Galois Theory - MAT00008H
- Department: Mathematics
- Credit value: 10 credits
- Credit level: H
- Academic year of delivery: 2022-23
Related modules
Additional information
Pre-requisite modules: students must have taken Pure Mathematics or Pure Mathematics Option 1.
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Autumn Term 2022-23 |
Module aims
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To introduce one of the high points of 19th century algebra.
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To exhibit the unity of mathematics by using ideas from different modules.
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To show how very abstract ideas can be used to derive concrete results.
Module learning outcomes
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Construct fields as quotients of polynomial rings by maximal ideals.
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Irreducibility criteria.
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Any irreducible polynomial has a suitable extension field.
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The degree of a field extension, and its multiplicativity.
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The form of the elements in a simple extension.
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Splitting fields.
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The allowable operations with straightedge and compasses.
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Constructible complex numbers form a field which is closed under extraction of square roots.
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Each constructible number lies in a field of degree a power of two over Q, and the consequences of that fact.
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Some of the results about automorphisms of an extension field, and the fixed field of a group of automorphisms.
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The Galois Correspondence Theorem, and the ability to apply it to straightforward examples.
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Some of the consequences of the Galois Correspondence.
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
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