Course detail

# 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.
NP-complete problems.
Travelling salesman problem.
Linear programming.
Transport prpoblem.
Integer programming.
Basics of the theory of games.

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.

Plesník, Ján: Grafové algoritmy. Bratislava: Veda 1983
DEMEL, J.: Grafy. SNTL, Sešit XXXIV 1989

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

Teacher / Lecturer