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# Course detail

## Applications of mathematical methods in economics

Course unit code: FAST-DA67
Type of course unit: optional
Level of course unit: Doctoral (3rd cycle)
Year of study: 2
Semester: winter
Number of ECTS credits: 10
 Learning outcomes of the course unit: Not applicable.
 Mode of delivery: 20 % face-to-face, 80 % distance learning
 Prerequisites: Základní znalosti z teorie množin a zběhlost v manipulaci se symbolickými hodnotami.
 Co-requisites: Not applicable.
 Recommended optional programme components: Not applicable.
 Course contents (annotation): 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.
 Recommended or required reading: Plesník, Ján: Grafové algoritmy. Bratislava: Veda 1983DEMEL, J.: Grafy. SNTL, Sešit XXXIV 1989Rychetník, 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.

Type of course unit:

Lecture: 39 hours, optionally RNDr. Karel Mikulášek, Ph.D.

The study programmes with the given course