PdF:MA0022 Set Theory - Course Information
MA0022 Set Theory
Faculty of EducationAutumn 2019
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jan Chvalina, DrSc. (lecturer)
Mgr. Helena Durnová, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jan Chvalina, DrSc.
Department of Mathematics – Faculty of Education
Supplier department: Department of Mathematics – Faculty of Education - Timetable
- Mon 14:00–15:50 učebna 10
- Timetable of Seminar Groups:
- 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
- there are 7 fields of study the course is directly associated with, display
- 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
- Written and oral exam.
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually.
- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/ped/autumn2019/MA0022