Course Details

Applications of mathematical methods in economics

DAB033 course is part of 20 study plans

Ph.D. full-t. program DPC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKC-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. full-t. program DPA-E compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-S compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-M compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-K compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-V compulsory-elective Winter Semester 2nd year 10 credits

Ph.D. combi. program DKA-E 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

Learning outcomes

The aim of the course is to teach the doctoral students the methods and algorithms used to deal with economic applications. The students will learn about the theoretical background, mainly the theory of graphs, needed to formulate and solve problems. These include optimisation problems solved by the method of linear programming, transport problem, dynamic programming problems, finding the cheapest spanning tree, shortest path in a graph, travelling-salesman problem, and determining the maximum flow in a network.

Prerequisites

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

Corequisites

Not required.

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.

Forms and criteria of assessment

A student will only receive credit if he will solve individual problems assigned by the teacher. The final examination will be only a written one lasting 90 minutes and consisting of 4 problems to calculate.

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.