Elements of Basic Mathematics 2

The course is comprised of two parts. The first part is an introduction to the analysis and to the formalisation of mathematical reasoning. Starting from a series of case studies based on the students' experience in Analysis, Algebra, and Geometry, we will arrive at a discussion of the basic notions of contemporary mathematical logic. The second part puts to work the knowledge and the competence acquired in the first part to survey a number of answers that, in the course of time, have been given to the question: What are the foundations of Mathematics? Within this survey, special attention will be given to the theory of sets, both in its naive and in its formalised version.

By the end of the first part of the course students will be able to recognise, critically discuss, and use the main logico-mathematical tools employed in a given mathematical proof. By the end of the second part, students will have acquired basic knowledge of naive and formalised set theory. Further, students will have learned the essential features of a number of approaches to the foundation of mathematics that are alternative to the theory of sets.