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  6. MX4082: Galois Theory

MX4082: GALOIS THEORY (2020-2021)

Last modified: 05 Aug 2021 13:04


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 Alexey Sevastyanov

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

  • Field Theory, Field Extensions.
  • Constructible Numbers.
  • The Galois Group of a Field Extension.
  • Cyclotomic Fields.
  • Splitting Fields of Polynomials.
  • Normal Extensions, Separable Extensions.
  • Simple Fields Extensions.
  • Counting Field Homomorphisms.
  • Galois Extensions.
  • The Galois Correspondence.
  • Cyclic Galois Groups.
  • Radical Extensions and Solvable Galois Groups.
  • The Galois Group of a Polynomial. Applications.

Syllabus

  • Constructible numbers.
  • The impossibility of trisecting an angle and squaring the circle.
  • Normal and separable field extensions. Galois extensions. Galois groups.
  • The Galois correspondence.
  • The Galois group of a polynomial.
  • The use of Galois theory in the solution of polynomial equations.
  • 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

4 assignments (25% 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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