MA0022 Set Theory

Faculty of Education
Autumn 2024
Extent and Intensity
2/2/1.3. 6 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Dr. András Rontó (lecturer)
RNDr. Petra Antošová, Ph.D. (seminar tutor)
Guaranteed by
doc. Dr. András Rontó
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education
Timetable of Seminar Groups
MA0022/KombiSem01: Fri 27. 9. 14:00–17:50 učebna 4, Fri 4. 10. 13:00–16:50 učebna 5, Fri 18. 10. 12:00–15:50 učebna 5, Fri 1. 11. 12:00–15:50 učebna 5, P. Antošová
MA0022/PrezPred01: Mon 8:00–9:50 učebna 7, A. Rontó
MA0022/PrezSem01: Wed 16:00–17:50 učebna 34, P. Antošová
MA0022/PrezSem02: Mon 14:00–15:50 učebna 11, P. Antošová
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
At the end of the course students should be able to understand of concepts and differents between notions of the potential infinity and the actual infinity, be able to calculate with quantitative and qualitative characteristics of infinit sets, namely with cardinal and ordinal numbers. Students obtains a survey concerning the connectedness between various mathematical disciplines witch the set theory is a certain roof discipline for.
Learning outcomes
In order to successfully pass the course, the students have to show understanding of and ability to differentiate between the notions potential infinity and actual infinity as well as the ability to use the arithmetic of the quantitative and qualitative characteristics of the infinite sets (i.e. cardinal and ordinal numbers). They also have to show basic understanding of the following areas: - well-ordered sets; - sum and product of ordered sets; - axiom of choice; - cardinal numbers; countable sets; - inequalities among cardinal numbers; - arithmetic of cardinal numbers; - ordinal types and ordinal numbers.
Syllabus
  • 1. Basic notions in set theory. 2. Elementary operations on systems of sets. 3. Well-ordered sets. 4. Sum and product of ordered sets. 5. Axiom of choice. 6. Cardinal numbers. Countable sets. 7. Inequalities among cardinal sets. 8. Arithmetic of cardinal sets. 9. Ordinal types. Ordinal numbers.
Literature
    required literature
  • FUCHS, Eduard. Teorie množin pro učitele. Vyd. 1. Brno: Masarykova univerzita, 1999, 200 s. ISBN 8021022019. info
    recommended literature
  • FUCHS, Eduard. Diskrétní matematika a Teorie množin pro učitele (CD-ROM) (Discrete Mathematics and Set Theory for Teachers). Brno: Masarykova univerzita, 2000, 890 pp. Matematika na CD-ROM, sv. 2. ISBN 80-210-2463-1. info
  • BALCAR, Bohuslav and Petr ŠTĚPÁNEK. Teorie množin. 2. opr. a rozš. vyd. Praha: Academia, 2000, 462 s. ISBN 802000470X. info
  • KURATOWSKI, Kazimierz and Andrzej MOSTOWSKI. Teorija množestv. Moskva: Mir, 1970, 416 s. info
Teaching methods
Theoretical lecture and seminar.
Assessment methods
Oral exam, topic assigned by a draw from the list of 11 topics (see the folder Course-related instructions). Before sitting for the oral exam, students fulfil one of the requirements below: presence-form of study: active participation in seminars; combined form of study: handing in the assignments.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Information on the extent and intensity of the course: 16 hodin (kombinovaná forma).
The course is also listed under the following terms Autumn 2019, autumn 2020, Autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/ped/autumn2024/MA0022