Undergraduate Course: Jewels of Algebra (MATH10050)
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 | 20 |
| Home subject area | Mathematics |
Other subject area | Specialist Mathematics & Statistics (Honours) |
| Course website |
https://info.maths.ed.ac.uk/teaching.html |
Taught in Gaelic? | No |
| Course description | Course for final year students in Honours programmes in Mathematics.
This course will cover some of the jewels in the crown of undergraduate mathematics, drawing together group, ring and number theory to solve problems that resisted the efforts of the world's best mathematicians for many centuries. The powerful central ideas of this course are now crucial to many modern problems in algebra, geometry, number theory and differential equations.
Groups and their actions : isomorphism theorems; Sylow theorems, Cauchy's theorem; nilpotent groups and solvable groups.
Rings : examples and groups acting on rings; Hilbert's basis theorem; integrality; finiteness of group invariants.
Fields and polynomials; Galois groups; the fundamental theorem of Galois theory; ruler & compass constructions; insolubility of the quintic. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Algebra (MATH10021) AND
Numbers & Rings (MATH10023) AND
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
|
| Delivery period: 2013/14 Full Year, Available to all students (SV1)
|
Learn enabled: Yes |
Quota: None |
Web Timetable |
Web Timetable |
| Course Start Date |
16/09/2013 |
| Breakdown of Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 44,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
139 )
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| Additional Notes |
|
| Breakdown of Assessment Methods (Further Info) |
Written Exam
95 %,
Coursework
5 %,
Practical Exam
0 %
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| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S2 (April/May) | | 3:00 | | |
Summary of Intended Learning Outcomes
1. Familiarity with abstract ideas.
2. Working knowledge of fundamental notions and techniques in group and ring theory.
3. Ability to apply this knowledge to concrete examples.
4. Working knowledge of field theory and polynomials and their roots.
5. Ability to calculate Galois groups and understand their properties. |
Assessment Information
See 'Breakdown of Assessment Methods' and 'Additional Notes', above.
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Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Not entered |
| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | JoA |
Contacts
| Course organiser | Prof Tom Lenagan
Tel: (0131 6)50 5078
Email: T.Lenagan@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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© Copyright 2013 The University of Edinburgh - 10 October 2013 4:51 am
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