Course detail

Applications of mathematical methods in economics

FAST-DA67Acad. year: 2018/2019

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.

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

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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-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-K-E-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-P-C-SI (N) Doctoral

    branch KDS , 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 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
    branch FMI , 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-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-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-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-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

Type of course unit

 

Lecture

39 hours, 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.