Galois Theory - MAT00008H

« Back to module search

  • Department: Mathematics
  • Module co-ordinator: Dr. Emilie Dufresne
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2019-20

Related modules

Co-requisite modules

  • None

Prohibited combinations

  • None

Module will run

Occurrence Teaching cycle
A Spring Term 2019-20

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.

Module content

[Pre-requisite modules: students must have taken Pure Mathematics or Pure Mathematics Option 1.]

Assessment

Task Length % of module mark
University - closed examination
Galois Theory
2 hours 100

Special assessment rules

None

Reassessment

Task Length % of module mark
University - closed examination
Galois Theory
2 hours 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 is constantly exploring 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 by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.