MB005 Foundations of mathematics

Faculty of Informatics
Autumn 2002
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)
doc. Mgr. Jaroslav Hrdina, Ph.D. (seminar tutor)
Roman Rožník (seminar tutor)
doc. Mgr. Lenka Zalabová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable
Mon 14:00–15:50 D1
  • Timetable of Seminar Groups:
MB005/01: Tue 8:00–9:50 B007, J. Hrdina
MB005/02: Tue 10:00–11:50 B007, J. Hrdina
MB005/03: Tue 12:00–13:50 B007, L. Zalabová
MB005/04: Wed 8:00–9:50 B007, L. Zalabová
MB005/05: Wed 10:00–11:50 B007, L. Zalabová
MB005/06: Wed 8:00–9:50 B011, R. Rožník
MB005/07: Thu 10:00–11:50 B011, R. Rožník
Prerequisites
(! M005 Foundations of mathematics )&&! MB101 Foundations of mathematics I &&!NOW( MB101 Foundations of mathematics I )
Knowledge of 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 / 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.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught each semester.
Teacher's information
ftp://math.muni.cz/pub/math/people/Niederle/info/index.html
The course is also listed under the following terms Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011.
  • Enrolment Statistics (Autumn 2002, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2002/MB005