GALOIS THEORY
- Course Code
- MX 4082
- Credit Points
- 15
- Course Coordinator
- Dr J Elmer
Pre-requisites
Notes
This course will run in 2013/14.
Overview
- 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.
Structure
2 one-hour lectures and 1 one-hour tutorial per week.
Assessment
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.