Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Assuming only an elementary background in discrete mathematics, this textbook is an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It includes random sampling, expectations, Markov’s and Chevyshev’s inequalities, Chernoff bounds, balls and bins models, the probabilistic method, Markov chains, MCMC, martingales, entropy, and other topics. The book is designed to accompany a one- or two-semester course for graduate students in computer science and applied mathematics.
1. Events and probability
2. Discrete random variables and expectation
3. Moments and deviations
4. Chernoff bounds
5. Balls, bins and random graphs
6. The probabilistic method
7. Markov chains and random walks
8. Continuous distributions and the Poisson process
9. Entropy, randomness and information
10. The Monte Carlo method
11. Coupling of Markov chains
12. Martingales
13. Pairwise independence and universal hash functions
14. Balanced allocations
