Course Details

# Applications of mathematical methods in economics

DA67 course is part of 23 study plans

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D-K-E-SI (N) Winter Semester 1st year

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D-K-C-SI (N) Winter Semester 1st year

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D-P-E-SI (N) Winter Semester 1st year

D-P-E-SI (N) Winter Semester 1st year

D-P-E-SI (N) Winter Semester 1st year

D-P-E-SI (N) Winter Semester 1st year

D-P-E-SI (N) Winter Semester 1st year

D-P-C-SI (N) Winter Semester 1st year

D-P-C-SI (N) Winter Semester 1st year

D-P-C-SI (N) Winter Semester 1st year

D-P-C-SI (N) Winter Semester 1st year

D-P-C-SI (N) Winter Semester 1st year

D-P-C-GK Winter Semester 1st year

D-K-C-GK Winter Semester 1st 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.

Course Guarantor

RNDr. Karel Mikulášek, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Objective

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.

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.

Prerequisites

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

Language of instruction

Czech

Credits

10 credits

Semester

summer

Forms and criteria of assessment

examination

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/256038

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.