PřF:M7532 Foundations of mathematics - Course Information
M7532 Logic foundations of mathematics
Faculty of ScienceAutumn 2016
- Extent and Intensity
- 2/0/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: graded credit.
- Teacher(s)
- doc. RNDr. Eduard Fuchs, CSc. (lecturer)
- Guaranteed by
- doc. RNDr. Eduard Fuchs, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science - Timetable
- Mon 19. 9. to Sun 18. 12. Fri 8:00–9:50 M5,01013
- 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
- Some formal aspects of mathematics are studied. The main objectives of the couurses is the Godel theorem of incompleteness.
- Syllabus
- Origins of set theory and its impact on the 20th century mathematics.
- Formalization of mathematics: propositional calculus, first order logic calculus, axiomatic theories.
- Axioms for set theory: Zermelo-Fraenkel set theory and Gödel-Bernays set theory, construction of natural and real numbers in set theory.
- Cardinal and ordinal numbers: ordering and arithmetics of cardinal numbers, arithmetics of ordered sets, ordinal types and their arithmetics, well-ordering sets, ordinal numbers, transfinite induction.
- Axiom of choise and equivalent theorems.
- Peano arithmetics.
- Literature
- FUCHS, Eduard. Teorie množin pro učitele. 1st ed. Brno: Masarykova univerzita, 1999. info
- FUCHS, Eduard. Základy teorie množin. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1986, 146 s. info
- FUCHS, Eduard. Logika a teorie množin : (úvod do oboru). Vyd. 1. Brno: Rektorát UJEP, 1978, 175 s. info
- FUCHS, Eduard. Teorie množin. Vyd. 1. Brno: Rektorát UJEP, 1974, 176 s. info
- BLAŽEK, Jaroslav, Emil CALDA and Blanka KUSSOVÁ. Algebra a teoretická aritmetika. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1979, 244 s. info
- TARSKI, Alfred. Úvod do logiky a metodologie deduktivních věd. Translated by Pavel Materna. Vyd. 1. Praha: Academia, 1966, 245 s. URL info
- Teaching methods
- Theoretical explanation with practical examples
- Assessment methods
- Written test (50 % success rate)
- Language of instruction
- Czech
- Further Comments
- Study Materials
The course is taught annually. - Listed among pre-requisites of other courses
- Enrolment Statistics (Autumn 2016, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2016/M7532