ADVANCED ALGEBRA - 2017/8
Module code: MAT3032
FISHER D Dr (Maths)
Number of Credits
FHEQ Level 6
Module cap (Maximum number of students)
Overall student workload
Lecture Hours: 35
|Assessment type||Unit of assessment||Weighting|
|School-timetabled exam/test||IN-SEMESTER TEST (50 MINS)||20|
Prerequisites / Co-requisites
MAT2048 Groups and Rings
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.
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.
|1||Demonstrate an enhanced knowledge of groups and rings.||K|
|2||Understand the concept of a group action and identify some of its applications.||KC|
|3||Analyse the structure of finite groups by methods including the Sylow thoerems.||KC|
|4||Know the definition of an algebra and appreciate its relation to other structures.||KC|
|5||Construct simple proofs similar to those encountered in the module.||KCT|
C - Cognitive/analytical
K - Subject knowledge
T - Transferable skills
P - Professional/Practical skills
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.
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.
The learning and teaching methods include:
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.
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 Semester 2, worth 75% of the module mark.
· One or more in-semester tests, together worth 25% of the module mark.
Formative assessment and feedback
Students receive written comments on their marked coursework assignments. Maple TA may be used in assignments to provide immediate is used for part of the assignments and provides instant grading and feedback.s to solve problemsials, complex numbers,grading and feedback. Verbal feedback is provided in lectures and office hours.
Reading list for ADVANCED ALGEBRA : http://aspire.surrey.ac.uk/modules/mat3032
Programmes this module appears in
|Mathematics and Physics MPhys||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 with Statistics 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 MSc||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 2017/8 academic year.