Course: Mathematical Principles in Informatics

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Course title Mathematical Principles in Informatics
Course code KMI/YMAT3
Organizational form of instruction Lecture + Lesson
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction English
Status of course unspecified
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Roskovec Tomáš, Mgr. Ph.D.
  • Šulista Marek, PhDr. Ph.D.
Course content
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.

Learning activities and teaching methods
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
Learning outcomes
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.
Prerequisites
Basic knowledge of mathematics on the Bc. level.

Assessment methods and criteria
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.
Recommended literature
  • Anděl, J. Základy matematické statistiky. Praha : Matfyzpress, 2005..
  • 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.
  • JANACEK, G. J. and M. L. CLOSE. Mathematics for Computer Scientists. Ventus Publishing Aps, 2011. ISBN 978-87-7681-524-0.
  • MEJLBRO, L. Introduction to Probability. Ventus Publishing Aps, 2009. ISBN 978-87-7681-515-8.
  • Rosen, K., H. Discrete Mathematics and Its Applications.. New York: McGraw-Hill, 1988.
  • Tlustý, P.:. Algebra I. České Budějovice, PF JU, 1994.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester