Topology (MAT301) | GSÜ - ECTS Information Guide

Content

Objective

Master elementary topology via the study of the topology of metric spaces.

Course Content

Metric spaces (main inequalities, distances, equivalent distances, examples of metric sapces, normed vector spaces and convexity, distance between two sets and diametre, open and closed balls, neighborhood, open and closed sets, closure and interior, dense subsets). Topology (topological spaces, induced topology). Sequences in metric spaces (convergence, convergence in a product of metric spaces, limit point, caractersation of closed sets with sequences, Cauchy sequences, complete spaces). Continuous maps between metric spaces (sequential and topological caracterisation of continuity, uniform continuity, lipshizt maps). Compacity. Connectedness

Weekly Contents

Theory Topics
Week	Weekly Contents
1	Metric Spaces
2	Metric Spaces
3	Metric spaces
4	Metric spaces
5	Topological spaces
6	Topological spaces
7	Topological spaces
8	Topological spaces
9	Continuity
10	Continuity
11	Continuity
12	Compacity
13	Compacity
14	Connexity

Assessment System

Contribution to Overall Grade
Activities	Number	Contribution
Contribution of in-term studies to overall grade	0	60
Contribution of final exam to overall grade	0	40
Total	0	100

In-Term Studies
Activities	Number	Contribution
Assignments	0	0
Presentation	0	0
Midterm Examinations (including preparation)	2	50
Project	0	0
Laboratory	0	0
Other Applications	0	0
Quiz	2	50
Term Paper/ Project	0	0
Portfolio Study	0	0
Reports	0	0
Learning Diary	0	0
Thesis/ Project	0	0
Seminar	0	0
Other	0	0
Total	4	100

Relation of Proficiency

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	understands principles of deductive reasoning; has experience to verify well-foundedness and exactness of mathematical statements in systematic ways;				X
2	can properly state and use concepts and results of major mathematical interest;				X
3	masters current computational techniques and algorithms; has a good ability in their use; can identify relevant tools, among those one has learned, suitable to solve a problem and is able to judge whether or not one is in possession of these tools;			X
4	is able to express one’s mathematical ideas in an organised way both in written and oral forms;				X
5	understands relations connecting substantial concepts and results; can switch from one viewpoint to another on mathematical objects (pictures, formulae, precise statements, heuristic trials, list of examples,...);			X
6	has followed individually a guided learning strategy; has pursued steps toward the resolution of unfamiliar problems;
7	has a theoretical and practical knowledge in computer science well adapted for learning a programming language;
8	has investigated the relevance of modeling and using mathematical tools in natural sciences and in the professional life; is conscious about historical development of mathematical notions;
9	has followed introduction to some mathematical or non-mathematical disciplines after one’s proper choice; had experience to learn selected subjects according to one’s proper arrangement;		X
10	masters French language as well as other foreign languages, to a level sufficient to study or work abroad.		X

ECTS

Activities	Number	Period	Total Workload
Class Hours	14	4	56
Assignments	6	3	18
Midterm Examinations (including preparation)	2	25	50
Final Examinations (including preparation)	1	25	25
Quiz	4	1	4
Total Workload			153
Total Workload / 25			6.12
Credits ECTS			6