LECTURES: Tuesday, Thursday 9:30-11:00 in 306 Soda

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

TA: Jonah Brown-Cohen (jonahbc@eecs, 633 Soda)

OFFICE HOURS: Tuesday 2:00-3:00, Wednesday 2:00-3:00 in 611 Soda

- Lecture 1 (1/16)
- Lecture 2 (1/18)
- Lecture 3 (1/23)
- Lecture 4 (1/25)
- Lecture 5 (1/30)
- Lecture 6 (2/1)
- Lecture 7 (2/6)
- Lecture 8 (2/8)
- Lecture 9 (2/13)
- Lecture 10 (2/15)
- Lecture 11 (2/20)
- Lecture 12 (2/22)
- Lecture 13 (2/27)
- Lecture 14 (3/1)
- Lecture 15 (3/6)
- Lecture 16 (3/8)
- Lecture 17 (3/13)
- Lecture 18 (3/15)
- Lecture 19 (3/20)
- Lecture 20 (3/22)
- Lecture 21 (4/3)
- Lecture 22 (4/5) [Taught by Jonah, lecture notes by Ryan O'Donnell]
- Lecture 23 (4/10)
- Lecture 24 (4/12)
- Lecture 25 (4/17)
- Lecture 26 (4/19)
- Lecture 27 (4/24)
- Lecture 28 (4/26)

- Problem Set 1 (Out 1/29; Due 2/8)
- Problem Set 1 solutions
- Problem Set 2 (Out 2/19; Minor Correction 2/21; Due 3/1)
- Problem Set 2 solutions
- Problem Set 3 (Out 3/12; Due 4/5)
- Problem Set 3 solutions
- Problem Set 4 (Out 4/17; Q3(a) Correction 4/22; Due 4/26)
- Problem Set 4 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.