Computational Complexity is the mathematical investigation of several broad questions that have to do with computation. In this class, we shall develop the mathematics required to ask:

- What is hard to compute and why?
- How useful is access to various resources like time, memory, randomness and advice, when it comes to computation?

We seek to give a rigorous mathematical framework that will enable us to answer some of these questions. Along the way, we shall encounter several interesting mathematical tools. Complexity theory has been around as an area for more than 50 years, but it is still in its infancy. It is notorious for generating the hardest open questions in computer science.

#### Logistics

- Professor: Anup Rao, TAs: Siddharth Iyer, Oscar Sprumont
- Time and Location: Tuesdays and Thursdays 1130-1250, here.
- Office Hours: Anup, Wednesdays from 1-2, and after class for half an hour, here; Siddharth, Thursdays from 2-3 here; Oscar, Fridays from 3-4 here.
- Work: The class willl involve biweekly homework (50%), a take-home midterm (20%), and a take-home final exam (30%). Collaboration is allowed on the homework, but you must write-up solutions by yourself.
- There is a class discussion board.
- Course Materials: All material covered in this course will be posted in the form of lecture notes on this website (see the Schedule and Notes tab). You can also refer to this textbook by Arora and Barak.