Global Opportunities

MAS3708 : Graphs and symmetry

Semester 2 Credit Value: 10
ECTS Credits: 5.0


To equip students with a range of basic tools and methods for analysing geometric and algebraic structures. To enable the students to apply these techniques to naturally occurring phenomena involving symmetries or transformations. To reinforce the students’ ability to read, understand and develop mathematical proofs.

Module summary

Groups arise naturally as concise and tractable characterisations of geometries: for example, as symmetries of regular Euclidean figures, of lattices and of graphs and their higher dimensional analogues. The interaction between group theory and geometry will be the main focus of this course. Various examples of groups given by presentations and groups acting on graphs will be studied, and the interplay between the algebraic and geometric sides of the theory exploited to understand properties of groups.

Outline Of Syllabus

Graph theory. Symmetries of graphs. Group actions on graphs and Cayley graphs. Free groups and Stallings foldings. Presentations of groups and algorithmic problems.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures – Present in Person
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes – Synchronous On-Line
Guided Independent StudyIndependent study151:0015:00Completion of in course assessments
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Jointly Taught With
Code Title
MAS8708Graphs and symmetry
Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1202A80N/A
Exam Pairings
Module Code Module Title Semester Comment
MAS8708Graphs and symmetry2N/A
Other Assessment
Description Semester When Set Percentage Comment
Written exercise2M10Each coursework assignment is expected to consist of two assignments of equal weight
Written exercise2M10Each coursework assignment is expected to consist of two assignments of equal weight
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

In the event of on-campus examinations not being possible, an on-line alternative assessment will be used for written examination 1.

Reading Lists