# PřF:M1120 Discrete Mathematics - Course Information

## M1120 Discrete mathematics

**Faculty of Science**

Autumn 2022

**Extent and Intensity**- 2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Taught in person. **Teacher(s)**- Mgr. David Kruml, Ph.D. (lecturer)

Mgr. Miloslav Štěpán (seminar tutor) **Guaranteed by**- 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 12:00–13:50 M1,01017
- Timetable of Seminar Groups:

*M. Štěpán*

M1120/02: Mon 18:00–19:50 M4,01024,*D. Kruml*

M1120/03: Mon 16:00–17:50 M4,01024,*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 / plans 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, notions of mappings and relations, combinatorics and graph theory. After passing the course, a student will be able to understand and explain basic mathematical notions and techniques and their mutual context. A student knows about practical applications of the methods and notions of discrete mathematics (function as a mapping, relations in databases, problems treated by graph theory).
**Learning outcomes**- After passing the course, a student will be able to understand and explain basic mathematical notions and techniques and their mutual context. A student knows about practical applications of the methods and notions of discrete mathematics (function as a mapping, relations in databases, problems treated by graph theory).
**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, spanning trees, 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. Student's advances are checked by automatized testing.
**Assessment methods**- The examination consists of written and oral part. The written part is typically of more importance. The oral part tests student's ability to react and to discuss his/her work during the term.
**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****Teacher's information**- The course is a neccessary background for following subjects of the programs Mathematics and Applied mathematics.

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2022/M1120