Undergraduate Course: Galois Theory (MATH10080)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Mathematics |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This 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. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2014/15 Semester 2, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
|
Web Timetable |
Web Timetable |
| Course Start Date |
12/01/2015 |
| Breakdown of 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 )
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| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %
|
| No Exam Information |
Summary of Intended 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. |
Assessment Information
| Coursework 20%, Examination 80% |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
· 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
· Transcendence |
| Transferable skills |
Not entered |
| Reading list |
Recommended :
- J J Rotman, Galois Theory
- I Stewart, Galois Theory (QA214 Ste)
- D J H Garling, A Course in Galois Theory (QA211 Gar)
- J-P Escofier, Galois Theory (QA174.2 Esc)
- J-P Tignol, Galois theory of algebraic equations (QA211 Tig)
- H M Edwards, Galois Theory (QA274 Edw) |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | GaTh |
Contacts
| Course organiser | Dr Martin Dindos
Tel:
Email: M.Dindos@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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