#
FI:IV111 Probability in CS - Course Information

## IV111 Probability in Computer Science

**Faculty of Informatics**

Autumn 2021

**Extent and Intensity**- 2/2/0. 3 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).

Taught in person. **Teacher(s)**- doc. RNDr. Vojtěch Řehák, Ph.D. (lecturer)

Dr. rer. nat. Achim Blumensath (seminar tutor)

Mgr. Libor Caha, PhD. (seminar tutor)

RNDr. David Klaška (assistant) **Guaranteed by**- doc. RNDr. Vojtěch Řehák, Ph.D.

Department of Computer Science - Faculty of Informatics

Supplier department: Department of Computer Science - Faculty of Informatics **Timetable**- Mon 13. 9. to Mon 6. 12. Mon 12:00–13:50 D3
- Timetable of Seminar Groups:

*V. Řehák*

IV111/02: Tue 14. 9. to Tue 7. 12. Tue 14:00–15:50 A320,*A. Blumensath*

IV111/03: Wed 15. 9. to Wed 8. 12. Wed 12:00–13:50 A320,*V. Řehák*

IV111/04: Mon 13. 9. to Mon 6. 12. Mon 10:00–11:50 A217,*A. Blumensath* **Prerequisites**- Knowledge of basic discrete mathematics (e.g. as presented in the course IB000).
**Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**fields of study / plans the course is directly associated with**- there are 74 fields of study the course is directly associated with, display
**Course objectives**- 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.
**Learning outcomes**- 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.
**Syllabus**- 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).

**Literature**- MITZENMACHER, Michael and 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. and 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. and 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

- MITZENMACHER, Michael and Eli UPFAL.
**Teaching methods**- Theoretical lectures and practical examples in tutorials.
**Assessment methods**- 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.
**Language of instruction**- English
**Further Comments**- Study Materials

The course is taught annually.

- Enrolment Statistics (recent)

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