Course: Set Theory

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Course title Set Theory
Course code KMA/XTMN
Organizational form of instruction no contact
Level of course Doctoral
Year of study not specified
Semester Winter and summer
Number of ECTS credits 30
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction unspecified
Work placements unspecified
Recommended optional programme components None
Lecturer(s)
  • Fuchs Eduard, doc. RNDr. CSc.
Course content
Problems of infinity in mathematics. Position of infinity in antiquity, in the European Middle Ages and at present time. Origin of the set theory and its influence on 20th century mathematics. Origin of the set-logical language of contemporary mathematics. Relation between intuitive and formal constructions of mathematics. Construction of natural and real numbers in the set theory. Cardinal and ordinal numbers, transfinite induction and its connection with the mathematical induction in school mathematics. Axiom of choice and its role in contemporary mathematics. Gödel's incompleteness theorem and its impact on modern science.

Learning activities and teaching methods
Monologic (reading, lecture, briefing)
Learning outcomes
The set theory has become the world of modern mathematics. Not only has it postulated the mathematical concept of infinity in modern mathematics, it has also become the basis of almost all current mathematical disciplines. At the beginning of the 20th century it, however, largely contributed to the collapse of existing notions about the ways mathematics shoud be built. Without understanding the modern development of the set theory, the modern construction of mathematics in the 20th century cannot, therefore, be understood. Gödel's results, on the other hand, fundamentally limited the strength of the formal construction of mathematics, and completely changed existing views of the strength of exact theories. Students will be acquainted with these results as well.
basic orientation in university mathematics
Prerequisites
Successful completion of the course requires understanding of the basic concepts of the explained theory, and knowledge of definitions, theorems and proofs. The aim of the exam is to test whether a student has understood the explained theory and is able to apply it.

Assessment methods and criteria
Combined exam

Basic orientation in university mathematics.
Recommended literature
  • Fraenkel, A. A., Bar-Hillel, Y.:. Foundations of Set Theory, Amsterdam, 1958.
  • Fuchs, E.:. Teorie množin pro učitele, MU, Brno, 2003.
  • Tarski, A.:. Úvod do logiky a metodologie deduktivních věd, Academia, Praha, 1966.


Study plans that include the course
Faculty Study plan (Version) Category of Branch/Specialization Recommended year of study Recommended semester
Faculty: Faculty of Education Study plan (Version): Theory of Mathematics Education (2) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -
Faculty: Faculty of Education Study plan (Version): Theory of Mathematics Education (2) Category: Pedagogy, teacher training and social care - Recommended year of study:-, Recommended semester: -