Undergraduate Course: General and Algebraic Topology (MATH10075)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Credits | 20 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course will introduce students to essential notions in topology, such as topological spaces, continuous functions, and compactness, and move on to study of compact surfaces, homotopies, fundamental groups and covering spaces. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
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| Delivery period: 2014/15 Full Year, Available to all students (SV1)
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Learn enabled: Yes |
Quota: None |
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Web Timetable |
Web Timetable |
| Course Start Date |
15/09/2014 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
139 )
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| Additional Notes |
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| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
|
| No Exam Information |
Summary of Intended Learning Outcomes
1. State and prove standard results regarding topological spaces and
continuous functions, and decide whether a simple unseen statement about them is true, providing a proof or counterexample as appropriate.
2. Construct homotopies and prove homotopy equivalence for simple examples.
3. Calculate fundamental groups of simple topological spaces, using generators and relations or covering spaces as necessary.
4. Calculate simple topological invariants, such as numbers of path components, degrees and winding numbers.
5. State and prove standard results about homotopy, and decide whether a simple unseen statement about them is true, providing a proof or counterexample as appropriate.
6. Provide an elementary example illustrating specified behaviour in relation to a given combination of basic definitions and key theorems across the course. |
Assessment Information
| Coursework 5%, Examination 95% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Topological spaces.
Continuous functions.
Compactness, connectedness, path-connectedness.
Identification spaces.
Compact surfaces.
Homotopy.
Fundamental groups and their calculation.
Covering spaces. |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | GATop |
Contacts
| Course organiser | Dr Thomas Leinster
Tel: (0131 6)50 5057
Email: Tom.Leinster@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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