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Galois Theory - MAT00074H

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  • Department: Mathematics
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2022-23

Module summary

This is for postgraduate students only.

Related modules

Pre-requisite modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Additional information

MSc students should have taken a suitable first course in Pure Mathematics

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

Module aims

  • To introduce one of the high points of 19th century algebra.

  • To exhibit the unity of mathematics by using ideas from different modules.

  • To show how very abstract ideas can be used to derive concrete results.

Module learning outcomes

  • Construct fields as quotients of polynomial rings by maximal ideals.

  • Irreducibility criteria.

  • Any irreducible polynomial has a suitable extension field.

  • The degree of a field extension, and its multiplicativity.

  • The form of the elements in a simple extension.

  • Splitting fields.

  • The allowable operations with straightedge and compasses.

  • Constructible complex numbers form a field which is closed under extraction of square roots.

  • Each constructible number lies in a field of degree a power of two over Q, and the consequences of that fact.

  • Some of the results about automorphisms of an extension field, and the fixed field of a group of automorphisms.

  • The Galois Correspondence Theorem, and the ability to apply it to straightforward examples.

  • Some of the consequences of the Galois Correspondence.

Indicative assessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Special assessment rules

Pass/fail

Indicative reassessment

Task % of module mark
Closed/in-person Exam (Centrally scheduled) 100

Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Indicative reading

I Stewart, Galois Theory, Chapman and Hall


The information on this page is indicative of the module that is currently on offer. The University constantly explores ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary. In some instances it may be appropriate for the University to notify and consult with affected students about module changes in accordance with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.