|
Lecturer(s)
|
-
Koucký Miroslav, doc. RNDr. CSc.
-
Jirsák Čeněk, Mgr.
|
|
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.
|