Objectives and competences
Students learn how to use the basic notions and results of mathematical logic and set theory.
Content (Syllabus outline)
The basic notions of mathematical logic. The methods of denoting sets. The basic relations among sets, the basic operations on sets or families of sets. Relations. Equivalence relations. Order. Well order. Mathematical induction. Functions. Special types of functions.
Finite and infinite, countable and uncountable sets.
Fundamentals of cardinal and ordinal numbers.
Learning and teaching methods
Lectures
Theoretical exercises
Intended learning outcomes - knowledge and understanding
Be able to use the basic notions of mathematical logic (statements, predicates, logical operations, quantifiers)
Be able to use the basic notions and results of set theory (sets, operations on sets and families of sets, relations, functions, cardinal and ordinal numbers)
Intended learning outcomes - transferable/key skills and other attributes
The obtained knowledge forms a foundation for all the other mathematical subjects.
Readings
N.Prijatelj: Matematične strukture I, Ljubljana,Društvo matematikov, fizikov in astronomov Slovenije, 1996
R.R.Stoll:Set theory and logic, New York, Dover Publications, 1979
S.Lipschutz: Schaum's outline of theory and problems of set theory and related topics, New York (etc.), McGraw-Hill, 1998
Prerequisits
There are none.
Additional information on implementation and assessment Exams:
Written exam – problems
Oral exam – theory
Each of the mentioned assessments must be assessed with a passing grade.
Passing grade of the written exam – problems is required for taking the oral exam – theory.
Written exam – problems can be replaced by two mid-term tests
