Topology (MSc) - MAT00067H
- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Module summary
This module is for postgraduate students only.
Related modules
Additional information
MSc students should have taken a first course in Pure Mathematics
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Spring Term 2022-23 |
Module aims
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To introduce the theory of abstract topological spaces and their properties.
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To introduce the notion of a topological invariant and study fundamental ones such as connectedness, compactness and that of being Hausdorff.
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To introduce the notion of homotopy and the fundamental group.
Module learning outcomes
Subject content
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Fundamental abstract notions of general topology including topological spaces, continuous maps, subspaces, connectedness, compactness, homeomorphisms, and examples of separation properties. Basic examples of topological spaces, particularly “non-Euclidean” ones.
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Homotopies of maps, homotopy equivalence and an intuitive construction of the fundamental group of a space. Basic properties of the fundamental group. Be able to compute the fundamental group of simple spaces.
Academic and graduate skills
- Develop the ability to think abstractly about mathematics learnt in the first two years of the mathematics programme, particularly in calculus and analysis. Understand the fundamentals of topology for those who wish to continue further study in pure mathematics.
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
Pass/fail
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Module feedback
Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Indicative reading
J. Munkres, Topology 2ed., Prentice Hall 2000