| Course title | Set Theory |
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| Course code | KMA/MNO |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | unspecified |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 4 |
| Language of instruction | Czech |
| Status of course | unspecified |
| Form of instruction | Face-to-face |
| Work placements | Course does not contain work placement |
| Recommended optional programme components | None |
| Course availability | The course is available to visiting students |
| Lecturer(s) |
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| Course content |
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Lectures: 1. Development of the set theory as a part of the development of mathematics: Bolzano, Cantor, paradoxes, different approaches to removing them, axiomatic approach, its advantages and drawbacks, the position the set theory in the contemporary mathematics. 2. Language of the set theory: Language and metalanguage, formulae, independent and dependent variables, basic language and its extension. 3. Axioms of the set theory: Zermelo-Fraenkel system, inclusion, intersection, difference, pair, union, power. 4. Classes: Classes and formulae, sets and classes, class operations. 5. Relations, mappings, orderings, partitions of sets: Cartesian product, relations, mappings, systems of sets, orderings, completions, equivalences, partitions, cardinalities. 6. Finite and infinite sets: Finite set, induction, cardinality, hypothesis of continuum, existence proofs. 7. Countable sets and natural numbers: Countability, a model of natural numbers in the set theory. 8. Axiom of choice and principle of maximality: Principle of choice, selector, equivalents of the axiom of choice.
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| Learning activities and teaching methods |
Monological explanation (lecture, presentation,briefing)
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| Learning outcomes |
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Basic notions of set theory and fundamental mathematical structures.
Knowledge of fundamental concepts and methods of the set theory and mathematical structures. |
| Prerequisites |
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Unspecified
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| Assessment methods and criteria |
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Oral exam
Material specified in the curriculum. |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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