## M005 Foundations of mathematics

Faculty of Informatics
Autumn 1999
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)
doc. RNDr. Josef Niederle, CSc. (lecturer)
prof. RNDr. Jiří Rosický, DrSc. (lecturer)
Mgr. Martin Ander, Ph.D. (seminar tutor)
Mgr. Richard Lastovecki (seminar tutor)
Mgr. Leni Lvovská, Ph.D. (seminar tutor)
Ing. Zdeněk Mrázek (seminar tutor)
Mgr. Kamil Obořil (seminar tutor)
Mgr. Denisa Škrabáková (seminar tutor)
Mgr. Daniel Vybíral (seminar tutor)
Guaranteed by
prof. RNDr. Jan Slovák, DrSc.
Departments - Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
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
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
Language of instruction
Czech