Mathematics

Pre-requisites: High school mathematics education; finished first year course Logic.

Course objectives: Introduction to: notions of the foundations of mathematics; results and problems of mathematics from which philosophical problems emerged; problems of contemporary mathematics from philosophical perspective

Course description: Students will gain knowledge of: results and problems related to the notion of a number and geometry, which are sources of philosophical problems; various philosophies of mathematics; problems of contemporary mathematics from philosophical perspective; proving simple consequences of axioms in: geometry, Peano's arithmetic and algebraic structures (groups and fields); making simple programs for Turing machine and proving that same basic functions are recursive.

Learning Outcomes: Students will gain knowledge of: results and problems related to geometry and the notion of a number, which are sources of philosophical problems; various philosophies of mathematics; problems of contemporary mathematics from philosophical perspective; proving simple consequences of axioms in: geometry, Peano's arithmetic and algebraic structures (groups and fields); making simple programs for Turing machine and proving that same basic functions are recursive.

Mathematics

Pre-requisites: High school mathematics education; finished first year course Logic.

Course objectives: Introduction to: notions of the foundations of mathematics; results and problems of mathematics from which philosophical problems emerged; problems of contemporary mathematics from philosophical perspective

Course description: Students will gain knowledge of: results and problems related to the notion of a number and geometry, which are sources of philosophical problems; various philosophies of mathematics; problems of contemporary mathematics from philosophical perspective; proving simple consequences of axioms in: geometry, Peano's arithmetic and algebraic structures (groups and fields); making simple programs for Turing machine and proving that same basic functions are recursive.

Learning Outcomes: Students will gain knowledge of: results and problems related to geometry and the notion of a number, which are sources of philosophical problems; various philosophies of mathematics; problems of contemporary mathematics from philosophical perspective; proving simple consequences of axioms in: geometry, Peano's arithmetic and algebraic structures (groups and fields); making simple programs for Turing machine and proving that same basic functions are recursive.

Literature/Reading:

• D. Strojk, Kratki pregled istorije matematike S. Barker, Filozofija matematike Ž. Mijajlović, Z. Marković, K. Došen, Hilbertovi problemi i logika