# GROUPS & RINGS - 2023/4

Module code: MAT2048

## Module Overview

This module provides an introduction to abstract algebra through elementary group and ring theory.  Thus it forms the starting point for all the algebraic modules that follow: MAT2005 Algebra and Codes, MAT3011 Galois Theory, MAT3032 Advanced Algebra and MATM011 Lie Algebras.

### Module provider

Mathematics & Physics

### Module Leader

PRINSLOO Andrea (Maths & Phys)

## Overall student workload

Independent Learning Hours: 73

Lecture Hours: 33

Tutorial Hours: 5

Guided Learning: 6

Captured Content: 33

Semester 1

MAT1031 Algebra

## Module content

Indicative content includes:

• Revision of the group axioms, permutations and the integers modulo n.

• Symmetries and the dihedral groups.

• Cyclic groups, direct products.

• Group homomorphisms and isomorphisms.

• Cosets, normal subgroups, quotient groups. Lagrange's theorem.

• Introduction to rings and fields.  Subrings, ideals and quotient rings.

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-semester test (50 minutes) 20
Examination Exam (2 hours) 80

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, worth 80% of the module mark.

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

Formative assessment and feedback

• feedback on two pieces of unassessed coursework

• verbal feedback at tutorial sessions

## Module aims

• introduce the axiomatic approach to group theory and ring theory
• develop confidence in working with algebraic structures
• provide a firm foundation for subsequent study of abstract algebra

## Learning outcomes

 Attributes Developed 001 Know the definition of a group and a ring and recognise standard examples KC 002 Carry out calculations involving groups and rings, selecting the appropriate method. KC 003 Have insight into the structure of groups, their subgroups and mappings between groups. KC 004 Have insight into the structure of rings, their subrings and mappings between rings. KC 005 Understand how to construct quotient groups or quotient rings. KC 006 Construct simple proofs similar to those encountered in the module. KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• An introduction to algebraic structure theory

• Experience of the methods used to interpret, understand and solve problems in group and ring theory

The learning and teaching methods include:

• Three 50-minute lectures per week for eleven weeks;

• Five biweekly 50-minute tutorials per semester;

• Module notes supplemented by additional exercises in tutorials and additional examples in lectures.

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: MAT2048

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module

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.