MT5864 Advanced Group Theory
Academic year
2023 to 2024 Semester 1
Curricular information may be subject to change
Further information on which modules are specific to your programme.
Key module information
SCOTCAT credits
15
SCQF level
SCQF level 11
Planned timetable
10am, Monday (odd weeks), Wednesday, Friday
Module description
Groups are important mathematical objects that arise in many contexts since they encode symmetry. The aim of this module is to build on the foundations established in MT4003 and to present more advanced techniques to handle and classify groups. It will focus on the use of group actions and upon the decomposition of groups into series via the quotient group construction.
Relationship to other modules
Pre-requisites
BEFORE TAKING THIS MODULE YOU MUST PASS MT4003
Anti-requisites
YOU CANNOT TAKE THIS MODULE IF YOU TAKE MT5824
Assessment pattern
2-hour Written Examination = 100%
Re-assessment
Oral examination = 100%
Learning and teaching methods and delivery
Weekly contact
2.5 lectures (x 10 weeks), 1 tutorial (x 10 weeks)
Scheduled learning hours
35
Guided independent study hours
115
Intended learning outcomes
- Demonstrate an understanding of core group theory topics including actions, subgroups, quotient groups, and extensions
- Be familiar with, and able to work with, more complicated groups than just those appearing at the 4000 level
- Be able to produce complete theoretical arguments (proofs) which establish general properties of groups
- Be able to state and to use some advanced theorems in group theory
- Apply the above competencies to discern properties of given groups and to demonstrate an understanding of advanced methods by being able to apply them to discern key features of given groups
- Obtain and be able to demonstrate a capacity in problem solving in group theory