ADVANCED ALGEBRA - 2023/4

Module Overview

This module extends the abstract algebra introduced in Year 2, providing a deeper insight into the structure of groups and introducing some additional algebraic structures.

Module provider

Mathematics & Physics

Module Leader

ROBERTS James (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

Module cap (Maximum number of students): N/A

Module Availability

Semester 1

Prerequisites / Co-requisites

MAT2048 Groups and Rings  

Module content

Indicative content includes:

• Further group theory.  Simple groups.


• Finite abelian groups.


• Group actions, conjugacy. 


• Burnside’s formula and application to colouring problems.


• The Sylow theorems and their applications 


• Further ring theory.   Division rings.  The quaternions.


• Idempotents and ring decompositions.


• Group algebras.  

Assessment pattern

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate their ability to

·         construct and interpret mathematical arguments in the context of this module;

·         display subject knowledge by recalling key definitions and results;

·         apply the techniques learnt to both routine and unfamiliar problems.

 

Thus, the summative assessment for this module consists of:

·         One two-hour examination at the end of the semester, worth 80% of the module mark.

·         One in-semester test, worth 20% of the module mark.

 

Formative assessment and feedback

 

Students receive written comments on their marked coursework assignments.  Verbal feedback is provided in lectures and office hours.

Module aims

• extend students' knowledge of abstract algebra and their appreciation of the inter-connectedness of the different areas of the subject.
• provide familiarity with some classical theorems in algebraic structure theory.
• establish a basis for further algebraic study, e.g. in Representation Theory or Lie Algebras.

Learning outcomes

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• An enhanced awareness of the theory and applications of abstract algebra.


• Experience of the methods used to interpret, understand and solve problems in the topics covered.

• Three 50-minute lectures per week for eleven weeks, some being used as tutorials, problem classes and in-semester tests.


• Online notes supplemented by additional examples in lectures.


• Two unassessed coursework assignments, marked and returned.


• Personal assistance given to individuals and small groups in office hours.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: MAT3032

Programmes this module appears in

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.