We will spend some time developing the underlying mathematics but mainly focus on the many applications within theory of computing and beyond.

Time permitting, we will also cover a few isolated topics of recent interest.

Text

There is no required text. Lecture notes will be made available from the course web page.

References

In recent years a number of similar courses have been offered at other places. Here are links to course pages I'm aware of: Berkeley, CMU, Georgia Tech, Hebrew U, Rutgers, the other UW.

Prerequisites

Introductory Complexity Theory at the level of CS 810, or consent of the instructor. Mathematical maturity can substitute for knowledge of the CS 810 material.

Lectures

Three 75-minute time slots are reserved for this course, namely MWF 2:30-3:45pm in 1257 CS&S. The plan is to use two of the three slots on average but to frontload the semester so that there is time to work on projects at the end of the semester.

Course Work

• Scribes (20%). Write lecture notes for two to three lectures. Someone who missed the class should be able to learn the material from the notes. I expect a draft within 24 hours after the lecture, and the final version a week later. You need to type your notes in LaTeX using the guidelines provided.

• Homework (45%). There will be 3 assignments. You are allowed to discuss the problems in group but you should write out the solutions on your own.

• Project (35%). There will be no exams. Instead, you are expected to work out a project on a topic of your own choosing. I will hand out a list with suggestions during the 5th week of the semester. You should discuss your selection with me, and settle down on a topic before spring break. More guidelines will be posted in due time.