Undergraduate Course: Galois Theory (MATH10080)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This is a course in abstract algebra, although connections with other fields will be stressed as often as possible. It will cover some of the jewels in the crown of undergraduate mathematics, drawing together groups, rings and fields to solve problems that resisted the efforts of mathematicians for many centuries. The powerful central ideas of this course are now crucial to many modern problems in algebra, differential equations, geometry, number theory and topology. |
| Course description |
- Fields: examples, constructions and extensions
- Separability, normality & splitting fields
- Field automorphisms & Galois groups
- The fundamental theorem of Galois Theory
- Solvable groups and the insolubility of the general quintic
- Ruler and Compass constructions
- Calculation of Galois groups
|
Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2024/25, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 2 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
69 )
|
| Assessment (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Coursework 20%, Examination 80% |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S2 (April/May) | MATH10080 Galois Theory | 2:00 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate facility with fields and their extensions, including expertise in explicit calculations with and constructions of examples with various relevant desired properties.
- Handle Galois groups, abstractly and in explicit examples, by using a variety of techniques including the Fundamental Theorem of Galois Theory and presentations of fields.
- Explain and work with the consequences of Galois Theory in general questions of mathematics addressed in the course, such as insolubility of certain classes of equations or impossibility of certain geometric constructions.
- Produce examples and counterexamples illustrating the mathematical concepts presented in the course.
- Understand the statements and proofs of important theorems and explain the key steps in proofs, sometimes with variation.
|
Reading List
| Galois Theory, Fourth Edition (Chapman and Hall / CRC) by Ian Nicholas Stewart. ISBN-13: 978-1482245820. |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | GaTh |
Contacts
| Course organiser | Dr Pavel Safronov
Tel:
Email: p.safronov@ed.ac.uk |
Course secretary | Miss Greta Mazelyte
Tel:
Email: greta.mazelyte@ed.ac.uk |
|
|
University Homepage