- Kalle Kytölä
- David Adame-Carrillo (Head TA)
- Kai Hippi (TA)
- Teemu Tasanen (TA)
- The lectures will be in the form of Zoom-meetings on Mondays 10-12 and Wednesdays 14-16. See the Lectures tab for zoom links.
- The exercise sessions will be in the form of Zoom-meetings. There are five groups, each with 2h/week exercise session.
- The course discussion forum is a Zulip chat hosted by Aalto CS. It will be used for announcemnts and discussions about the course topics, lectures, exercises, practicalities, etc., and some quizzes and polls will be held there. You can and should login with your Aalto account. The data is hosted at Aalto University servers, but the policy is to not post any sensitive information in this discussion forum; see the general rules of zulip.cs.aalto.fi.
Description of the course
Course contents and learning objectives
Key topics of the course include:
- real numbers, metric, norm, inner product, open and closed sets, continuous mappings, sequences and limits, compactness, completeness, connectedness.
- . . . recognize what structure different spaces are equipped with (e.g. inner product, norm, metric, topology, vector space structure, ...);
- . . . know the definitions and fundamental properties of continuous functions, convergent sequences, compact sets, completeness, and connectedness, required in advanced studies in mathematics;
- . . . can perform rigorous logical reasoning (specifically with concepts of metric space topology);
- . . . can apply abstract and general results (about metric spaces in particular) to concrete and specific cases(including the Euclidean space
The course starts from mathematical foundations, and therefore logically relies on minimal prerequisites. A broader prior familiarity with mathematics is of course helpful for putting the abstract results in context and for appreciating the achieved generalizations.
A sufficient prior knowledge is a good command of:
MS-A01XX Differential and integral calculus 1
Completing the course
- exercises 50% + course exam 50%
- final exam 100%.