ADVANCED ALGEBRA - 2024/5

Module code: MAT3032

Module Overview

This module extends the abstract algebra introduced in MAT2048 Groups & Rings. A deeper insight into groups and rings is developed, and further algebraic structures are introduced.

This module complements the module material in MATM035 Representation Theory and MATM011 Lie Algebras

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

Overall student workload

Independent Learning Hours: 64

Lecture Hours: 33

Tutorial Hours: 5

Guided Learning: 15

Captured Content: 33

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

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

Alternative Assessment

N/A

Assessment Strategy

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


  • Understanding of subject knowledge, and recall of key definitions, propositions and theorems in the theory of abstract algebra.

  • The ability to construct simple proofs similar to those in the module.

  • The ability to identify and use appropriate methods to solve problems in abstract algebra.



 Thus, the summative assessment for this module consists of:


  • One in-semester test (50 minutes), worth 20% of the module mark, corresponding to Learning Outcomes 1, 2 and 5.

  • A synoptic examination (2 hours), worth 80% of the module mark, corresponding to all Learning Outcomes 1 to 5.



Formative assessment

There are two formative unassessed courseworks over an eleven week period, designed to consolidate student learning. 

Feedback

Students will receive individual written feedback on both the formative unassessed courseworks and the in-semester test. The feedback is timed such that feedback from the first coursework will assist students with preparation for the in-semester test. The feedback from both courseworks and the in-semester test will assist students with preparation for the synoptic examination. Students also receive verbal feedback in tutorials and office hours.

Module aims

  • Extend students' knowledge of abstract algebra and the interconnectedness of different topics in algebra.
  • Provide students with knowledge of classical theorems in algebraic structure theory.
  • Develop students' understanding of rigorous proofs in the context of abstract algebra.
  • Provide students with a solid basis for further algebraic study.

Learning outcomes

Attributes Developed
001 Students will demonstrate an advanced knowledge of groups. K
002 Students will understand the concept of a group action and be able to construct the group action in various examples. KC
003 Students will analyse the structure of finite groups by methods including using the Sylow theorems. KC
004 Students will demonstrate an advanced knowledge of further algebraic structures, such as rings, fields and algebras. KC
005 Students will be able to 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:


  • Introduce students to advanced theory and applications of abstract algebra.

  • Provide students with experience of methods used to interpret, understand and solve problems in the theory of abstract algebra.



The learning and teaching methods include:


  • Three one-hour lectures for eleven weeks, with module notes provided to complement the lectures. These lectures provide a structured learning environment and opportunities for students to ask questions and to practice methods taught.

  • Five biweekly one-hour tutorials per semester. These tutorials provide an opportunity for students to gain feedback and assistance with the exercises which complement the module notes.

  • Two unassessed courseworks to provide students with further opportunity to consolidate learning. Students receive feedback on these courseworks as guidance on their progress and understanding.

  • Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students an opportunity to review parts of lectures which they may not fully have understood and should not be seen as an alternative to attending 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: MAT3032

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourceness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills and capabilities in the following areas:

Digital Capabilities: The SurreyLearn page for MAT3032 features a dynamic discussion forum where students can pose questions and engage with others using e.g. LaTeX and MathML tools. This enhances their digital competencies while facilitating collaborative learning and information sharing.

Employability: The module MAT3032 equips students with skills which significantly enhance their employability. The mathematical proficiency gained will hone their critical thinking and problem-solving abilities. Students will learn to evaluate complex algebraic problems, break them into manageable components, and apply abstract algebraic theory and logical reasoning to arrive at solutions. These are highly sought after skills in any profession.

Global and Cultural Capabilities: Students enrolled in MAT3032 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in tutorials and lectures, which naturally facilitates the sharing of different cultures.

Resourcefulness and Resilience: MAT3032 is a module which demands a rigorous approach to abstract algebra, to which students will learn to adapt. They will gain skills in analysing abstract algebraic problems using lateral thinking. Students will complete assessments which challenge them and build resilience.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Optional 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 2024/5 academic year.