Probability and Computing
Randomization and Probabilistic Techniques in Algorithms and Data Analysis

This greatly expanded new edition offers a comprehensive introduction to randomization and probabilistic techniques in modern computer science.

Michael Mitzenmacher (Author), Eli Upfal (Author)

9781107154889, Cambridge University Press

Hardback, published 3 July 2017

484 pages, 8 b/w illus. 1 table
26 x 18.2 x 2.5 cm, 1.15 kg

'By assuming just an elementary introduction to discrete probability and some mathematical maturity, this book does an excellent job of introducing a great variety of topics to the reader. I especially liked the coverage of the Poisson, exponential, and (multi-variate) normal distributions and how they arise naturally, machine learning, Bayesian reasoning, Cuckoo hashing etc. There is a broad range of exercises, including helpful ones on programming to get a feel for the numerics … This connection to practice is unusual and very commendable … Overall, I would highly recommend this book to anyone interested in probabilistic and statistical foundations as applied to computer science, data science, etc. It can be taught at the senior undergraduate or graduate level to students in computer science, electrical engineering, operations research, mathematics, and other such disciplines.' Frederic Green , SIGACT News

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.

1. Events and probability
2. Discrete random variables and expectations
3. Moments and deviations
4. Chernoff and Hoeffding bounds
5. Balls, bins, and random graphs
6. The probabilistic method
7. Markov chains and random walks
8. Continuous distributions and the Polsson process
9. The normal distribution
10. Entropy, randomness, and information
11. The Monte Carlo method
12. Coupling of Markov chains
13. Martingales
14. Sample complexity, VC dimension, and Rademacher complexity
15. Pairwise independence and universal hash functions
16. Power laws and related distributions
17. Balanced allocations and cuckoo hashing.

Subject Areas: Algorithms & data structures [UMB]