FI:MB005 Foundations of mathematics - Course Information
MB005 Foundations of mathematics
Faculty of InformaticsSpring 2003
- 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)
- prof. RNDr. Miroslav Novotný, DrSc. (lecturer)
Helena Dvořáčková (assistant) - Guaranteed by
- doc. RNDr. Jiří Kaďourek, CSc.
Faculty of Informatics
Contact Person: prof. RNDr. Jiří Rosický, DrSc. - Timetable
- Thu 11:00–12:50 D2, Fri 9:00–10:50 D2
- Prerequisites
- ! M005 Foundations of mathematics &&! 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
- Informatics (programme FI, B-IN)
- Informatics (programme FI, M-IN)
- Upper Secondary School Teacher Training in Informatics (programme FI, M-IN)
- Upper Secondary School Teacher Training in Informatics (programme FI, M-SS)
- 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
- The course is taught each semester.
- Enrolment Statistics (Spring 2003, recent)
- Permalink: https://is.muni.cz/course/fi/spring2003/MB005