MAS8708 : Groups, Graphs and Symmetry (Inactive)
- Inactive for Year: 2024/25
- Module Leader(s): Dr Andrew Duncan
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
Semesters
Your programme is made up of credits, the total differs on programme to programme.
Semester 2 Credit Value: | 10 |
ECTS Credits: | 5.0 |
European Credit Transfer System |
Aims
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
Direct and semi-direct products of groups. 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 Activities | Lecture | 2 | 1:00 | 2:00 | Revision Lectures |
Scheduled Learning And Teaching Activities | Lecture | 20 | 1:00 | 20:00 | Formal Lectures |
Scheduled Learning And Teaching Activities | Lecture | 5 | 1:00 | 5:00 | Problem Classes |
Guided Independent Study | Independent study | 58 | 1:00 | 58:00 | Preparation time for lectures, background reading, coursework review |
Guided Independent Study | Independent study | 15 | 1:00 | 15:00 | Completion of in course assessments |
Total | 100:00 |
Jointly Taught With
Code | Title |
---|---|
MAS3708 | Groups, Graphs and Symmetry |
Teaching Rationale And Relationship
The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking.
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
Exams
Description | Length | Semester | When Set | Percentage | Comment |
---|---|---|---|---|---|
Written Examination | 120 | 2 | A | 80 | N/A |
Exam Pairings
Module Code | Module Title | Semester | Comment |
---|---|---|---|
Groups, Graphs and Symmetry | 2 | N/A |
Other Assessment
Description | Semester | When Set | Percentage | Comment |
---|---|---|---|---|
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Prob solv exercises | 2 | M | 5 | Problem-solving exercises assessment |
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.
Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.
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.
Reading Lists
Timetable
- Timetable Website: www.ncl.ac.uk/timetable/
- MAS8708's Timetable