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PřF:M1120 Discrete Mathematics - Course Information

## M1120 Discrete mathematics

**Faculty of Science**

Autumn 2013

**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)**- Mgr. David Kruml, Ph.D. (lecturer)

prof. RNDr. Jiří Rosický, DrSc. (lecturer)

doc. Mgr. Josef Šilhan, Ph.D. (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**- Tue 14:00–15:50 M1,01017, Wed 8:00–9:50 A,01026
- Timetable of Seminar Groups:

*D. Kruml*

M1120/02: Thu 18:00–19:50 M1,01017,*D. Kruml*

M1120/03: Thu 16:00–17:50 M1,01017,*D. Kruml*

M1120/04: Mon 14:00–15:50 M2,01021,*J. Šilhan*

M1120/05: Mon 16:00–17:50 M2,01021,*J. Šilhan* **Prerequisites**- !
**M1125**Fundamentals of Mathematics && ! NOW (**M1125**Fundamentals of Mathematics )

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**- Applied Mathematics for Multi-Branches Study (programme PřF, B-MA)
- Financial and Insurance Mathematics (programme PřF, B-MA)
- 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 context.
**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 (Autumn 2013, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2013/M1120