česky | **in English**

Autumn 2018

**Extent and Intensity**- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
**Teacher(s)**- prof. RNDr. Jiří Rosický, DrSc. (lecturer)

Mgr. David Kruml, Ph.D. (seminar tutor)

Mgr. Radka Penčevová (seminar tutor) **Supervisor**- prof. RNDr. Jiří Rosický, DrSc.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Mon 17. 9. to Fri 14. 12. Tue 14:00–15:50 M1,01017
- Timetable of Seminar Groups:

*R. Penčevová*

M1120/02: Mon 17. 9. to Fri 14. 12. Fri 8:00–9:50 M1,01017,*D. Kruml* **Prerequisites**- ! OBOR ( AMV ) && ! OBOR ( FINPOJ ) && ! OBOR ( UM )

Knowledge of high-school mathematics is supposeed. **Course Enrolment Limitations**- The course is also offered to the students of the fields other than those the course is directly associated with.
**Fields of study the course is directly associated with**- Mathematics (programme PřF, B-MA)
- Statistics and Data Analysis (programme PřF, B-MA)

**Course objectives**- The course links up high school knowledge with basic concepts of discrete mathematics. It mainly deals with fundaments of mathematical logic, set theory, combinatorics and graph theory. After passing the course, the student will be able to understand and explain basic mathematical notions and techniques and their mutual connections.
**Syllabus**- Basic logical concepts (formulae, notation for mathematical statements, proofs)
- Basics of set theory (set operations, including the Cartesian product).
- Mappings (types of mappings, composition).
- Cardinality of a set (finite, countable and uncountable sets).
- Relations (types and properties of relations, composition).
- Equivalences and partitions (kernel of a mapping, constructions of selected number domains).
- Ordered sets (order relations, Hasse diagrams, complete lattices, isotone mappings).
- Combinatorics (permutation, combination, inclusion and exclusion principle).
- Graph theory (oriented and non-oriented graphs, conectedness, skeletons, Euler graphs, basic alghorithms).

**Literature**- Horák, Pavel. Základy matematiky. Učební text. Podzimní semestr 2010.
- MATOUŠEK, Jiří and Jaroslav NEŠETŘIL.
*Kapitoly z diskrétní matematiky*. Vyd. 2., opr. Praha: Univerzita Karlova v Praze, nakladatelství Karolinum, 2000. 377 s. ISBN 8024600846. info

**Teaching methods**- The subject consists of talks and obligatory seminars. The talk presents key notions, their properties and methods of use. Problems are collectively solved in seminars to develop student's insight.
**Assessment methods**- Students are examined in 2 tests during the term (10 pts per each) and in the final written test (80 pts). The mark is calculated as follows: A 90-100, B 80-89, C 70-79, D 60-69, E 50-59, F 0-49.
**Language of instruction**- Czech
**Further comments (probably available only in Czech)**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses**

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2018/M1120

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