Algebra and discrete mathematics

2022/2023
Programme:
Practical Mathematics
Year:
2 year
Semester:
first
Kind:
mandatory
ECTS:
6
Language:
slovenian
Hours per week – 1. semester:
Lectures
3
Seminar
0
Tutorial
3
Lab
0
Content (Syllabus outline)

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.

Readings

N. Prijatelj : Osnove matematične logike, 1. del. Simbolizacija, 4. natis, DMFA Slovenije, Ljubljana, 1992.
N. Prijatelj : Matematične strukture I. Množice – relacije – funkcije, 5. izdaja, DMFA Slovenije, Ljubljana, 1996.
J Grasselli : Osnove teorije števil, 2. predelana izdaja, DMFA Slovenije, Ljubljana, 1975.
V. Batagelj: Diskretne strukture – algebra, samozaložba, Ljubljana, 1998.
M. Juvan in P. Potočnik: Teorija grafov in kombinatorika: primeri in rešene naloge, 2. izdaja, DMFA Slovenije, Ljubljana 2007.
R. J. Wilson in J. J. Watkins: Uvod v teorijo grafov, DMFA Slovenije, Ljubljana, 1997.
D. Veljan, Kombinatorika in diskretna matematika, Algoritam, Zagreb, 2001.

Objectives and competences

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

Intended learning outcomes

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.

Learning and teaching methods

Lectures, exercises, homeworks, consultations

Assessment

Written exam
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]