Discrete structures 1

There are no prerequisites.

Predicate logic, predicate calculus.
Sets and relations.
Orders and lattices.
Functions and permutations.
Cardinality of sets.
Number theory.

1. V. Batagelj: Diskretne strukture : zapiski predavanj. Zv. 1, [Logika], Ljubljana : samozal. Z. Batagelj, cop. 1995.
2. V. Batagelj: Diskretne strukture : zapiski predavanj. Zv. 2, [Množice], Ljubljana : samozal. Z. Batagelj, 1996.
3. V. Batagelj: Diskretne strukture : zapiski predavanj. Zv. 1, [Logika in množice], 2. izd., Ljubljana : samozal. Z. Batagelj, 1996.
4. V. Batagelj, S. Klavžar: DS1. Logika in množice. Naloge, 3. razširjena izd., 3. natis. - Ljubljana : DMFA - založništvo, 2013.
5. G. Fijavž: Diskretne strukture, Ljubljana : Fakulteta za računalništvo in informatiko, 2015, e- knjiga: http://matematika.fri.uni-lj.si/ds/ds.pdf
6. M. Konvalinka in P. Potočnik: Diskretna matematika I, Založba FMF, Ljubljana, 2019, 140 strani, ISBN 978-961-6619-22-6.
7. A. Tepeh, R. Škrekovski: Diskretna matematika, Maribor : Univerzitetna založba Univerze, 2018, e-knjiga: https://press.um.si/index.php/ump/catalog/book/323

Discrete structures are the basis of computer science, because it is a working knowledge of the basic concepts of discrete structures needed in almost all areas of computing. In Discrete Structures I, the student learns the basic concepts of logic, set theory, number theory.

Knowledge and understanding: Students learn about: fundamentals of logic, set theory basics, basics of calculus queries, the basic concepts of the theory of numbers.
Application: Students know: a logical conclusion with the help of deduction, to determine the properties of relations and the structures of orders, solve linear Diophantine equations with two unknowns, to reckon with congruity.
Reflection: Students learn the difference between continuous and discrete mathematics.
Transferable skills: the use of mathematical logic for the analysis of reasoning, modeling relationships in the real world of relationships and networks.

Lectures and tutorial sessions, homework.

2 midterm exams instead of written exam, written exam
Oral exam / theoretical test.
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]
KAISER, Tomáš, ŠKREKOVSKI, Riste. T-joins intersecting small edge-cuts in graphs. Journal of graph theory, ISSN 0364-9024, 2007, vol. 56, no. 1, str. 64-71. [COBISS-SI-ID 14373977]
DVOŘÁK, Zdeněk, ŠKREKOVSKI, Riste. A theorem about a contractible and light edge. SIAM journal on discrete mathematics, ISSN 0895-4801, 2006, vol. 20, no. 1, str. 55-61. [COBISS-SI-ID 14249305]
JUNGIĆ, Veselin, KRÁL', Daniel, ŠKREKOVSKI, Riste. Colorings of plane graphs with no rainbow faces. Combinatorica, ISSN 0209-9683, 2006, vol. 26, no. 2, str. 169-182. [COBISS-SI-ID 13954393]