Mitzenmacher M., Upfal E. Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis

Cambridge: Cambridge University Press, 2017. — 490 p.Greatly expanded, this new edition requires only an elementary background in discrete mathematics and offers a comprehensive introduction to the role of randomization and probabilistic techniques in modern computer science. Newly added chapters and sections cover topics including normal distributions, sample complexity, VC dimension, Rademacher complexity, power laws and related distributions, cuckoo hashing, and the Lovasz Local Lemma. Material relevant to machine learning and big data analysis enables students to learn modern techniques and applications. Among the many new exercises and examples are programming-related exercises that provide students with excellent training in solving relevant problems. This book provides an indispensable teaching tool to accompany a one- or two-semester course for advanced undergraduate students in computer science and applied mathematics.Events and Probability
Discrete Random Variables and Expectation
Moments and Deviations
Chernoff and Hoeffding Bounds
Balls, Bins, and Random Graphs
The Probabilistic Method
Markov Chains and Random Walks
Continuous Distributions and the Poisson Process
The Normal Distribution
Entropy, Randomness, and Information
The Monte Carlo Method
Coupling of Markov Chains
Martingales
Sample Complexity, VC Dimension, and Rademacher Complexity
Pairwise Independence and Universal Hash Functions
Power Laws and Related Distributions
Balanced Allocations and Cuckoo Hashing