# Unit information: Galois Theory in 2015/16

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Unit name Galois Theory MATHM2700 20 M/7 Teaching Block 1 (weeks 1 - 12) Dr. Saha Not open MATH33300 Group Theory, MATH 21800 Algebra 2. None School of Mathematics Faculty of Science

## Description including Unit Aims

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.

General Description of the Unit

After reviewing some basic properties of polynomial rings, we will introduce the basic objects of study: field extensions and the automorphism groups associated to them. We will discuss certain desirable properties for field extensions and then demonstrate the fundamental Galois correspondence. This will be used to analyse some specific polynomials and in particular to exhibit a quintic which is not soluble by radicals. We will end with applications to finite fields and to the fundamental theorem of algebra.

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.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

## Intended Learning Outcomes

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.

## Teaching Information

Lectures and exercises.

## Assessment Information

100% Examination.

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.