Probability and Computing: Randomized Algorithms and Probabilistic Analysis

Probability and Computing: Randomized Algorithms and Probabilistic Analysis by Mitzenmacher, Michael. hardcover edition. ISBN: 9780521835404.

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, Markovs and Chevyshevs 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.