Caltech CS 150b Probability and Algorithms, Fall 2019 Leonard J. Schulman
(May 13, 2019):
This is a very early posting of the web page for CS150b,
Fall 2019. During Fall 2018 I taught the "a" course of
this sequence. Since 2019 is the first time "b" is being
offered, a few words about the plan:
There is a huge amount of
material that I would like to cover, and only a fraction
of that will fit. I will be making the topic selection
during the summer (which means you might influence it
if you get in touch early enough). Some of the possibilities are:
The question arises whether students need to have first taken cs150a. The answer
is No, But (a) you should have had some course in probability (with combinatorial
problems, not just an analysis course), (b) depending on the topics we wind up with, I might
point you to a few sections of the lecture notes for cs150a (which cover the material of that course
comprehensively). E.g., if we cover epsilon-biased spaces, I'll want you to review k-wise
independent spaces; if we cover analysis of boolean functions I'll want you to review the
material on the 0-1 law and thresholds. In any case, I'll be happy to help with the catch-up
process. Feel free to contact me a few weeks before the start of the term to see what the
more detailed plan is.
- Epsilon-biased k-wise independent sample spaces
- Talagrand-type large deviation inequalities
- Expanders: randomized existence; explicit constructions
- Markov Chain Monte Carlo algorithms for approximate sampling and counting
- Weighted sampling methods (e.g., #DNF, network reliability, VC theory for nonnegative functions)
- Introductory analysis of boolean functions (Kahn-Kalai-Linial, Friedgut)
- Other gems: sampling random factored integers, generating random spanning trees, De Finetti theorem, ...
There are several days during the term that lecture will
have to be canceled or rescheduled:
- Class is canceled on Oct 9, 14, 21.
- On Oct 18 there will be an extra class at 4pm in the usual
classroom (i.e., we'll meet twice that day).
- On Oct 25 class will be rescheduled: instead of 10am it will be at 4pm in the usual
Office Hours: Jenish on Mondays at 7pm in the classroom. (Ask Sheila Shull if you need to arrange after-hours access.)
Lecture Notes: I usually wind up revising my lecture notes after
teaching, so they will be gradually posted here, as we go. Corrections and comments are welcome.
- PS1; due date postponed to Oct. 22. Problem 4 has been corrected in this handout.