# GENERAL TOPOLOGY - 2022/3

Module code: MATM042

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 provider

Mathematics

PRINSLOO Andrea (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 7

JACs code: G100

Module cap (Maximum number of students): N/A

Independent Learning Hours: 101

Seminar Hours: 11

Guided Learning: 5

Captured Content: 33

Module Availability

Semester 1

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 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.

Assessment pattern

Assessment type Unit of assessment Weighting
Online Scheduled Summative Class Test ONLINE TEST 20
Examination Online ONLINE EXAM 80

Alternative Assessment

N/A

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.

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

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.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.