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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Galois Theory (MATH10080)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis is a course in abstract algebra, although connections with other
fields will be stressed as often as possible. It will cover some of thejewels 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
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Honours Algebra (MATH10069) AND Group Theory (MATH10079)
It is RECOMMENDED that students have passed Introduction to Number Theory (MATH10071)
Prohibited Combinations Students MUST NOT also be taking Group and Galois Theory (MATH10078)
Other requirements Students wishing to take both MATH10079 Group Theory and MATH10080 Galois Theory in the same academic session should register for the 20 credit course MATH10078 Group and Galois Theory.
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2015/16, 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 Theory2:00
Learning Outcomes
1. Facility with fields and their extensions, including expertise in explicit calculations with and constructions of examples with various relevant desired properties.
2. Ability to 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.
3. Capacity to 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.
4. Be able to produce examples and counterexamples illustrating the mathematical concepts presented in the course.
5. Understand the statements and proofs of important theorems and be able to explain the key steps in proofs, sometimes with variation.
Reading List
Students are expected to have a personal copy of 'Galois Theory', Fourth Edition (Chapman and Hall / CRC) by Ian Nicholas Stewart. ISBN-13: 978-1482245820.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Harry Braden
Tel: (0131 6)50 5072
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
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