MB005 Foundations of mathematics

Faculty of Informatics
Autumn 2006
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)
RNDr. Pavla Zagorová (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable
Tue 12:00–13:50 D3
  • Timetable of Seminar Groups:
MB005/01: Mon 16:00–17:50 B007, O. Klíma
MB005/02: Mon 10:00–11:50 B007, O. Klíma
MB005/03: Tue 8:00–9:50 B007, P. Zagorová
MB005/04: Tue 10:00–11:50 B007, P. Zagorová
MB005/05: Mon 14:00–15:50 B011, O. Klíma
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(20%) během semestru, druhá(80%) ve zkouškovém období. Budou právě 4 termíny ve zkouškovém - 2 řádné, první opravný a druhý opravný. K připuštění ke zkoušce je třeba aktivní účast na cvičení (jsou dovoleny tři neomluvené neúčasti a tři omluvené).
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
http://www.math.muni.cz/~klima/ZakladyM/zakladym-fi-06.html
The course is also listed under the following terms Autumn 2002, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011.
  • Enrolment Statistics (Autumn 2006, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2006/MB005