Jewels of Algebra (U04228)

? Credit Points : 20 ? SCQF Level : 10 ? Acronym : MAT-4-JoA

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

? This course is not accepting further student enrolments.

? Pre-requisites : MAT-3-CVD, MAT-3-PAA, MAT-3-Alg, MAT-3-MCC, MAT-3-NuR

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (School of Mathematics, Schedule P)

Other subject areas

Specialist Mathematics & Statistics (Pure), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 4th year

? Delivery Period : Full Year (Blocks 1-4)

? Contact Teaching Time : 2 hour(s) per week for 22 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
23/09/2008	11:10	12:00	Lecture Room 5327, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	12:10	13:00	KB
Lecture	Tuesday	11:10	12:00	KB
Lecture	Thursday	12:10	13:00	KB
Lecture	Friday	11:10	12:00	KB

? Additional Class Information : Semester 1 - Tue/Fri lectures
Semester 2 - Mon/Thu lectures

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.