production
Skip to Content

Log In

  1. University Home
  2. Catalogue of Courses
  3. Undergraduate
  4. 2021-2022
  5. Mathematical Sciences
  6. MX4082: Galois Theory

MX4082: GALOIS THEORY (2021-2022)

Last modified: 31 May 2022 13:05


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
Term First Term 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.

Contact Teaching Time

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

Teaching Breakdown

More Information about Week Numbers


Details, including assessments, may be subject to change until 30 August 2024 for 1st term courses and 20 December 2024 for 2nd term courses.

Summative Assessments

Alternative Assessment

3x Assignments (33% each)

Alternative Resit Assessment

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.
 

Compatibility Mode

We have detected that you are have compatibility mode enabled or are using an old version of Internet Explorer. You either need to switch off compatibility mode for this site or upgrade your browser.