MA3FTA-Further Topics in Algebra
Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:6
Terms in which taught: Spring term module
Pre-requisites: MA2ALA Algebra or MA2ALANU Algebra
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA4FTA Further Topics in Algebra
Current from: 2022/3
Module Convenor: Dr Basil Corbas
Email: b.corbas@reading.ac.uk
Type of module:
Summary module description:
This module builds on the introduction to Group Theory included in the second year Algebra module. (A brief summary of that will be provided at the beginning of the module.)
A number of interrelated concepts from the immense body of Group theory has been selected and put together in an elementary and coherent way. The selection of the topics was guided by three criteria. To be accessible and comprehensible to undergraduate students, to be interesting and surprising in their own right and to be relevant to the most recent applications of Algebra.
Aims:
- To provide a basic knowledge of finite groups that is necessary in order to understand an ever increasing topic in mathematics and its applications.
- To show the strength and the elegance of rational mathematical thinking that starting from a few modest assumptions can reach staggering and surprising conclusions.
Assessable learning outcomes:
To understand and apply correctly the concepts described in the outline content. In particular to find Sylow subgroups and their numbers in permutation groups. Or classify groups of certain orders.
Additional outcomes:
Outline content:
- Introduction to the theory of G-sets : Orbits, stabilizers, the class formula.
- Applications to finite groups: Normalizers, centralizers, p-groups and the Sylow theorems.
- The group of automorphisms and of inner automorphisms of a group. Semi-direct products and the holomorph of a group.
- Finite Abelian groups.
Brief description of teaching and learning methods:
Lectures with numerous examples and a number of extended homeworks with detailed feedback.
| Autumn | Spring | Summer | |
| Lectures | 20 | ||
| Tutorials | 5 | ||
| Guided independent study: | 75 | ||
| Total hours by term | 0 | 100 | 0 |
| Total hours for module | 100 |
| Method | Percentage |
| Written exam | 100 |
Summative assessment- Examinations:
2 hour exam.
The examination for this module will require a narrowly defined time window and is likely to be held in a dedicated exam venue.
Summative assessment- Coursework and in-class tests:
Formative assessment methods:
Eight homeworks with feedback provided
Penalties for late submission:
The Support Centres will apply the following penalties for work submitted late:
- where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
- where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.
Assessment requirements for a pass:
A mark of 40% overall.
Reassessment arrangements:
(During the August University Resit Period): One examination paper of 2 hours duration in August/September.
Additional Costs (specified where applicable):
1) Required text books:
2) Specialist equipment or materials:
3) Specialist clothing, footwear or headgear:
4) Printing and binding:
5) Computers and devices with a particular specification:
6) Travel, accommodation and subsistence:
Last updated: 22 September 2022
THE INFORMATION CONTAINED IN THIS MODULE DESCRIPTION DOES NOT FORM ANY PART OF A STUDENT'S CONTRACT.