Course Details

Applications of mathematical methods in economics

Academic Year 2024/25

DAB033 course is part of 19 study plans

​ DKA-E Winter Semester 2nd year

​ DKA-K Winter Semester 2nd year

​ DKA-M Winter Semester 2nd year

​ DKA-S Winter Semester 2nd year

​ DKA-V Winter Semester 2nd year

​ DPA-E Winter Semester 2nd year

​ DPA-K Winter Semester 2nd year

​ DPA-M Winter Semester 2nd year

​ DPA-S Winter Semester 2nd year

​ DPA-V Winter Semester 2nd year

​ DKC-E Winter Semester 2nd year

​ DKC-K Winter Semester 2nd year

​ DKC-M Winter Semester 2nd year

​ DKC-S Winter Semester 2nd year

​ DKC-V Winter Semester 2nd year

​ DPC-E Winter Semester 2nd year

​ DPC-K Winter Semester 2nd year

​ DPC-M Winter Semester 2nd year

​ DPC-S Winter Semester 2nd year

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.

Credits

10 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

prof. RNDr. Josef Diblík, DrSc.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

examination

Entry Knowledge

Základní znalosti z teorie množin a zběhlost v manipulaci se symbolickými hodnotami.

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.

Basic Literature

Plesník, Ján: Grafové algoritmy. Bratislava: Veda 1983
Švrček J., Lineární programování v úlohách, Skriptum UP Olomouc 2003, ISBN 80-744-0705-1

Recommended Reading

Rychetník, Zelinka, Pelzbauerová: Sbírka příkladů z lineárního programování. SNTL/ALFA 1968
DEMEL, J.: Grafy. SNTL, Sešit XXXIV 1989
Nešetřil, J. - Teorie grafů, SNTL 1979

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/282079

Lecture

13 weeks, 3 hours/week, elective

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.