What is the course about?
Symmetry is a fundamental aspect of pattern – the difference between order and chaos. For millennia it appeared to
be straightforward but in the nineteenth century a new theoretical perspective called “group theory” emerged,
bringing ancient procedures in visual art and design into the very heart of mathematics, science and many other
This course is an introduction to group theory, which studies the abstract structure of symmetrical objects. We
focus on its conceptual framework, covering the key ideas and discoveries that give a flavour of the subject. This is
maths, but of a very different kind from what most people experience at school: there will be no calculations and no
prior knowledge or experience is assumed. Optional additional material will be provided for those who want to go
further, turning this course into a gateway into higher mathematics.
Our study of groups in the abstract is motivated and enriched by a consideration of symmetry in the arts and
sciences, where group theory can provide deep insights, from graphic and textile design to molecular chemistry.
What will we cover?
Geometric notions of symmetry
• Key concepts from group theory
• Examples of symmetry in art and design
• Some of the roles symmetry has played in other applied areas such as physics, chemistry and music.
What will I achieve?
By the end of this course you should be able to...
• Outline the history of the study of symmetry, particularly as it developed in the nineteenth and twentieth centuries.
• Describe geometric reflections, rotations and translations.
• Identify different symmetries in visual design, music and arithmetic.
• Define a group of symmetries and describe a range of examples of groups.
• Draw diagrams of symmetry groups and understand their geometric significance.
• Characterise all the possible two-dimensional frieze and wallpaper patterns.
• Show how symmetry groups can be combined to create new ones.
• Outline the classification of the finite simple groups, one of the major achievements of twentieth century pure
What level is the course and do I need any particular skills?
This is an introductory course with no specific prerequisites.
How will I be taught, and will there be any work outside the class?
The sessions will be a mixture of lecture/demonstration, discussion and individual or small-group activities. Material
for use outside class will be provided but this is entirely optional – it is designed to expand the horizons of the main
course and will not be used in later sessions.
Are there any other costs? Is there anything I need to bring?
There are no additional costs or required materials. You only need bring whatever you prefer to use to take notes.
When I've finished, what course can I do next?
You might be interested in HP091 - Spatial languages: exploring higher dimensions, which starts in January 2020 at the same time on a Thursday.
General information and advice on courses at City Lit is available from the Student Centre and Library on Monday to Friday from 12:00 – 19:00.
See the course guide for term dates and further details