MWF, 14:00-14:50. Obrian 109 (map)

Instructor: Hung Q. Ngo

Probabilistic analysis and randomized algorithms have become an indispensible tool in virtually all areas of Computer Science, ranging from combinatorial optimization, machine learning, data streaming, approximation algorithms analysis and designs, complexity theory, coding theory, to communication networks and secured protocols. This course has two major objectives: (a) it introduces key concepts, tools and techniques from probability theory which are often employed in solving many Computer Science problems, and (b) it presents many examples from these major themes: combinatorial constructions and existential proofs, randomized algorithms, sampling, and statistical learning theory.

In addition to the probabilistic paradigm, students are expected to gain substantial discrete mathematics problem solving skills essential for computer scientists and engineers.

- Feel free to drop by, or by email appointment.

CSE 531 or equivalence, good grasp of discrete mathematic thinking. Rudimentary knowledge of discrete probability theory.

5 Written Assignments. 1 Final Presentation. No exam.

- Sep 05 (Labor day), Nov 23 to Nov 26 (Fall Recess)

- 5 written assignments: 16% each.
- Final presentation and report : 20%
- Assignments due at the end of the lecture on the due date
- 1 day (up to 24 hours) late: 20% reduction
- Each extra (24 hours) day late: 40% reduction (which means you don't have to bother submit your assignment if it's more than 2 days late)

- A: 85%, A-: 80%, B+: 72%, B: 65%, B-:55%, C:45%, D: 40%, F.

There is no official textbook for the course. I do believe that my lecture notes and pointers are sufficient. The following books should be helpful to you, especially the first four.

- (Free!) Ryan O'Donnell's Probability and Computing Lecture Notes. These are a set of (free) notes for an introductory undergraduate course on probability theory in computing.
- Michael Mitzenmacher and Eli Upfal, Probability and Computing: Randomized Algorithms and Probabilistic Analysis, Cambridge University Press, 2005.
- Rajeev Motwani and Prabhakar Raghavan, Randomized Algorithms, 492 pages, Cambridge University Press (August 25, 1995), ISBN: 0521474655
- Alon, Noga; Spencer, Joel H. The Probabilistic Method, Second edition. Wiley-Interscience Series in Discrete Mathematics and Optimization. John Wiley & Sons, New York, 2000. xviii+301 pp. ISBN: 0-471-37046-0
- [Won't be free for much longer] Russell Lyons (with Yuval Peres), Probability on Trees and Networks
- [Free!] David A. Levin, Yuval Peres, and Elizabeth L. Wilmer, Markov Chains and Mixing Times
- [Free!] Michael Luby and Avi Wigderson, Pairwise Independence and Derandomization, Foundation and Trends in Theoretical Computer Science, vol 1, no 4, pp 237--301, 2005. NOW Publishers Inc.
- Bella Bolobas, Random Graphs, Cambridge University Press, Studies in Advanced Mathematics, #73, September 2001.
- Mark Jerum, Counting, Sampling and Integrating: Algorithms and Complexity (Lectures in Mathematics. ETH Zürich), Birkhäuser Basel; 1 edition (April 28, 2003).
- T. Tao and V. Vu, Additive Combinatorics (Cambridge Studies in Advanced Mathematics).
- Molloy, Michael; Reed, Bruce, Graph Colouring and the Probabilistic Method. Algorithms and Combinatorics, 23. Springer-Verlag, Berlin, 2002. xiv+326 pp. ISBN: 3-540-42139-4
- Gamerman, D. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Second Edition (Chapman & Hall/CRC Texts in Statistical Science). Boca Raton, FL: CRC Press, 1997.