For delivery to students completing Stage 1 before September 2016:
Pre-requisite: MA552 (Analysis)
For delivery to students completing Stage 1 after September 2016:
Pre-requisite: MAST5013 (Real Analysis 2)
OverviewThis module is an introduction to point-set topology, a topic that is relevant to many other areas of mathematics. In it, we will be looking at the concept of topological spaces and related constructions. In an Euclidean space, an "open set" is defined as a (possibly infinite) union of open "epsilon-balls". A topological space generalises the notion of "open set" axiomatically, leading to some interesting and sometimes surprising geometric consequences. For example, we will encounter spaces where every sequence of points converges to every point in the space, see why for topologists a doughnut is the same as a coffee cup, and have a look at famous objects such as the Moebius strip or the Klein bottle.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
The module will not follow a specific text. However, the following texts cover the material.
J.G. Hocking and G. Young: Topology, Dover Publications, 1988
J.R. Munkres: Topology, a first course, Prentice-Hall, 1975
C. Adams and A. Franzosa: Introduction to Topology, pure and applied, Pearson Prentice-Hall, 2008
The intended subject specific learning outcomes. On successfully completing the level 6 module students will be able to:
1 demonstrate systematic understanding of key aspects of topology;
2 demonstrate the capability to deploy established approaches accurately to analyse and solve problems using a reasonable level of skill in calculation and manipulation of the material in the following areas: topological spaces, continuity, convergence, homotopy theory;
3 apply key aspects of topology in well-defined contexts, showing judgement in the selection and application of tools and techniques.
The intended generic learning outcomes. On successfully completing the level 6 module students will be able to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make competent use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation;
9 demonstrate the acquisition of the study skills needed for continuing professional development.