Pre-requisite: MAST4001 (Algebraic Methods), MAST4004 (Linear Algebra) and MAST5003 (Groups and Symmetries)
OverviewCan we square a circle? Can we trisect an angle? These two questions were studied by the Ancient Greeks and were only solved in the 19th century using algebraic structures such as rings, fields and polynomials. In this module, we introduce these ideas and concepts and show how they generalise well-known objects such as integers, rational numbers, prime numbers, etc. The theory is then applied to solve problems in Geometry and Number Theory. This part of algebra has many applications in electronic communication, in particular in coding theory and cryptography.
This module appears in:
Method of assessment
80% Examination, 20% Coursework
R. Allenby, Rings, fields and groups: an introduction to abstract algebra, Oxford: Butterworth/Heinemann, Second edition, 1991 (reprinted 2003).
J. Howie, Fields and Galois Theory, Springer, 2006.
A. Knapp, Basic Algebra, Birkhäuser, 2006
The intended subject specific learning outcomes. On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within abstract algebra and its applications;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: rings, fields and polynomials;
3 apply the concepts and principles in basic abstract algebra in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.
The intended generic learning outcomes. On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.