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Module Leader(s): Dr Andrew Duncan
Owning School: Mathematics, Statistics and Physics
Teaching Location: Newcastle City Campus
Semesters
Semester 2 Credit Value:
10
ECTS Credits:
5.0
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
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 Activities
Lecture
20
1:00
20:00
Formal Lectures – Present in Person
Scheduled Learning And Teaching Activities
Lecture
2
1:00
2:00
Revision Lectures – Present in Person
Scheduled Learning And Teaching Activities
Lecture
5
1:00
5:00
Problem Classes – Synchronous On-Line
Guided Independent Study
Independent study
15
1:00
15:00
Completion of in course assessments
Guided Independent Study
Independent study
58
1:00
58:00
Preparation time for lectures, background reading, coursework review
Total
100:00
Jointly Taught With
Code
Title
MAS8708
Graphs 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
Exams
Description
Length
Semester
When Set
Percentage
Comment
Written Examination
120
2
A
80
N/A
Exam Pairings
Module Code
Module Title
Semester
Comment
MAS8708
Graphs and symmetry
2
N/A
Other Assessment
Description
Semester
When Set
Percentage
Comment
Written exercise
2
M
10
Each coursework assignment is expected to consist of two assignments of equal weight
Written exercise
2
M
10
Each 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.
