Course Details

Applications of mathematical methods in economics

DA67 course is part of 22 study plans

Ph.D. full-t. program nD > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nD > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDK > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program nDA > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > PST compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > FMI compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > KDS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > MGS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program nDKA > VHS compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program I > GAK compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program IK > GAK compulsory-elective Winter Semester 2nd year 10 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.

Course Guarantor

RNDr. Karel Mikulášek, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Prerequisites

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

Planned educational 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.

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.

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

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

Lecture

3 hours/week, 13 weeks, elective

Syllabus of lectures

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.