Course detail
Applications of mathematical methods in economics
FAST-DA67Acad. year: 2020/2021
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.
Supervisor
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.
Recommended optional programme components
Not applicable.
Recommended or required reading
Plesník, Ján: Grafové algoritmy. Bratislava: Veda 1983
DEMEL, J.: Grafy. SNTL, Sešit XXXIV 1989
Rychetník, Zelinka, Pelzbauerová: Sbírka příkladů z lineárního programování. SNTL/ALFA 1968
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Language of instruction
Czech
Work placements
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.
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.
Classification of course in study plans
- Programme D-K-E-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch PST , 2. year of study, winter semester, 10 credits, compulsory-optional
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional - Programme D-K-E-SI (N) Doctoral
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional - Programme D-K-C-SI (N) Doctoral
branch MGS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-E-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch FMI , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-E-SI (N) Doctoral
branch KDS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-E-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-E-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-SI (N) Doctoral
branch VHS , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-P-C-GK Doctoral
branch GAK , 2. year of study, winter semester, 10 credits, compulsory-optional
- Programme D-K-C-GK Doctoral
branch GAK , 2. year of study, winter semester, 10 credits, compulsory-optional