Applications of mathematical methods in economics
FAST-DA67OptionalDoctoral (3rd cycle)Acad. year: 2017/2018Winter semester2. year of study10 credits
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.
Travelling salesman problem.
Basics of the theory of games.
Learning outcomes of the course unit
Mode of delivery
20 % face-to-face, 80 % distance learning
Základní znalosti z teorie množin a zběhlost v manipulaci se symbolickými hodnotami.
Recommended optional programme components
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
Assesment methods and criteria linked to learning outcomes
Language of instruction
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.
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.
Type of course unit
39 hours, optionally
Teacher / Lecturer