401-2554-00L Topology
| Semester | Spring Semester 2020 |
| Lecturers | A. Carlotto |
| Periodicity | yearly recurring course |
| Language of instruction | English |
Courses
| Number | Title | Hours | Lecturers | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 401-2554-00 V | Topology | 3 hrs |
| A. Carlotto | ||||||||||||||||||
| 401-2554-00 U | Topology Groups are selected in myStudies. | 2 hrs |
| A. Carlotto |
Catalogue data
| Abstract | Topics covered include: Topological and metric spaces, continuity, connectedness, compactness, product spaces, separation axioms, quotient spaces, homotopy, fundamental group, covering spaces. |
| Objective | An introduction to topology i.e. the domain of mathematics that studies how to define the notion of continuity on a mathematical structure, and how to use it to study and classify these structures. |
| Literature | We will follow these, freely available, standard references by Allen Hatcher: i) http://pi.math.cornell.edu/~hatcher/Top/TopNotes.pdf (for the part on General Topology) ii) http://pi.math.cornell.edu/~hatcher/AT/ATch1.pdf (for the part on basic Algebraic Topology). Additional references include: "Topology" by James Munkres (Pearson Modern Classics for Advanced Mathematics Series) "Counterexamples in Topology" by Lynn Arthur Steen, J. Arthur Seebach Jr. (Springer) "Algebraic Topology" by Edwin Spanier (Springer). |
| Prerequisites / Notice | The content of the first-year courses in the Bachelor program in Mathematics. In particular, each student is expected to be familiar with notion of continuity for functions from/to Euclidean spaces, and with the content of the corresponding basic theorems (Bolzano, Weierstrass etc..). In addition, some degree of scientific maturity in writing rigorous proofs (and following them when presented in class) is absolutely essential. |
Performance assessment
| Performance assessment information (valid until the course unit is held again) | |
Performance assessment as a semester course | |
| In examination block for | Bachelor's Degree Programme in Mathematics 2016; Version 25.02.2020 (Examination Block 2) Bachelor's Programme in Mathematics 2010; Version 24.02.2016 (Examination Block 2) |
| ECTS credits | 6 credits |
| Examiners | A. Carlotto |
| Type | session examination |
| Language of examination | English |
| Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |
| Mode of examination | written 120 minutes |
| Written aids | None. |
| If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding. | |
Learning materials
| Main link | Vorlesungshomepage |
| Only public learning materials are listed. | |
Groups
| 401-2554-00 U | Topology | ||||||
| Registration for groups in myStudies is possible until 17.03.2020. | |||||||
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| Groups | G-01 |
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| G-02 |
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| G-03 |
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| G-04 |
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| G-05 |
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Restrictions
| Groups | Restrictions are listed under Groups |
Offered in
| Programme | Section | Type | |
|---|---|---|---|
| Mathematics Bachelor | Examination Block II | O |  |