Module overview
Aims and Objectives
Learning Outcomes
Learning Outcomes
Having successfully completed this module you will be able to:
- Understand presentation of groups
- Understand free groups
Syllabus
Free groups
-Definition of terms of words
-Universal property
-Rank and bases
-Group actions and the Cayley Theorem
-Nielsen-Schreier Theorem
-Stallings graphs and algorithmic applications
Presentations of groups
-Quotients groups and the first isomorphism theorem
-Von Dyck's theorem
-Examples of presentations
-Classification of finitely generated abelian groups
Learning and Teaching
Teaching and learning methods
Lectures, problem classes
| Type | Hours |
|---|---|
| Teaching | 48 |
| Independent Study | 102 |
| Total study time | 150 |
Assessment
Summative
This is how we’ll formally assess what you have learned in this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Referral
This is how we’ll assess you if you don’t meet the criteria to pass this module.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |
Repeat
An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.
| Method | Percentage contribution |
|---|---|
| Exam | 100% |