M005 Foundations of mathematics

Faculty of Informatics
Spring 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. Miroslav Novotný, DrSc. (lecturer)
Andrea Harnachová (assistant)
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
Further Comments
The course is taught each semester.
The course is taught: every week.
The course is also listed under the following terms Autumn 1995, Autumn 1996, Autumn 1997, Autumn 1998, Autumn 1999, Autumn 2000, Spring 2001, Autumn 2001, Spring 2002.
  • Enrolment Statistics (Spring 2000, recent)
  • Permalink: https://is.muni.cz/course/fi/spring2000/M005