## MA4FTA-Further Topics in Algebra

Module Provider: Mathematics and Statistics
Number of credits: 10 [5 ECTS credits]
Level:7
Terms in which taught: Autumn term module
Pre-requisites: MA2AL2 Algebra II or MA2ALA Algebra
Non-modular pre-requisites:
Co-requisites:
Modules excluded: MA3FTA Further Topics in Algebra
Current from: 2018/9

Module Convenor: Dr Basil Corbas

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.

This module will be assessed to a greater depth than the excluded module MA3FTA.

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.

Contact hours:
 Autumn Spring Summer Lectures 20 Guided independent study 80 Total hours by term 100.00 Total hours for module 100.00

Summative Assessment Methods:
 Method Percentage Written exam 80 Set exercise 20

Summative assessment- Examinations:

2 hour exam

Summative assessment- Coursework and in-class tests:

A number of written assignments, worth 20% in total.

Formative assessment methods:

Eight homeworks with feedback provided

Penalties for late submission:
The Module Convener 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[1] (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.

• The University policy statement on penalties for late submission can be found at: http://www.reading.ac.uk/web/FILES/qualitysupport/penaltiesforlatesubmission.pdf
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 50% overall.

Reassessment arrangements:

(During the August University Resit Period): One examination paper of 2 hours duration in August/September.