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 |
http://student.maths.ed.ac.uk |
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| 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. |
Course Delivery Information
|
| Delivery period: 2010/11 Full Year, Available to all students (SV1)
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WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | | 1-22 | 11:10 - 12:00 | | | | | | King's Buildings | Lecture | | 1-22 | | | | 11:10 - 12:00 | |
| First Class |
Week 1, Monday, 11:10 - 12:00, Zone: King's Buildings. JCMB, room 6206 |
| Additional information |
The above times are for 1st Semester only.
For 2nd Semester lecture times are:
Mon & Thu at 14:00-14:50 |
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
Coursework: 15%; Degree Examination: 85%.
|
| Please see Visiting Student Prospectus website for Visiting Student Assessment information |
Special Arrangements
| Not entered |
Contacts
| Course organiser |
Dr Liam O'Carroll
Tel: (0131 6)50 5070
Email: L.O'Carroll@ed.ac.uk |
Course secretary |
Mrs Alison Fairgrieve
Tel: (0131 6)50 6427
Email: Alison.Fairgrieve@ed.ac.uk |
|
copyright 2010 The University of Edinburgh -
1 September 2010 6:18 am
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