IV111 Probability in Computer Science

Fakulta informatiky
podzim 2019
Rozsah
2/2/0. 3 kr. (plus ukončení). Ukončení: zk.
Vyučující
doc. RNDr. Vojtěch Řehák, Ph.D. (přednášející)
Dr. rer. nat. Achim Blumensath (cvičící)
Mgr. Libor Caha, PhD. (pomocník)
Mgr. Matej Gallo (pomocník)
RNDr. Bc. Dominik Velan, Ph.D. (pomocník)
Garance
doc. RNDr. Vojtěch Řehák, Ph.D.
Katedra teorie programování – Fakulta informatiky
Dodavatelské pracoviště: Katedra teorie programování – Fakulta informatiky
Rozvrh
Po 14:00–15:50 A318
  • Rozvrh seminárních/paralelních skupin:
IV111/01: Út 12:00–13:50 A217, A. Blumensath
IV111/02: Út 16:00–17:50 A319, V. Řehák
IV111/03: Pá 8:00–9:50 A218, V. Řehák
Předpoklady
Knowledge of basic discrete mathematics (e.g. as presented in the course IB000).
Omezení zápisu do předmětu
Předmět je nabízen i studentům mimo mateřské obory.
Mateřské obory/plány
Cíle předmětu
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 to 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.
Výstupy z učení
Student is able: to define basic terms of the mentioned topics (e.g., random variable, expectation, variance, random process, Markov chain, channel capacity, code rate); to explain meaning on the terms on practical examples; to solve simple examples e.g. using linearity o expectation; to provide basic analysis on both discrete- and continuous-time Markov chains; to compute (conditional) expectation, mutual information, and entropy random variables with given probability distribution; to demonstrate basic proof mentioned during lectures.
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. ISBN 0521835402. info
  • GRIMMETT, Geoffrey R. a David STIRZAKER. Probability and random processes. 3rd ed. Oxford: Oxford University Press, 2001, xii, 596 s. ISBN 0-19-857222-0. info
  • TRIVEDI, Kishor Shridharbhai. Probability and statistics with reliability, queuing, and computer science applications. 2nd ed. New York: Wiley, 2002, xv, 830. ISBN 0471333417. info
  • COVER, T. M. a Joy A. THOMAS. Elements of information theory. 2nd ed. Hoboken, N.J.: Wiley-Interscience, 2006, xxiii, 748. ISBN 0471241954. info
  • STINSON, Douglas Robert. Cryptography : theory and practice. 3rd ed. Boca Raton: CRC Press, 2006, 593 s. ISBN 1584885084. info
  • FELLER, William. An introduction to probability theory and its applications. 3rd ed. [New York]: John Wiley & Sons, 1968, xviii, 509. ISBN 9780471257080. info
Výukové metody
Theoretical lectures and practical examples in tutorials.
Metody hodnocení
Combination of a written test and an oral exam. Student successful in the written test should pass the oral exam in order to achieve grade C or better.
Vyučovací jazyk
Angličtina
Další komentáře
Studijní materiály
Předmět je vyučován každoročně.
Předmět je zařazen také v obdobích jaro 2007, jaro 2008, jaro 2009, jaro 2010, jaro 2011, jaro 2012, jaro 2013, jaro 2014, jaro 2015, jaro 2016, jaro 2017, podzim 2017, podzim 2018, podzim 2020, podzim 2021, podzim 2022, podzim 2023, podzim 2024.