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Topology - MAT00044H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Jason Levesley
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Spring Term 2017-18

Module aims

To introduce the theory of abstract topological spaces and their properties.

To introduce the notion of a topological invariant and the fundamental ones: connectedness, compactness, separation, etc.

To introduce the notion of homotopy and the fundamental group and study some applications.

Module learning outcomes

At the end of the module you should be able to:

Understand the fundamental abstract notions of general topology including topological spaces, continuous maps, subspaces, connectedness, compactness, homeomorphisms, and separation properties. Work with basic examples of topological spaces, particularly non-Euclidean ones.

Understand homotopies of maps, homotopy equivalence and the construction of the fundamental group of a space. Understand basic properties of the fundamental group. Be able to compute the fundamental group of simple spaces.

Understand applications of topological invariants to proving results in algebra and analysis.

Assessment

Task Length % of module mark
University - closed examination
Topology
2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
University - closed examination
Topology
2 hours 100

Module feedback

Information currently unavailable

Indicative reading

Basic Topology, M. A. Armstrong, Springer UTM, 1983.

Algebraic Topology, Allen Hatcher, CUP, 2002.



The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.