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Lecturer(s)
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Roskovec Tomáš, RNDr. Ph.D.
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Šulista Marek, PhDr. Ph.D.
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Course content
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Topics: 1. Basic concepts and properties of mathematical logic. 2. Boolean algebra, identities, propositional calculus, quantifiers. 3. Veen diagram. 4. Binary numeral systems. 5. General numeral systems. 6. Euclidean algorithm, algorithms for integer operations. 7. Modular calculations, cryptography. 8. Public encrypting, the RSA cryptosystem, digital signature 9. Approximation theory basics 10. Least squares, spline, Fourier series 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), Individual preparation for exam
- Class attendance
- 63 hours per semester
- Semestral paper
- 20 hours per semester
- Preparation for credit
- 40 hours per semester
- Preparation for exam
- 40 hours per semester
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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, approximation and probability theory are covered.
The student is able to apply the knowledge of logic, number theory, approximation 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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Student performance assessment, Combined exam
Active attendance of all seminars including homework deliverance. Passing both written (score more than 50%, six problems) and oral examination parts.
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Recommended literature
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Anděl, J. Základy matematické statistiky. Praha : Matfyzpress, 2005..
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ANTOCH, J.;HLUBINKA D.; SAXL, I. Pravděpodobnost a statistika na střední škole: sborník prací didaktického semináře pořádaného Matematicko-fyzikální fakultou Univerzity Karlovy v Praze v akademickém roce 2003/2004. Praha: Matfyzpress, 2005. ISBN 80-86732-23-1.
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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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Rosen, K., H. Discrete Mathematics and Its Applications.. New York: McGraw-Hill, 1988.
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Tlustý, P.:. Algebra I. České Budějovice, PF JU, 1994.
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