Course: Discrete Mathematics

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Course title Discrete Mathematics
Course code KAP/DMA
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 Czech
Status of course Compulsory
Form of instruction unspecified
Work placements Course does not contain work placement
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Jirsák Čeněk, Mgr.
  • Koucký Miroslav, doc. RNDr. CSc.
Course content
Lectures: 1.-6. Euler's totient function, Möbius function, Fermats's theorem. Primes, Factorization theorem, primality testing. Congruences, solution of first order congruences and their systems, aplications. Congruences of higher orders. Legendre symbol, Jacobi symbol, properties, calculations. Primitive roots, indexes. 7.-12. Basic algebraic structures. Group, subgroups, normal subgroups, Lagrange's theorem. Abel Groups, cyclic groups. Symmetric group. Rings, Eucleidian integral domains R[x], C[x], Zn[x]. Irreducibility. Finite fields. 13.-14. Some applications of theory of groups and finite fields.

Learning activities and teaching methods
Monological explanation (lecture, presentation,briefing)
  • Preparation for exam - 90 hours per semester
  • Class attendance - 56 hours per semester
Learning outcomes
The subject involves two parts - introduction to the theory of divisibility and algebraic structures.
Theoretical knowledge and ability to apply them.
Prerequisites
Knowledge of the secondary level mathematics

Assessment methods and criteria
Combined examination

Active participation in seminars, credit, knowledge accordant with syllabus.
Recommended literature
  • Bican, L. Algebra (pro učitelské studium). Praha, Academia, 2001. ISBN 80-200-0860-8.
  • Koucký, M. Sbírka příkladů z diskrétní matematiky. Skripta TUL, 2003.
  • KOUCKÝ Miroslav. Matematika pro informatiky I.
  • ROSEN, Kenneth. ed. Handbook of discrete and combinatorial mathematics. Boca Raton: CRC Press, 2000. ISBN 0-8493-0149-1.


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