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MX4082: GALOIS THEORY (2021-2022)

Last modified: 20 Oct 2021 12:50


Course Overview

Galois theory is based around a simple but ingenious idea: that we can study field extensions by instead studying the structure of certain groups associated to them. This idea can be employed to solve some problems which confounded mathematicians for centuries, including the impossibility of trisecting an angle with ruler and compass alone, and the insolubility of the general quintic equation.



Course Details

Study Type Undergraduate Level 4
Session First Sub Session Credit Points 15 credits (7.5 ECTS credits)
Campus Aberdeen Sustained Study No
Co-ordinators
  • Dr Jean-Baptiste Gramain

Qualification Prerequisites

  • Programme Level 4

What courses & programmes must have been taken before this course?

What other courses must be taken with this course?

None.

What courses cannot be taken with this course?

None.

Are there a limited number of places available?

No

Course Description

  • Reminders from Group Theory and Field Theory.
  • Algebraic and Transcendental Field Extensions.
  • Constructible Numbers - The impossibility of trisecting an angle and squaring the circle.
  • Splitting Fields of Polynomials.
  • Normal Extensions, Separable Extensions.
  • The Galois Group of a field extension.
  • The Galois Correspondence.
  • Radical Extensions and Solvable Galois Groups.
  • The Galois Group of a Polynomial - The impossibility of solving general polynomial equations of degree five or greater by radicals.

In light of Covid-19 this information is indicative and may be subject to change.

Contact Teaching Time

Information on contact teaching time is available from the course guide.

Teaching Breakdown

  • 2 Lectures during University weeks 9 - 19
  • 1 Tutorial during University weeks 10 - 19

More Information about Week Numbers


In light of Covid-19 and the move to blended learning delivery the assessment information advertised for second half-session courses may be subject to change. All updates for second-half session courses will be actioned in advance of the second half-session teaching starting. Please check back regularly for updates.

Summative Assessments

First Attempt

3 assignments (33% each)

Alternative Resit Arrangements for students taking course in Academic Year 2020/21

Resubmission of failed elements (pass marks carried forward).

 

Formative Assessment

There are no assessments for this course.

Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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