Applied discrete mathematics

2022/2023
Programme:
Mathematics, Second Cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M2
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
1
Lab
1
Content (Syllabus outline)

Several model problems are presented and modeled by using methods from discrete mathematics.
We focus on the process of addressing a problem: identification of entities and relationships among them, identification of goals, data model design, algorithm implementation, design of testing procedures and test data, specification, implementation, evaluation and qualitative evaluation of the results.
Depending on the choice of the model problems, students get familiar with various mathematical tools and methodoogies for addressing the problems, e.g. heuristic optimization procedures, data visualisation methods (graphs, charts, etc.), qualitative analysis of discrete dynamic systems, etc.
During the course seminar work, students will be assigned individual and team applied and research projects. If possible the students will be involved in projects with companies or in national or international applied research projects.

Readings

E. Zakrajšek: Matematično modeliranje, DMFA-založništvo, Ljubljana, 2004.
R. Aris: Mathematical modelling techniques, Dover, 1994.
M. Jünger, P. Mutzel: Graph Drawing Software, Springer-Verlag, Berlin, 2004.
Z. Michalewicz: Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin, 1999.
R. A. Holmgren: A First Course in Discrete Dynamical Systems, Springer-Verlag, Berlin, 1996.

Objectives and competences

Students become capable of identifying problems that can be addressed by various mathematical techniques. They learn how to formulate problems in mathematical form, identify relevant tools to deal with the problem, search through the relevant literature, develop or adapt a relevant model for solving the problem, find critical aspects of it and implement a solution in practice. Specifics of team work are emphasised during the work on projects.

Intended learning outcomes

Knowledge and understanding: Learning of the process of a problem identification and problem addressing, starting by forming of a model, dealing with it and progressing towards a solution implementation.
Application: Construction of models for solving of real problems.
Reflection: evaluation of validity of assumptions for theoretical models, critical evaluation of constructed solutions, evaluation of team work.
Transferable skills:. Capabilities of recognizing of relevant facts, problem formulation, adaptation of known solutions, concept presentation.

Learning and teaching methods

Lectures, exercises, team solution planning, projects, seminar presentations, consulatations

Assessment

Project assignment (plan, execution, documentation, report, presentation, defense)
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

Alen Orbanić:
HUBARD, Isabel, ORBANIĆ, Alen, PELLICER, Daniel, IVIĆ WEISS, Asia. Symmetries of equivelar 4-toroids. Discrete & computational geometry, ISSN 0179-5376, 2012, vol. 48, iss. 4, str. 1110-1136. [COBISS-SI-ID 16478297]
ORBANIĆ, Alen, PELLICER, Daniel, IVIĆ WEISS, Asia. Map operations and k-orbit maps. Journal of combinatorial theory. Series A, ISSN 0097-3165, 2010, vol. 117, iss. 4, str.411-429. [COBISS-SI-ID 15553625]
HUBARD, Isabel, ORBANIĆ, Alen, IVIĆ WEISS, Asia. Monodromy groups and self-invariance. Canadian journal of mathematics, ISSN 0008-414X, 2009, vol. 61, no. 6, str. 1300-1324. [COBISS-SI-ID 15369817]
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]
Riste Škrekovski:
GOVORČIN, Jelena, KNOR, Martin, ŠKREKOVSKI, Riste. Line graph operation and small worlds. Information processing letters, ISSN 0020-0190. [Print ed.], 2013, vol. 113, iss. 5-6, str. 196-200. [COBISS-SI-ID 16561497]
DVOŘÁK, Zdeněk, LIDICKÝ, Bernard, ŠKREKOVSKI, Riste. Randić index and the diameter of a graph. European journal of combinatorics, ISSN 0195-6698, 2011, vol. 32, iss. 3, str. 434-442. [COBISS-SI-ID 17410905]
KAISER, Tomáš, STEHLÍK, Matěj, ŠKREKOVSKI, Riste. On the 2-resonance of fullerenes. SIAM journal on discrete mathematics, ISSN 0895-4801, 2011, vol. 25, no. 4, str. 1737-1745. [COBISS-SI-ID 16244569]