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Metric Spaces - MAT00037H

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  • Department: Mathematics
  • Module co-ordinator: Prof. Sanju Velani
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Autumn Term 2017-18

Module aims

A metric space consists of a set of points, together with a function which describes the "distance" between any two points - this could be the familiar Euclidean distance in 2, 3 or more dimensions, or something more abstract, such as the "distance" between two continuous functions. The main aim of the module is to introduce students to metric spaces, to show how the ideas of limits and continuity developed in Real Analysis generalise to the Metric Space context, and to apply these ideas to two of the most fundamental topics in Mathematics: the solution of equations (completeness, the Contraction Mapping Theorem, connectedness, the Intermediate Value Theorem) and the maximisation and minimisation of real functions (compactness). This module also develops some important ideas needed for later modules on Lebesgue Integation and Hillbert Space

Module learning outcomes

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

recognise metric spaces, and know the definitions of important properties of metric spaces;

utilise metric space arguments to obtain a variety of results;

understand the difference between various modes of convergence (e.g. pointwise, uniform);

understand the ideas of completeness and compactness, in preparation for Lebesgue Integration and Hilbert Space.

Assessment

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

Special assessment rules

None

Reassessment

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

Module feedback

Information currently unavailable

Indicative reading

W A Sutherland, Introduction to Metric and Topological Spaces, Clarendon Press, Oxford. (S 7.8 SUT).



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.