Instructor | Hamed Hatami | |
TA's | Teaching assistant: Ran Tao (ran.tao6@mail.mcgill...) | |
Lecture | Tuesday, Thursday 8:35-9:55 at EGNTR 2120 | |
Course Outline | Download | |
Office hours: | Tuesdays 10:05-10:55. If you want to meet outside office hours, the best thing is to send me an email, but you can also just drop by my office, and if I'm not busy I will answer your questions. | |
Lecture notes: | Here is a draft of the Lecture Notes. It will be updated as we go. |
This is a rigorous course with an emphasis on mathematical proofs. This course is a continuation of Comp 330 and as a result it requires Comp 330 as a prerequisite. You must be comfortable with basic concepts from logic, linear algebra, Turing Machines, and you must be able to read and write precise mathematical statements.
Homework (80% = 4 x 20%). There will be four homework assignments. The due dates are going to be announced. The homework and the exams will be graded based on correctness rather than effort alone. Each assignment will be posted on the course web page. Your grades will be posted on mycourses.
Late homeworks can be submitted for valid reasons.
Group project. 20%
Part I | ||
Lecture | Topic | Reading |
1 (9/2) | Computational model, Time and Space classes | Chapter 1, Chapter 3 of notes until the beginning of time Hierarchy Theorems. |
2 (9/7) | Time Hierarchy Theorems, Polynomial Hierarchy. | Chapter 3, Chapter 4 |
3 (9/9) | Collapse of Polynomial Hierarchy if P=NP, Space complexity | Chapter 5 until the beginning of logspace reductions. |
4 (9/14) | L and NL, Savitch's Theorem | Chapter 6 |
5 (9/16) | NL=coNL, Immerman-Szelepcsenyi's Theorem | Chapter 7 |
6 (9/21) | Ladner's Theorem and reletivization | Chapter 8 and 9 |
7 (9/23) | PH through Reletivization, and NP vs P | Chapter 9 |
8 (9/28) | A crash course in Probabilistic Method I | Alon-Spencer Chapter 1 |
9 (9/30) | A crash course in Probabilistic Method II | Alon-Spencer Chapter 2 |
10 (10/5) | Randomized Classes I | Chapter 10 |
11 (10/7) | Randomized Classes II | Chapter 10 |
Part II | ||
Lecture | Topic | Reading |
12 (10/15) | Circuit complexity I | Chapter 11 |
13 (10/19) | Circuit complexity II | Chapter 11 |
14 (10/21) | AC circuits I | Chapter 12 |
15 (10/26) | AC circuits II | Chapter 12 |
16 (10/28) | Razborov-Smolensky | Chapter 13 |
17 (11/02) | Monotone Circuit Lower-bounds | Chapter 14 |
18 (11/04) | Natural Proofs | Chapter 15 |
19 (11/09) | Fourier Analysis of Boolean functions | Chapter 16 |
Academic honesty. McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offenses under the Code of Student Conduct and Disciplinary Procedures (see http://www.mcgill.ca/integrity for more information). Most importantly, work submitted for this course must represent your own efforts. Copying assignments or tests from any source, completely or partially, allowing others to copy your work, will not be tolerated, and they will be reported to disciplinary office.
Submission of written work in French. In accord [sic] with McGill University's Charter of Students' Rights, students in this course have the right to submit in English or in French any written work that is to be graded.