Algebra and discrete mathematics

There are no prerequisites.

Basics of Logic. Introduction to logic, logic operations, proof, predicats in quantifiers, writing mathematical propositions in formal language.
Sets. Intersections and unions of families of sets. Infinite sets: countable in non-countable. Relations. Partial and linear order.
Combinatorics. Basic combinatorial counting. Inclusion-exclusion formula.
Graph theory. Basic definitions. Eulerian trails and Hamilton cycles. Trees. Connectivity. Planar graphs. Coloring of vertices and edges.
Algebra. Semigroups. Groups. Rings and fields.

1. V. Batagelj: Diskretne strukture : zapiski predavanj. Zv. 3, [Algebra], Ljubljana : samozal. Z. Batagelj, 1996.
2. J Grasselli : Osnove teorije števil, 2. predel. izd., Ljubljana : Državna založba Slovenije, 1975.
3. M. Juvan, P. Potočnik: Teorija grafov in kombinatorika : primeri in rešene naloge, 2. natis, Ljubljana: DMFA-založništvo, 2007.
4. N. Prijatelj: Matematične strukture. 1, Množice, relacije, funkcije, 5. izd. - Ljubljana : Društvo matematikov, fizikov in astronomov Slovenije, 1996.
5. N. Prijatelj: Osnove matematične logike. Del 1, Simbolizacija, Ljubljana : Društvo matematikov, fizikov in astronomov, 1982, 1992.
6. D. Veljan: Kombinatorna i diskretna matematika, Zagreb : Algoritam, 2001.
7. R. J. Wilson, J. J. Watkins: Uvod v teorijo grafov, Ljubljana : Društvo matematikov, fizikov in astronomov Slovenije, 1997.

Students will acquire knowledge about some basic notions from abstract algebra, discrete mathematics, logic and set theory.

Knowledge and understanding:
Students will learn the topics presented in the classroom.
Application:
Students will be able to use the acquired knowledge.
Reflection:
Students will reflect the acquired knowledge.
Transferable skills:
The knowledge is fullt transferable anywhere.

Lectures, exercises, homeworks, consultations

Written exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Primož Potočnik:
POTOČNIK, Primož. Tetravalent arc-transitive locally-Klein graphs with long consistent cycles. European journal of combinatorics, ISSN 0195-6698, 2014, vol. 36, str. 270-281. [COBISS-SI-ID 16862041]
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. Cubic vertex-transitive graphs on up to 1280 vertices. Journal of symbolic computation, ISSN 0747-7171, 2013, vol. 50, str. 465-477. [COBISS-SI-ID 16520537]
POTOČNIK, Primož. Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2004, vol. 91, no. 2, str. 289-300. [COBISS-SI-ID 13087321]