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

OFFICE HOURS: Tuesday, Thursday 11:00-12:00 in 677 Soda

READER: Vilas Winstein (vilas@berkeley.edu)

OFFICE HOUR: Wednesday 1:00-2:00 in 1044 Evans

- (11/5) Lecture Note 18 is posted below. Also, Quiz 8 has been graded and the solutions are posted below.
- (10/31)
**Important guidance and clarification on HW3:****(i)**Q1 and Q3 on HW3 are quite lengthy and tricky. I recommend tackling the other three problems (which are more straightforward) first. Also, you should not stress out too much about completing every problem: e.g., if you run out of time, omitting part or all of Q1 or Q3 is fine.**(ii)**In Q3, a point*u*is connected to a point*v*if*u*is one of the*k*closest neighbors of*v or vice versa*. (Note that this relation is not necessarily symmetric!) In other words, we include the edge (*u,v*) in the undirected graph*G*if at least one of the conditions is satisfied. This means that the degree of some points may be larger than*k*. - (10/31) Lecture Note 17 and Quiz 8 are posted below. Quiz 8 is due at 5pm on Sunday, Nov 3 and is based on Lectures 16 & 17.
- (10/29) Lecture Note 16 is posted below. Also, Quiz 7 has been graded and the solutions are posted below.
- (10/25) Quiz 7 is posted below; it is due at 5pm on Sunday, Oct 27. It's based on Lectures 14 & 15 and shouldn't take much time if you're on top of those.
- (10/24) Lecture Note 15 and HW3 are posted below. HW3 is due on Friday November 8th (~ 2 weeks). As usual, you are strongly encouraged to start work on this now; you already have all the necessary material. If you are not already doing so, I also strongly recommend working in small groups (2-3 people) to discuss the problems.
- (10/22) Lecture Note 14 is posted below.
- (10/21) Quiz 6 has been graded; solutions are below. Since people had a bit more trouble than usual with this Quiz, the solutions include brief explanations.
- (10/17) A reminder that students are expected to attend class regularly. Most of you are doing this already, but some are not. The intention in this class is that you follow the material in real time, and participate in active learning in class. Students are asking insightful questions that often lead to important clarifications of the explanations in the notes. I'm not taking formal attendance, and occasional absences are fine, but please plan to attend by default.
- (10/17) Lecture Note 13 and Quiz 6 are posted below. Quiz 6 is based on lectures 11, 12 and 13 and should only take a few minutes if you've followed that material. It's due as usual this Sunday, 10/20, at 5pm.
- (10/15) Lecture Note 12 is posted below. Also, HW2 has been graded. Please carefully review your graded solutions on Gradescope and check the sample solutions below.
- (9/17) A student in the class, Bhaskar Mishra, has set up a class discord server to make it easier for students to disucss lecture topics and homework questions outside class. Here is the link to the server: https://discord.gg/pY5P59v7. Thanks to Bhaskar for setting this up.

- Lecture 1 (8/29)
- Lecture 2 (9/3)
- Lecture 3 (9/5 & 9/10). Updated 9/10
- Lecture 4 (9/12)
- Lecture 5 (9/17)
- Lecture 6 (9/19)
- Lecture 7 (9/24)
- Lecture 8 (9/26)
- Lecture 9 (10/1)
- Lecture 10 (10/3)
- Lecture 11 (10/10)
- Lecture 12 (10/15)
- Lecture 13 (10/17)
- Lecture 14 (10/22)
- Lecture 15 (10/24)
- Lecture 16 (10/29)
- Lecture 17 (10/31)
- Lecture 18 (11/5)

- Homework 1 (Out 9/10; Due 9/20) Solutions
- Homework 2 (Out 9/27; Due 10/11) Solutions
- Homework 3 (Out 10/24; Due 11/8)

- Quiz 1 (Out 9/5; Due 9/8) Solutions
- Quiz 2 (Out 9/12; Due 9/15) Solutions
- Quiz 3 (Out 9/20; Due 9/22) Solutions
- Quiz 4 (Out 9/27; Due 9/29) Solutions
- Quiz 5 (Out 10/4; Due 10/6) Solutions
- Quiz 6 (Out 10/17; Due 10/20) Solutions
- Quiz 7 (Out 10/25; Due 10/27) Solutions
- Quiz 8 (Out 10/31; Due 11/3) 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*(4th ed.), Wiley, 2016. - Svante Janson, Tomasz Łuczak and Andrzej Ruciński,
*Random Graphs*, Wiley, 2000. - Geoffrey Grimmett and David Stirzaker,
*Probability and Random Processes*(4th ed.), Oxford Univ Press, 2020. - 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.

In addition, there may also be a short weekly or bi-weekly quiz consisting of a few multiple-choice questions designed to test your understanding of that week's lectures. This should take minimal additional time if you are following the class.

Finally, for full credit students are expected to attend class regularly. Occasional absences are fine, but systematic non-attendance is not.