Course detail
Applications of mathematical methods in economics
FAST-DAB033Acad. year: 2024/2025
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
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Entry knowledge
Základní znalosti z teorie množin a zběhlost v manipulaci se symbolickými hodnotami.
Rules for evaluation and completion of the course
Extent and forms are specified by guarantor’s regulation updated for every academic year.
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.
Study aids
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
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
Nešetřil, J. - Teorie grafů, SNTL 1979
Rychetník, Zelinka, Pelzbauerová: Sbírka příkladů z lineárního programování. SNTL/ALFA 1968
Classification of course in study plans
- Programme DKA-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DKA-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPA-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-V Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-E Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-K Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-M Doctoral 2 year of study, winter semester, compulsory-optional
- Programme DPC-S Doctoral 2 year of study, winter semester, compulsory-optional
Type of course unit
Lecture
39 hod., optionally
Teacher / Lecturer
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.