Czech

5

Not applicable.

Acquired knowledge will facilitate analysing of problems and will enable solving of managerial tasks in economics.

Secondary school mathematics and informatics.

Not applicable.

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

Conditions for awarding course-unit credits:
- active participation in seminars where the attendance is compulsory,
- completion of two partial written tests marked at least with grade "E",

The exam has a written and an oral part with the written part being more important. The written part takes two hours and contains the following types of tasks with maximum points awarded in brackets:
1. Verbally formulated statements and operations with them (10 points).
2. Application of laws of prepositional calculus (10 points).
3. Boolean function (15 points).
4. Relations (15 points).
5. Basic properties and classification of graphs (10 points).
6. Definitions of terms or formulation of properties in the graph theory (10 points).
7. Finding the language of grammar (10 points).
8. Finding the language of automat and its grammar (20 points).

Other conditions include: being awarded at least 10 points in tasks 1, 2 and 3 together, achieving at least 8 points in tasks 5 and 6 together, and 10 points in tasks 7 and 8 together. The written part is marked in points and reflects the points achieved in individual tasks. If any task is marked "0" then the student can not obtain grading A,B,C. If the student does not achieve at least 50 points out of 100 or if any other condition is not fulfilled, the whole exam will be graded as "F" (failed). Grading of the written part is as follows: "A" is awarded for 90-100 points, "B" for 80-89 points, "C" for 70-79 points, "D" for 60-69 points, "E" for 50-59 points.

Mathematical logic - constants, variables, statenaents, logical operations,laws of mathematical logic, Boolean algebras and functions, representation of Boolean functions, applications in logical circuit design.
Relations - relations on a set, properties of relations, equivalence.
Graphs - types of graphs, basic notions of undirected graphs, directed graphs,weighted graphs, Dijkstra algorithm of shortest path.
Languages, grammars, automata- concept of a language and a grammar, Chomsky hierarchy, finite automaton, Kleene characterization.

Not applicable.

The goal of the course is to make students familiar with basic concepts and relations of mathematical logic, relations, graph theory and principles of theory of graphs and automats, with possibilities of their applications in the field.

Attendance at lectures is not checked. Attendance at exercises (seminars) is compulsory and is regularly checked. A student is obliged to give reasons for his/her absence. If the teacher accepts the reason for the absence (which is completely under his/her competence), he/she will decide about the form of compensation for the missed lessons.

Not applicable.

Not applicable.

1) Mezník, I: Diskrétní matematika. FP VUT v Brně v Akademickém nakladatelství CERM, s.r.o. Brno, Brno 2004. ISBN 80-214-2754-X. (CS)

Wiitala, S. A: Discrete Mathematics. McGraw-Hill, New York 1987 (EN)
Šlapal, J.: Metody diskrétní matematiky. FSI VUT v Brně, Brno 2001 (CS)

26 hours, compulsory

Topics of lectures:
- mathematical logic,
- graphs,
- languages and automats.

Topics of exercises:
- practising of topics discussed in lectures,
- working out of individual assignments.