Course detail

Applications of mathematical methods in economics

FAST-DAB033Acad. year: 2022/2023

Basics of graph theory, finding optimum graph solutions.
Finding the cheapest 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

prof. RNDr. Josef Diblík, DrSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Not applicable.

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

After the course, the students should be familiar with the basics of the theory of graphs necessary to formulate combinatorial problems on graphs. They should know how to solve the most frequently occurring problems using efficient algorithms. They will know about some heuristic approaches to intractable problems. They will learn 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
Švrček J., Lineární programování v úlohách, Skriptum UP Olomouc 2003, ISBN 80-744-0705-1

Recommended reading

DEMEL, J.: Grafy. SNTL, Sešit XXXIV 1989
Nešetřil, J. - Teorie grafů, SNTL 1979
Rychetník, Zelinka, Pelzbauerová: Sbírka příkladů z lineárního programování. SNTL/ALFA 1968

Classification of course in study plans

  • Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-E Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-S Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-V Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-V Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-V Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-K Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DKA-M Doctoral 2 year of study, winter semester, compulsory-optional
  • Programme DPA-M Doctoral 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 metoda. 12. Integer programming. 13. Matrix games, solutions in mixed strategies.