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Galois Theory - MAT00008H

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  • Department: Mathematics
  • Module co-ordinator: Dr. Brent Everitt
  • Credit value: 10 credits
  • Credit level: H
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Spring Term 2017-18

Module aims

The aim of the module is:

To show how unified mathematics is by using ideas from different modules.

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

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

Module learning outcomes

At the end of the module you should be able to:

construct fields by quotienting polynomial rings by maximal ideals;

know Eisenstein's irreducibility criterion;

know that any irreducible polynomial has a suitable extension field;

know what the degree of a field extension is and that it is multiplicative;

know about the form of the elements in a simple extension;

know what a splitting field of a polynomial is;

know about the allowable operations with straightedge and compasses;

know that the constructible real numbers form a field which is closed under extraction of square roots;

understand that each constructible real number lies in a field of degree a power of two over Q and the consequences of that fact;

understand some of the results about automorphisms of an extension field and the fixed field of a group of automorphisms;

know the statement of the Galois Correspondence Theorem and be able to apply it to straightforward examples;

understand some of the consequences of the Galois Correspondence.

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

Information currently unavailable

Indicative reading

E Artin, Galois Theory, University of Notre Dame Press (S 2.82 ART).

H M Edwards, Galois Theory, Springer (S 2.82 EDW).

J Rotman, Galois Theory, Springer (S 2.82 ROT).

I Stewart, Galois Theory, Chapman and Hall (S 2.82 STE).



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.