Undergraduate Course: Galois Theory (MATH10080)
|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
|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.
- 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
|High Demand Course?
Course Delivery Information
|Academic year 2023/24, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||MATH10080 Galois Theory||2:00|
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.
|Galois Theory, Fourth Edition (Chapman and Hall / CRC) by Ian Nicholas Stewart. ISBN-13: 978-1482245820.|
|Graduate Attributes and Skills
|Course organiser||Dr Pavel Safronov
|Course secretary||Miss Greta Mazelyte