# GENERAL TOPOLOGY - 2017/8

Module code: MATM042

Module provider

Mathematics

GRANT JD Dr (Maths)

Number of Credits

15

ECTS Credits

7.5

Framework

FHEQ Level 7

JACs code

G100

Module cap (Maximum number of students)

N/A

Module Availability

Semester 2

Independent Study Hours: 117

Lecture Hours: 33

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION - 2 HOURS 80
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 20

Alternative Assessment

N/A

Prerequisites / Co-requisites

The course will be self-contained, and there are no prerequisites. Students may find it useful to have attended the Year 3 module MAT 3009 Manifolds and Topology.

Module overview

This module will give a self-contained, rigorous, formal treatment of basic topics in point set topology. Topology is an important topic in modern mathematics, and the module will give the thorough grounding in the field. The course will expose students to abstract, general mathematical arguments and techniques. The style and content of the course suggest that it will fit well with their general Programme of mathematical education.

Module aims

Give a self-contained, rigorous, formal treatment of basic topics in point set topology.

Learning outcomes

Attributes Developed
1 State the basic definitions and state/prove basic results in those topics in topology listed in the Module Content. K
2 Solve examples and problems in these topics. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Module content

Indicative content includes:

Open sets, closed sets, neighbourhoods, bases;
Continuity, initial and final topologies;
Quotients and products;
Filters, ultrafilters, limits;
Hausdorff spaces and separation conditions, compactness, local compactness, connectedness;
Uniform spaces;
Metric spaces.

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

A detailed introduction to the fundamental topics in point-set topology.

The learning and teaching methods include:

Lectures: 3 hours per week x 11 weeks, augmented with tutorials when appropriate.
Exercise sheets will be handed out weekly. Working through the exercises will help the students develop and expand their understanding of the subject matter. It is expected that each exercise sheet should take approximately 4 hours of the students’ individual study time to complete.
Two unassessed courseworks. These will consist of exercises that will be handed in and marked by the lecturer. Feedback will be given to the students on their work. It is expected that the assignments will take approximately 6 hours of individual study time to complete.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

·         Subject knowledge through the recall of key definitions, theorems and their proofs.

·         Analytical ability through the solution of unseen problems in the test and exam.

Thus, the summative assessment for this module consists of:

·         One two hour examination (best three of four questions contribute to exam mark) at the end of Semester 1; worth 80% module mark.

·         One In-Semester test; worth 20% module mark.

Formative assessment and feedback

The students will be given example sheets each week, and it will be suggested that they work through the examples as part of their independent study. This will aid the students with the development of mathematical technique and knowledge. The students will receive feedback on their work in tutorials. There will be two pieces of unassessed coursework, one early in Semester to help the students prepare for the in-semester test, the other close to the end of Semester to help them prepare for the final examination. The students will receive detailed feedback on this work in the tutorials.