# FI:M005 Foundations of mathematics - Course Information

## M005 Foundations of mathematics

**Faculty of Informatics**

Autumn 2000

**Extent and Intensity**- 2/2. 4 credit(s) (plus extra credits for completion). Recommended Type of Completion: zk (examination). Other types of completion: k (colloquium), z (credit).
**Teacher(s)**- prof. RNDr. Ladislav Skula, DrSc. (lecturer)

Mgr. Jiří Zelinka, Dr. (lecturer)

Mgr. Lucie Burianová (seminar tutor)

Mgr. Zdeněk Polický, Ph.D. (seminar tutor)

Mgr. Jan Vitula (seminar tutor)

Mgr. Daniel Vybíral (seminar tutor) **Guaranteed by**- doc. RNDr. Jiří Kaďourek, CSc.

Departments - Faculty of Science

Contact Person: prof. RNDr. Ladislav Skula, DrSc. **Prerequisites**(in Czech)- NOW (
**M005c**Foundations of mathematics ) **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**- Informatics (programme FI, B-IN)
- Informatics (programme FI, M-IN)
- Upper Secondary School Teacher Training in Informatics (programme FI, M-IN)
- Upper Secondary School Teacher Training in Informatics (programme FI, M-SS)
- Information Technology (programme FI, B-IN)

**Syllabus**- Sets: set, subset, union, intersection, cartesian product
- Mappings: mapping, injection, surjection, bijection, inverse mapping, composition of mappings, cardinality of a set, Cantor theorem, cardinality of sets of numbers
- Relations: relations between sets, composition of relations, inverse relation, relation on a set, transitive hull, equivalence relation, decompositions, construction of integers and rational numbers
- Ordered sets: ordered set, preordered set, complete lattice, fixpoint theorem, construction of real numbers
- Combinatorics: variantions, combinations (with and without repetitions), inclusion and exclusion principle
- Elements of Graph Thoery: graphs, connected graphs, trees, Euler graphs, plane graphs

**Literature**- KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL.
*Logika, algebry a grafy*. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1989. 434 s. info - J. Rosický, Základy matematiky, učební text
- GRUSKA, Jozef.
*Foundations of computing*. London: International Thompson Computer Press, 1997. xv, 716 s. ISBN 1-85032-243-0. info

- KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL.
**Language of instruction**- Czech
**Further Comments**- The course is taught each semester.

The course is taught: every week.

- Enrolment Statistics (Autumn 2000, recent)
- Permalink: https://is.muni.cz/course/fi/autumn2000/M005