PřF:M4155 Set Theory - Course Information
M4155 Set Theory
Faculty of ScienceSpring 2012
- Extent and Intensity
- 2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- Teacher(s)
- prof. RNDr. Jiří Rosický, DrSc. (lecturer)
doc. Mgr. Michal Kunc, Ph.D. (seminar tutor) - Guaranteed by
- prof. RNDr. Jiří Rosický, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Tue 14:00–15:50 M1,01017
- Prerequisites
- ! M4150 Set Theory && ( M1120 Discrete Mathematics || FI:MB005 Foundations of mathematics || M1125 Fundamentals of Mathematics )
Knowledge of basic set theoretical concepts is welcome. - 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
- Applied Informatics (programme FI, B-AP)
- Applied Informatics (programme FI, N-AP)
- Informatics (programme FI, B-IN)
- Informatics (programme FI, N-IN)
- Logics (programme PřF, N-MA)
- Mathematics (programme PřF, B-MA)
- Mathematics (programme PřF, B-MA)
- Course objectives
- The course introduces basic set theory and its significance for mathematics. At the end of the course a student: understands basic set theoretical concepts; masters the set theoretical way of thinking; is able to analyze set theoretical context of mathematical concepts and results; is aware of possibilities and limitations of a formalization of mathematics.
- Syllabus
- 1. Set theory: origin of set theory, set theory as a fundament of mathematics, concept of infinity, the construction of natural and real numbers 2. Cardinal numbers: cardinal numbers, ordering of cardinal numbers, Cantor-Bernstein theorem, operations with cardinal numbers 3. Well-ordered sets: well-ordered sets, transfinite induction, operations with well-ordered sets 4. Ordinal numbers: ordinal numbers, ordering of ordinal numbers, ordinal arithmetic, countable ordinal numbers 5. Axiom of choice: axiom of choice, well-ordering principle, maximality principle, applications of the axiom of choice to cardinal arithmetics 6. Elements of axiomatic set theory.
- Literature
- J. Rosický, Teorie množin II., http://www.math.muni.cz/~rosicky/
- KOLÁŘ, Josef, Olga ŠTĚPÁNKOVÁ and Michal CHYTIL. Logika, algebry a grafy. 1. vyd. Praha: SNTL - Nakladatelství technické literatury, 1989, 434 s. info
- BALCAR, Bohuslav and Petr ŠTĚPÁNEK. Teorie množin. 1. vyd. Praha: Academia, 1986, 412 s. info
- FUCHS, Eduard. Teorie množin. Vyd. 1. Brno: Rektorát UJEP, 1974, 176 s. info
- Teaching methods
- The course: presents required knowledge and ways of thinking; shows their applications; provides a feeling about axiomatic set theory; stimulates a discussion about its subject.
- Assessment methods
- Course ends by an oral exam. Presence at the course recommended. Homeworks are given but not controled.
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- Study Materials
The course is taught annually.
- Enrolment Statistics (Spring 2012, recent)
- Permalink: https://is.muni.cz/course/sci/spring2012/M4155