Předmět Probability in Computer Science (IV111)
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Další informace
Cíl
At the end of the course student should have a broad knowledge and an ability of independent study of problems based on the probability theory and its computer science applications. Will be able apply the results of the probability theory in practical examples. Should be able to learn independently new problems requiring knowledge of probability theory. Will be able to characterise basic principles of data compression and error correction. Should be able to apply information theory results in practice.
Osnova
Probability. Discrete probabilistic space.Random variable and its applications. Expectation and variation.Markov and Chebyshev inequalities. Chernoff bounds. Weak and strong law of large numbers.Random processes. Markov processes.Entropy. Information.Applications in computer science (information theory, coding theory, cryptography etc).
Literatura
MITZENMACHER, Michael a Eli UPFAL. Probability and computing :an introduction to randomized algorithms and probabilistic analysis. New York: Cambridge University Press, 2005. xvi, 352 s. ISBN 0-521-83540-2. infoGRIMMETT, Geoffrey R. a David STIRZAKER. Probability and random processes. 3rd ed. Oxford: Oxford University Press, 2001. xii, 596 s. ISBN 0-19-857222-0. infoTRIVEDI, Kishor Shridharbhai. Probability and statistics with reliability, queuing, and computer science applications. 2nd ed. New York: Wiley, 2002. xv, 830 s. ISBN 0-471-33341-7. infoElements of information theory. Edited by T. M. Cover - Joy A. Thomas. 2nd ed. Hoboken, N.J.: Wiley-Interscience, 2006. xxiii, 748. ISBN 9780471241959. infoSTINSON, Douglas Robert. Cryptography :theory and practice. 3rd ed. Boca Raton: CRC Press, 2006. 593 p. ISBN 1-58488-508-4. infoFELLER, William. An introduction to probability theory and its applications. 3rd ed. [New York]: John Wiley & Sons, 1968. xviii, 509. ISBN 0-471-25708-7. info
Požadavky
Knowledge of basic discrete mathematics (e.g. as presented in the course IB000).
Garant
prof. RNDr. Mojmír Křetínský, CSc.
Vyučující
RNDr. Vojtěch Řehák, Ph.D.RNDr. Matej Pivoluska, Ph.D.Zbyněk Cincibus