MB005 Foundations of mathematics

Faculty of Informatics
Autumn 2004
Extent and Intensity
2/2. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Ondřej Klíma, Ph.D. (lecturer)
Mgr. Aleš Návrat, Dr. rer. nat. (seminar tutor)
Mgr. Jan Pavlík, Ph.D. (seminar tutor)
Mgr. Miroslava Tkadlecová, Ph.D. (seminar tutor)
RNDr. Lenka Viskotová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable
Mon 8:00–9:50 D3
  • Timetable of Seminar Groups:
MB005/01: Mon 10:00–11:50 B007, L. Viskotová
MB005/02: Mon 12:00–13:50 B007, M. Tkadlecová
MB005/03: Mon 12:00–13:50 B411, O. Klíma
MB005/04: Tue 12:00–13:50 B003, J. Pavlík
MB005/05: Fri 8:00–9:50 B011, A. Návrat
MB005/06: Fri 10:00–11:50 B011, A. Návrat
MB005/07: Tue 14:00–15:50 B003, J. Pavlík
Prerequisites
(! M005 Foundations of mathematics )&&! MB101 Mathematics I &&! NOW ( MB101 Mathematics I )
Knowledge of high school mathematics.
Course Enrolment Limitations
The course is only offered to the students of the study fields the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course links up high school knowledge with basic mathematical concepts and ideas which a student needs. It mainly deals with fundaments of mathematical logic, set theory, algebra and combinatorics.
Syllabus
  • 1. Basic logical notions (propositions, quantification, mathematical theorems and their proofs).
  • 2. Basic properties of integers (division theorem, divisibility, congruences).
  • 3. Basic set-theoretical notions (set-theoretical operations including cartesian product).
  • 4. Mappings (basic types of mappings, composition of mappings).
  • 5. Elements of combinatorics (variations, combinations, inclusion-exclusion principle)
  • 6. Cardinal numbers (finite, countable and uncountable sets).
  • 7. Relations (relations between sets, composition of relations, relations on a set).
  • 8. Ordered sets (order and linear order, special elements, Hasse diagrams, supremum a infimum).
  • 9. Equivalences and partitions (relation of equivalence, partition and their mutual relationship).
  • 10. Basic algebraic structures (grupoids, semigroups, groups, rings, integral domains, fields).
  • 11.Homomorphisms of algebraic structures (basic properties of homomorphisms, kernel and image of a homomorphism).
Literature
  • Balcar, Bohuslav - Štěpánek, Petr. Teorie množin [Balcar, Štěpánek, 1986]. 1. vyd. Praha : Academia, 1986. 412 s. r87U.
  • Childs, Lindsay. A Concrete Introduction to Higher Algebra, Springer-Verlag, 1979, 338s. ISBN 0-387-90333-x
  • Horák, Pavel. Algebra a teoretická aritmetika. 1 [Horák]. Brno : Rektorát Masarykovy univerzity Brno, 1991. 196 s. ISBN 80-210-0320-0.
  • Rosický, Jiří. Algebra. I [Rosický, 1994]. 2. vyd. Brno : Vydavatelství Masarykovy univerzity, 1994. 140 s. ISBN 80-210-0990-.
  • J. Rosický, Základy matematiky, učební text
Assessment methods (in Czech)
Zkouška je písemná a má dvě části-první písemka(25%) během semestru, druhá(75%) ve zkouškovém období. Budou právě 4 termíny ve zkouškovém - 2 řádné, první opravný a druhý opravný. K připuštění ke zkoušce je třeba získat zápočet ze cvičení. Ten je podmíněn účastí, jsou dovoleny tři neomluvené neúčasti (a tři omluvené).
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Teacher's information
http://math.muni.cz/~klima/ZakladyM/zakladym-fi-04.html
The course is also listed under the following terms Autumn 2002, Spring 2003, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011.
  • Enrolment Statistics (Autumn 2004, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2004/MB005