Undergraduate Course: General and Algebraic Topology (MATH10075)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | 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. |
| Course description |
Topological spaces.
Continuous functions.
Compactness, connectedness, path-connectedness.
Identification spaces.
Compact surfaces.
Homotopy.
Fundamental groups and their calculation.
Covering spaces.
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Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- 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.
- Construct homotopies and prove homotopy equivalence for simple examples.
- Calculate fundamental groups of simple topological spaces, using generators and relations or covering spaces as necessary, and calculate simple topological invariants, such as numbers of path components, degrees and winding numbers.
- 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.
- Provide an elementary example illustrating specified behaviour in relation to a given combination of basic definitions and key theorems across the course.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | GATop |
Contacts
| Course organiser | Dr Jonathan Pridham
Tel: (0131 6)50 3300
Email: |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: |
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