Course detail

Applications of mathematical methods in economics

FAST-DA67Acad. year: 2022/2023

Basics of graph theory, finding optimum graph solutions.
Finding the minimum spanning tree of a graph.
Finding the shortest path in a graph.
Determining the maximum flow in a network.
NP-complete problems.
Travelling salesman problem.
Linear programming.
Transport prpoblem.
Integer programming.
Basics of the theory of games.

Language of instruction

Czech

Number of ECTS credits

10

Mode of study

Not applicable.

Guarantor

RNDr. Karel Mikulášek, Ph.D.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

The students will know the basics of the theory of graphs necessary to formulate combinatorial problems on graphs. They will be able to solve the most frequently occurring problems using efficient algorithms. They will also be familiar with some heuristic approaches to intractable problems. They will learn the basics of linear programming and the theory of games and their applications in business.

Prerequisites

Základní znalosti z teorie množin a zběhlost v manipulaci se symbolickými hodnotami.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Basics of graph theory I
2. Basics of graph theory II.
3. Finding the minimum soanning tree in a graph.
4. Finding the shortest path in a graph.
5. Determining a maximum flow in a network I.
6. Determining a maximum flow in a network II.
7. NP-complete problems.
8. Travelling salesman problem.
9. Travelling salesman problem, heuristic methods.
10. Linear programming, theoretical basis.
11. Simplex metoda.
12. Integer programming.
13. Matrix games, solutions in mixed strategies.

Work placements

Not applicable.

Aims

Teach the students the basics of the theory of graphs necessary to formulate combinatorial problems on graphs. Teach them how to solve the most frequently occurring problems using efficient algorithms. Make them familiar with some heuristic approaches to intractable problems. Teach them the basics of linear programming and the theory of games and their applications in business.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Plesník, Ján: Grafové algoritmy. Bratislava: Veda 1983 (CS)
Švrček J., Lineární programování v úlohách,  Skriptum UP Olomouc 2003, ISBN 80-744-0705-1 (CS)

Recommended reading

DEMEL, J.: Grafy. SNTL, Sešit XXXIV 1989 (CS)
Nešetřil, J. - Teorie grafů, SNTL 1979 (CS)

Classification of course in study plans

  • Programme D-K-E-CE (N) Doctoral

    branch FMI , 2 year of study, winter semester, compulsory-optional
    branch KDS , 2 year of study, winter semester, compulsory-optional
    branch MGS , 2 year of study, winter semester, compulsory-optional
    branch VHS , 2 year of study, winter semester, compulsory-optional
    branch PST , 2 year of study, winter semester, compulsory-optional

  • Programme D-K-C-SI (N) Doctoral

    branch VHS , 2 year of study, winter semester, compulsory-optional
    branch MGS , 2 year of study, winter semester, compulsory-optional
    branch PST , 2 year of study, winter semester, compulsory-optional
    branch FMI , 2 year of study, winter semester, compulsory-optional
    branch KDS , 2 year of study, winter semester, compulsory-optional

  • Programme D-P-E-CE (N) Doctoral

    branch PST , 2 year of study, winter semester, compulsory-optional
    branch FMI , 2 year of study, winter semester, compulsory-optional
    branch KDS , 2 year of study, winter semester, compulsory-optional
    branch MGS , 2 year of study, winter semester, compulsory-optional
    branch VHS , 2 year of study, winter semester, compulsory-optional

  • Programme D-P-C-SI (N) Doctoral

    branch PST , 2 year of study, winter semester, compulsory-optional
    branch FMI , 2 year of study, winter semester, compulsory-optional
    branch KDS , 2 year of study, winter semester, compulsory-optional
    branch MGS , 2 year of study, winter semester, compulsory-optional
    branch VHS , 2 year of study, winter semester, compulsory-optional

  • Programme D-P-C-GK Doctoral

    branch GAK , 2 year of study, winter semester, compulsory-optional

  • Programme D-K-C-GK Doctoral

    branch GAK , 2 year of study, winter semester, compulsory-optional

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

RNDr. Karel Mikulášek, Ph.D.

Syllabus

1. Basics of graph theory I 2. Basics of graph theory II. 3. Finding the minimum soanning tree in a graph. 4. Finding the shortest path in a graph. 5. Determining a maximum flow in a network I. 6. Determining a maximum flow in a network II. 7. NP-complete problems. 8. Travelling salesman problem. 9. Travelling salesman problem, heuristic methods. 10. Linear programming, theoretical basis. 11. Simplex method. 12. Integer programming. 13. Matrix games, solutions in mixed strategies.