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
Prerequisites  Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite 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. ISBN13: 9781482245820. 
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 

