Michael Mitzenmacher, Eli UpfalCambridge University PressEdition: 2, 7/3/2017EAN 9781107154889, ISBN10: 110715488XHardcover, 484 pages, 26.1 x 18.9 x 2.9 cmLanguage: EnglishOriginally published in EnglishGreatly 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 probability2. Discrete random variables and expectations3. Moments and deviations4. Chernoff and Hoeffding bounds5. Balls, bins, and random graphs6. The probabilistic method7. Markov chains and random walks8. Continuous distributions and the Polsson process9. The normal distribution10. Entropy, randomness, and information11. The Monte Carlo method12. Coupling of Markov chains13. Martingales14. Sample complexity, VC dimension, and Rademacher complexity15. Pairwise independence and universal hash functions16. Power laws and related distributions17. Balanced allocations and cuckoo hashing.
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