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Metric and Topological Spaces
| Faculteit | Science and Engineering |
| Jaar | 2021/22 |
| Vakcode | WBMA036-05 |
| Vaknaam | Metric and Topological Spaces |
| Niveau(s) | bachelor |
| Voertaal | Engels |
| Periode | semester I a |
| ECTS | 5 |
| Rooster | rooster.rug.nl |
| Uitgebreide vaknaam | Metric and Topological Spaces | ||||||||||||||||||||||||||||||||
| Leerdoelen | At the end of the course, the student is able to: 1) recognize and to apply abstract results in concrete situations (for example using the fixed point theorem in order to prove existence and uniqueness of solutions of differential equations). 2) reproduce and prove the results handled in the course. 3) analyse and synthesise the properties of a number of standard classes of metric spaces (for example Euclidean spaces, function spaces, etc.). 4) verify the axioms of (Hausdorff) topology, induce the topology on a subset of a given space, and inspect whether or not a mapping of topological spaces is continuous. 5) apply proof techniques in order to show abstract results. |
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| Omschrijving | In Euclidean spaces, continuity is defined using the familiar Euclidean distance between points. In this course we generalize the concept of continuity first to metric and then to topological spaces. In metric spaces we are given the concept of distance between its "points". Function spaces are some of the most useful examples of metric spaces. In topological spaces we know only which subsets are open. It turns out that this is all we need in order to study continuity. We discuss further some important geometrical concepts such as compactness, connectedness, and completeness, and we apply the Banach fixed point theorem in analysis. | ||||||||||||||||||||||||||||||||
| Uren per week | |||||||||||||||||||||||||||||||||
| Onderwijsvorm | Hoorcollege (LC), Opdracht (ASM), Werkcollege (T) | ||||||||||||||||||||||||||||||||
| Toetsvorm |
Opdracht (AST), Schriftelijk tentamen (WE)
(Final grade = max(exam, 0.6*exam + 0.4*(homework+tutorial presentations)).) |
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| Vaksoort | bachelor | ||||||||||||||||||||||||||||||||
| Coördinator | A.V. Kiselev | ||||||||||||||||||||||||||||||||
| Docent(en) | A.V. Kiselev | ||||||||||||||||||||||||||||||||
| Verplichte literatuur |
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| Entreevoorwaarden | Background knowledge from Analysis and Linear Algebra is required. | ||||||||||||||||||||||||||||||||
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