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Unit information: Galois Theory in 2015/16

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Unit name Galois Theory
Unit code MATHM2700
Credit points 20
Level of study M/7
Teaching block(s) Teaching Block 1 (weeks 1 - 12)
Unit director Dr. Saha
Open unit status Not open

MATH33300 Group Theory, MATH 21800 Algebra 2.



School/department School of Mathematics
Faculty 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:

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.

Reading and References

Recommended Text:

  • D. J. H. Garling, A Course in Galois Theory, Cambridge University Press, 1986.

See also:

  • Ian Stewart, Galois Theory, 3rd ed. Chapman & Hall, 2003;
  • Emil Artin, Galois Theory, New ed. Dover, 1998.