(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

- 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 classroom.

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.- Lectures 1 and 2 (Oct 2 and 4). Appetizer: random factored numbers. Query complexity for game tree and boolean formula evaluation.
- Lecture 3 (Oct 7). Randomized game tree evaluation. Branching processes.
- Lecture 4 (Oct 11). Probability generating functions.
- Lecture 5 (Oct 16). Cont. game tree evaluation. Randomized and Distributional complexity.
- Lectures 6 and 7 (Oct 18). Randomized and Distributional complexity. Communication complexity.
- Lectures 8 and 9 (Oct 23 and 25). Linear programming in low dimension.
- Lecture 10 (Oct 28). Multiplicative weights update.
- Lectures 11 and 12 (Oct 30 and Nov 1). #DNF approximation.
- Lecture 13 (Nov 4). Min-Cut.
- Lecture 14 (Nov 6). Faster Min-Cut.
- Lecture 15 (Nov 8). Network reliability.
- Lecture 16 (Nov 11). Approximate counting vs. approximate sampling
- Lectures 17 and 18 (Nov 13 and 15). Introduction to and examples of Markov chains. See Sinclair notes.
- Lectures 19 and 20 (Nov 18 and 20). Perron theorem; fundamental theorem of Markov chains.
- Lectures 21 and 22 (Nov 22 and 25). Coupling: basic definitions, inequalities, examples.
- Lecture 23 (Nov 27). Coupling: sampling graph colorings.
- Lecture 24 (Dec 2). Path coupling: sampling graph colorings.
- Lectures 25 and 26 (Dec 4 and 6). Lozenge tilings, monotone coupling, coupling from the past.