Predicate logic, predicate calculus.
Sets and relations.
Orders and lattices.
Functions and permutations.
Cardinality of sets.
Number theory.
Discrete structures 1
2023/2024
Programme:
Interdisciplinary University Study Programme Computer Science and Mathematics
Year:
1 year
Semester:
first
Kind:
mandatory
ECTS:
6
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
3
Seminar
0
Tutorial
3
Lab
0
Content (Syllabus outline)
Readings
Riste Škrekovski: Diskretne strukture I [Elektronski vir] : zapiski predavanj, http://www.fmf.uni-lj.si/skreko/Gradiva/DS1-skripta.pdf , ISBN 978-961-92887-2-6, 88 str.
G. Fijavž, Diskretne strukture, Ljubljana, 2014, matematika.fri.uni-lj.si/ds/ds.pdf.
Vladimir Batagelj, Izidor Hafner: Matematika – logika, Drzavna zalozba Slovenije, Ljubljana 1991, 62 str.
Vladimir Batagelj: Diskretne strukture – logika, samozaložba, Ljubljana 1998, 100.
Vladimir Batagelj: Diskretne strukture – množice, samozaložba, Ljubljana 1998, 40.
Vladimir Batagelj in Sandi Klavžar: DS1 – Logika in množice: naloge, Društvo matematikov, fizikov in astronomov Slovenije, Ljubljana 2000, ISBN: 961-212-039-0, 126 str.
Objectives and competences
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.
Intended learning outcomes
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.
Learning and teaching methods
Lectures and tutorial sessions, homework.
Assessment
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)
Lecturer's references
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]
