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Topology (MSc) - MAT00067H

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  • 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

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations


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

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

  • To introduce the notion of a topological invariant and study fundamental ones such as connectedness, compactness and that of being Hausdorff.

  • To introduce the notion of homotopy and the fundamental group.

Module learning outcomes

Subject content

  • 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.

  • 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


The information on this page is indicative of the module that is currently on offer. The University constantly explores 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. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.