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:

• M. Božić, Pregled istorije i filozofije matematike, Zavod za udžbenike i nastavna sredstva, Beograd, 2002
• Ž. Mijajlović i dr., Hilbertovi problemi i logika, Zavod za udžbenike i nastavna sredstva, Beograd, prvo izd. 1986
• D. Strojk, Kratak pregled istorije matematike, Zavod za udžbenike i nastavna sredstva, Beograd, 1987 (neka poglavlja)
• D. Lopandić, Geometrija, Naučna knjiga, Beograd, 1981 (neka poglavlja)
• M. Božić i S. Vujić, Matematička logika sa elementima opšte logike, Naučna knjiga, Beograd, 1980 (neka poglavlja)
• P. Janičić, Matematička logika u računarstvu, Matematički fakultet, Beograd, prvo izd. 2004 (neka poglavlja)
• S. Barker, Filozofija matematike, Nolit, Beograd, 1973
• G.S. Boolos and R.C. Jeffrey, Computability and Logic, Cambridge Univesity Press, 1974