LECTURES: Tuesday, Thursday 9:30-11:00 in 310 Soda

OFFICE HOURS: Monday 1:00-2:00, Thursday 11:00-12:00 in 677 Soda

READER: Pranav Trivedi (pranavtrivedi@berkeley.edu)

OFFICE HOUR: Wednesday 12:00-1:00 in 1044 Evans

- (12/8) HW4 has been graded. Solutions are posted below, and you can view your corrected submissions on Gradescope. This concludes the course! Thanks for your participation. Grades will be posted before the end of next week. If you haven't already done so, please take a moment to fill out the course evaluation. Thanks and best wishes.
- (12/1) Here is a zoom link for today's lecture, for use by those who don't want to cross a picket line.
- (11/29) Lecture Note 26 is posted below; you now have all the information you need to complete HW4, which is due this coming Friday, Dec 2.
- (11/28) Lectures resume tomorrow (Nov 29). Please remember that the deadline for HW4 is this coming Friday, Dec 2. Please also take a few moments to fill out the online course evaluation by logging in to course-evaluations.berkeley.edu. I very much value your feedback on the class.
- (11/18) Lecture Notes 24 and 25 are posted below.
- (11/16) Here is a zoom link for tomorrow's lecture, for use by those who don't want to cross a picket line.
- (11/15) Homework 4 is posted below, and is due by 5pm on Friday, Dec. 2. This is the last homework, and is slightly shorter than the previous ones. However, you are advised as usual not to leave it until the last few days. You already have all the material needed to complete this homework, except for the last problem (Q4), which will require material from Lectures 25 and 26. As always, you are encouraged to work in pairs or small groups but please be sure to write up your solutions on your own.

- Lecture 1 (8/25)
- Lecture 2 (8/30)
- Lecture 3 (9/1)
- Lecture 4 (9/6)
- Lecture 5 (9/8)
- Lecture 6 (9/13)
- Lecture 7 (9/15)
- Lecture 8 (9/20)
- Lecture 9 (9/22)
- Lecture 10 (9/27)
- Lecture 11 (9/29)
- Lecture 12 (10/4)
- Lecture 13 (10/6)
- Lecture 14 (10/11)
- Lecture 15 (10/13)
- Lecture 16 (10/18)
- Lecture 17 (10/20)
- Lecture 18 (10/25)
- Lecture 19 (10/27)
- Lecture 20 (11/1)
- Lecture 21 (11/3)
- Lecture 22 (11/8)
- Lecture 23 (11/10)
- Lecture 24 (11/15)
- Lecture 25 (11/17)
- Lecture 26 (11/29)

- Homework 1 (Out 9/6; Due 9/16) Solutions
- Homework 2 (Out 9/27; Due 10/7) Solutions
- Homework 3 (Out 10/21; Due 11/4) Solutions
- Homework 4 (Out 11/15; Due 12/2) Solutions

- Elementary examples: e.g., checking identities, fingerprinting and pattern matching, primality testing.
- Moments and deviations: e.g., linearity of expectation, universal hash functions, second moment method, unbiased estimators, approximate counting.
- The probabilistic method: e.g., threshold phenomena in random graphs and random k-SAT formulas; Lovász Local Lemma.
- Chernoff/Hoeffding tail bounds: e.g., Hamilton cycles in a random graph, randomized routing, occupancy problems and load balancing, the Poisson approximation.
- Martingales and bounded differences: e.g., Azuma's inequality, chromatic number of a random graph, sharp concentration of Quicksort, optional stopping theorem and hitting times.
- Random spatial data: e.g, subadditivity, Talagrand's inequality, the TSP and longest increasing subsequences.
- Random walks and Markov chains: e.g., hitting and cover times, probability amplification by random walks on expanders, Markov chain Monte Carlo algorithms.
- Miscellaneous additional topics as time permits: e.g., statistical physics, reconstruction problems, rigorous analysis of black-box optimization heuristics,...

- Noga Alon and Joel Spencer,
*The Probabilistic Method*(3rd ed.), Wiley, 2008. - Svante Janson, Tomasz Łuczak and Andrzej Ruciński,
*Random Graphs*, Wiley, 2000. - Geoffrey Grimmett and David Stirzaker,
*Probability and Random Processes*(3rd ed.), Oxford Univ Press, 2001. - Michael Mitzenmacher and Eli Upfal,
*Probability and Computing: Randomized Algorithms and Probabilistic Analysis*(2nd ed.), Cambridge Univ Press, 2017. - Rajeev Motwani and Prabhakar Raghavan,
*Randomized Algorithms*, Cambridge Univ Press, 1995.