Topology and Groups (MATH0074)

Key information

Faculty: Faculty of Mathematical and Physical Sciences
Teaching department: Mathematics
Credit value: 15

Restrictions: This module is normally taken by fourth year students on single or combined honours mathematics degrees, who have taken MATH0051 Analysis 4, MATH0053 Algebra 4 and ideally also MATH0052 Geometry and Groups.
Timetable

Alternative credit options

There are no alternative credit options available for this module.

Description

The course starts with the basics of general topology. The fundamental group is then defined and studied, with an emphasis on examples: graphs and their fundamental groups, free groups, are especially motivating. Fundamental groups of general complexes are discussed, along with group presentations. Some applications will be given, such as winding number and the Brouwer Fixed point theorem. Students should finish the course able to compute: bases for the subgroup of a free group corresponding to an explicit covering space of a graph; presentations for fundamental groups of cell complexes; Cayley graphs of finite groups. The course could be taken as a complement to the course Algebraic Topology.

Module deliveries for 2024/25 academic year

Intended teaching term: Term 1 听听听 Undergraduate (FHEQ Level 7)

Teaching and assessment

Mode of study: In person
Methods of assessment: 90% Exam

10% Coursework
Mark scheme: Numeric Marks

Other information

Number of students on module in previous year: 7
Module leader: Dr Lars Louder
Who to contact for more information: math.ugteaching@ucl.ac.uk

Last updated

This module description was last updated on 8th April 2024.

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Important information

The catalogue has been updated with key information about the modules that will run during the 2024/25 academic session. Current and prospective students can browse through the catalogue to consider possible module choices for the coming year.

Please note,听information in the catalogue is听subject to change as teaching and assessment arrangements for 2024/25 may need to be adjusted in line with the University's Feedback and Assessment principles and operating model.

Centrally managed exam durations will be provided on students' individual exam timetables. Arrangements for locally managed exams and in-class activity will be confirmed by the teaching department for the module.

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