## M005 Foundations of mathematics

Faculty of Informatics
Autumn 2001
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)
Guaranteed by
doc. RNDr. Jiří Kaďourek, CSc.
Departments - Faculty of Science
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable of Seminar Groups
M005/P1: Mon 15:00–16:50 UKP, J. Rosický
M005/P2: Tue 14:00–15:50 D1, J. Niederle
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
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