| Unit name | Galois Theory |
|---|---|
| Unit code | MATHM2700 |
| Credit points | 20 |
| Level of study | M/7 |
| Teaching block(s) |
Teaching Block 2 (weeks 13 - 24) |
| Unit director | Dr. McInroy |
| Open unit status | Not open |
| Pre-requisites | |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Lecturers
Justin McInroy
Unit Aims
To present an introduction to Galois theory in the context of arbitrary field extensions and apply it to a number of historically important mathematical problems.
Unit Description
Consider a field, such as the rational numbers, and consider a larger field containing it, which can also be thought of as a vector space over the original field. One question that can be asked is: what symmetries (or automorphisms) of the bigger field exist that act as the identity on the smaller field? The Galois Correspondence connects the answer to this question with the properties of a group of permutations of the roots of a polynomial. This relationship can be used in different directions to translate a problem from one part of algebra to another part where it may be easier to solve.
Relation to Other Units
This is one of three Level 7 units which develop group theory in various directions. The others are Representation Theory and Algebraic Topology.
Learning Objectives
To gain an understanding and appreciation of Galois theory and its most important applications. To be able to use the theory in specific examples.
Transferable Skills
Using an abstract framework to better understand how to attack a concrete problem.
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.
If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. MATHM2700).
How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours
of study to complete. Your total learning time is made up of contact time, directed learning tasks,
independent learning and assessment activity.
See the Faculty workload statement relating to this unit for more information.
Assessment
The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit.
The Board considers each student's outcomes across all the units which contribute to each year's programme of study. If you have self-certificated your absence from an
assessment, you will normally be required to complete it the next time it runs (this is usually in the next assessment period).
The Board of Examiners will take into account any extenuating circumstances and operates
within the Regulations and Code of Practice for Taught Programmes.
