Credits: 4. Grading scale: TH. Optional for: D3, E3, F3. Course coordinator: Studierektor, Matematik. Recommended prerequisites: FMA037 Complex analysis or FMA280 Analytical Functions. Assessment: Written or oral test. Further information: The course is given every second year. Homepage: http://www.maths.lth.se/matematiklth/vitahyllan/vitahyllan.html.

Aim
The course is designed for those who may use mathematics extensively in the future, but also for other interested students. The aim is to throw light on the theoretical structure of the mathematics in the first courses. Besides the mere conveying of knowledge the goal is to give practise in the art of proof making, and to bring out the possibilities of abstraction of the concepts discussed.

Contents
Sets. Real numbers. Metric spaces. Overview of different spaces. Completeness. Compact sets. Continuous functions. Connected sets. Mixed entertainment.

Literature
Handouts.