MB101 Mathematics I

Faculty of Informatics
Autumn 2003
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Kaďourek, CSc. (lecturer)
RNDr. Kateřina Dvořáková, Ph.D. (seminar tutor)
RNDr. Jarmila Elbelová, PhD. (seminar tutor)
Mgr. Andrea Pavliňáková (seminar tutor)
RNDr. Blanka Sedlačíková, Ph.D. (seminar tutor)
RNDr. Veronika Svobodová, Ph.D. (seminar tutor)
Mgr. Michaela Vokřínková (seminar tutor)
RNDr. Jan Vondra, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Faculty of Informatics
Contact Person: doc. RNDr. Jiří Kaďourek, CSc.
Timetable
Mon 8:00–9:50 TA (Aula Technická)
  • Timetable of Seminar Groups:
MB101/01: Mon 18:00–19:50 B003, J. Elbelová
MB101/02: Mon 16:00–17:50 B003, B. Sedlačíková
MB101/03: Tue 12:00–13:50 B003, A. Pavliňáková
MB101/04: Tue 14:00–15:50 B003, A. Pavliňáková
MB101/05: Thu 16:00–17:50 B003, V. Svobodová
MB101/06: Thu 18:00–19:50 B003, V. Svobodová
MB101/07: Tue 12:00–13:50 B007, J. Vondra
MB101/08: Tue 14:00–15:50 B007, J. Vondra
MB101/09: Tue 16:00–17:50 B003, K. Dvořáková
MB101/10: Tue 18:00–19:50 B003, K. Dvořáková
MB101/11: Thu 16:00–17:50 B007, M. Vokřínková
MB101/12: Thu 18:00–19:50 B007, M. Vokřínková
Prerequisites
(! M005 Foundations of mathematics )&&(! MB005 Foundations of mathematics )&&(! NOW ( MB005 Foundations of mathematics ))
High school 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 the course is directly associated with
Course objectives
The course is the first part of the four semestr block, Mathematics I - IV. In the whole block the fundamentals of general algebra, linear algebra and analysis, including their application in probability, and graph theory are presented. The course Mathematics I, in particular, is concerned with the principles of set theory, combinatorics and with the basic concepts from group theory.
Syllabus
  • Sets, algebra of sets, construction of natural numbers.
  • Relations between sets, composition of relations, inverse relations.
  • Mappings, injective and surjective mappings, cardinality of sets, Cantor theorem
  • Equivalences and partitions of sets, construction of rational numbers.
  • Ordered sets, isotone mappings, Dedekind's construction of real numbers.
  • Lattices and complete lattices, suprema and infima of bounded sets of real numbers.
  • Basic combinatorial functions and combinatorial identities, variations and combinations.
  • Inclusion-exclusion principle.
  • Permutations of finite sets, parity of permutations.
  • Semigroups, monoids, groups.
  • Divisibility of integers, decomposition to prime numbers.
  • Groups of residue classes.
  • Subgroups, homomorphisms and isomorphisms of groups, Cayley theorem.
Literature
  • FUCHS, Eduard. Logika a teorie množin (Úvod do oboru). 1. vyd. Brno: Rektorát UJEP, 1978. 175 s. info
  • FUCHS, Eduard. Kombinatorika a teorie grafů. 1. vyd. Praha: Státní pedagogické nakladatelství, 1986. 138 s. info
  • ROSICKÝ, Jiří. Algebra. I. 1. vyd. Brno: Rektorát UJEP, 1982. 140 . info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Rektorát Masarykovy univerzity, 1991. 196 s. ISBN 8021003200. info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 2. vyd. Brno: Masarykova univerzita, 1993. 145 s. ISBN 8021008164. info
Bookmarks
https://is.muni.cz/ln/tag/FI:MB101!
Assessment methods (in Czech)
Dvouhodinová přednáška a cvičení zakončené písemnou zkouškou.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2002, Autumn 2004, Autumn 2005, Spring 2006, Autumn 2006, Spring 2007, Autumn 2007, Spring 2008, Autumn 2008, Spring 2009, Autumn 2009, Spring 2010, Autumn 2010, Spring 2011, Autumn 2011, Spring 2012, Autumn 2012, Spring 2013, Autumn 2013, Spring 2014, Autumn 2014, Spring 2015, Autumn 2015, Spring 2016, Autumn 2016, Spring 2017, Autumn 2017, Spring 2018, Autumn 2018, Spring 2019.
  • Enrolment Statistics (Autumn 2003, recent)
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