Course description:
This is a graduate level course that covers probability techniques in the design and the analysis of randomized algorithms. Topics include measure concentration results such as Chernoff Bound, Hoeffding's Inequality and martingale inequalities. We also cover classical results such as the Johnson-Lindenstrauss Lemma and the Lovasz Local Lemma. This course puts emphasis on understanding how the various techniques work. However, we would explain the proofs from the computer scientist's viewpoint and avoid the pedantic axiomatic approach.
Prerequisites:Students should have a basic knowledge of probability and algorithms. For example, probability space, discrete and continuous random variables, expectation, independence, probability density function, normal (Gaussian) distribution. However, we would also recall the necessary concepts as the course proceeds.
Method of Assessment: There will be 4 or 5 homeworks (25%), a mid-term exam (25%) and a final exam (50%).
Textbook: There is no compulsory text, but here are some suggested textbooks:
- Randomized Algorithms, Motwani and Raghavan
- The Probabilistic Method, Alon and Spencer