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  6. MX4082: GALOIS THEORY

MX4082: GALOIS THEORY (2016-2017)

Last modified: 28 Jun 2018 10:27


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 None. Sustained Study No
Co-ordinators
  • Dr Jean-Baptiste Gramain

Qualification Prerequisites

None.

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

  • MX3531 Rings & Fields (Passed)
  • Any Undergraduate Programme (Studied)
  • MX3020 Group Theory (Passed)

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.

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

1st Attempt: 1 two-hour written examination (80%); in-course assessment (20%). Resit: If required and permitted by Regulations, there will be 1 two-hour written examination. The CAS mark will be based on the maximum of examination (100%) and examination (80%) together with in-course assessment (20%).

Only the marks obtained on first sitting can be used for Honours classification.

Formative Assessment

Informal assessment of weekly homework through discussions in tutorials.

Feedback

In-course assignments will normally be marked within one week and feedback provided to students in tutorials. Students will be invited to contact Course Coordinators for feedback on the final examination.

Course Learning Outcomes

None.
 

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