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Lecturer(s)
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Roskovec Tomáš, RNDr. Ph.D.
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Mrkvička Tomáš, prof. RNDr. Ph.D.
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Course content
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Topics: 1. Basic concepts and properties of mathematical logic. 2. Propositional calculus, quantifiers. 3. Boolean algebra, identities. 4. Boolean functions and their representations. 5. Basic concepts of number theory, divisibility, prime numbers. 6. Modular arithmetic. 7. Euclidean algorithm, algorithms for integer operations. 8. Linear congruence, Chinese remainder theorem 9. Cryptography, public encrypting, the RSA cryptosystem, digital signature 10. Survey of basic concepts and rules of probability theory. 11. Discrete probability 12. Independent events, conditional probability, Bayes theorem. 13. Selected applications of probability reasoning in economy.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)
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Learning outcomes
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The course is targeted at the fundaments of mathematics necessary for the study of the master program. Selected topics of mathematical logic, number theory and probability theory are covered.
The student is able to apply the knowledge of the theory of boolean functions, number theory and probability models to concrete real-life motivated situations.
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Prerequisites
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Basic knowledge of mathematics on the Bc. level.
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Assessment methods and criteria
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Combined exam
Active attendance of all seminars including homework deliverance. Passing both written (score more than 50%) and oral examination parts.
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Recommended literature
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DUŽÍ, M. Matematická logika. VŠB Ostrava, 2012.
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JANACEK, G. J. and M. L. CLOSE. Mathematics for Computer Scientists. Ventus Publishing Aps, 2011. ISBN 978-87-7681-524-0.
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MEJLBRO, L. Introduction to Probability. Ventus Publishing Aps, 2009. ISBN 978-87-7681-515-8.
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PLOCKI, A., P. TLUSTÝ. Pravděpodobnost a statistika pro začátečníky a mírně pokročilé. Praha: Prometheus, 2007. ISBN 978-80-7196-330-1.
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Rosen, K., H. Discrete Mathematics and Its Applications.. New York: McGraw-Hill, 1988.
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TLUSTÝ, P. Obecná algebra. České Budějovice: Jihočeská univerzita, 2006. ISBN 978-80-7040-828-6.
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