corso|33603

General aims: to acquire basic knowledge and skills in axiomatic set theory and to be able to apply them in various contexts, including teaching. Specific aims: Knowledge and understanding: The successful student will have acquired basic notions and results in mathematical logic: axioms and main results of the theory ZF; ordinal numbers; the axiom of choice; cardinal numbers; paradoxes in several areas of mathematics. Applying knowledge and understanding: The successful student will be able to solve exercises and problems referring to the topics covered and to application in other mathematical areas. S/he will perform computations with ordinal numbers and cardinal numbers; s/he is familiar with mathematical translations of the notion of infinity. S/he will be able to apply her/his knowledge in an education context. Critical and judgmental skills: The successful student will be familiar with mathematical rigor and formalism. S/he will have reflected on known mathematical contents; s/he knows how to tackle questions about the foundations of mathematics in a critical way. S/he will be able to discuss the role of intuition and rigor in teaching mathematics in different situations. Communication skills: The successful student will be able to present subjects and arguments in the oral test, and to explain what s/he learned. Learning skills: The acquired knowledge will allow to study more specialized subjects. The student will be motivated to extend the acquired knowledge.