MB005 Foundations of mathematics

Faculty of Informatics
Autumn 2010
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)
Guaranteed by
prof. RNDr. Jiří Rosický, DrSc.
Faculty of Informatics
Contact Person: prof. RNDr. Jiří Rosický, DrSc.
Timetable
Fri 10:00–11:50 D2
  • Timetable of Seminar Groups:
MB005/01: Fri 12:00–13:50 B003, O. Klíma
MB005/02: Tue 10:00–11:50 B007, O. Klíma
MB005/03: Tue 12:00–13:50 B007, O. Klíma
Prerequisites
! MB101 Mathematics I &&!NOW( MB101 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.
At the end of this course, students should be able to: read and understand formal mathematical texts; use basic notions of set theory, mathematical logic, 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 and Petr ŠTĚPÁNEK. Teorie množin. 1. vyd. Praha: Academia, 1986, 412 s. info
  • CHILDS, Lindsay. A concrete introduction to higher algebra. 2nd ed. New York: Springer, 1995, xv, 522. ISBN 0387989994. info
  • HORÁK, Pavel. Algebra a teoretická aritmetika. 1 [Horák]. Brno: Rektorát Masarykovy univerzity Brno, 1991, 196 s. ISBN 80-210-0320-0. info
  • ROSICKÝ, Jiří. Algebra. 2. vyd. Brno: Vydavatelství Masarykovy univerzity, 1994, 140 s. ISBN 802100990X. info
  • J. Rosický, Základy matematiky, učební text
Teaching methods
Lectures: theoretical explanation with examples. Seminars: solving problems for understanding of basic concepts and theorems.
Assessment methods
Written intrasemestral test and written final test. Results of the intrasemestral test is included in the overall evaluation. Students will be asked to have an active participation at seminars. Tests are written without any reading materials.
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-10.html
The course is also listed under the following terms Autumn 2002, Spring 2003, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011.
  • Enrolment Statistics (Autumn 2010, recent)
  • Permalink: https://is.muni.cz/course/fi/autumn2010/MB005