Algebra (U01616)

? Credit Points : 20 ? SCQF Level : 10 ? Acronym : MAT-3-Alg

Core course for Honours Degrees in Mathematics and/or Statistics. Syllabus summary: Fields (including finite fields), revision of linear maps and the Rank Theorem as a classification result, diagonalisability and minimal polynomials (phenomenological discussion only), symmetric bilinear and quadratic forms, quotient spaces, discretization of DEs, discrete Fourier transform, singular value decomposition. Groups, cosets and Lagrange's theorem, group actions, normal subgroups and quotient groups, homomorphisms and the first isomorphism theorem.

Entry Requirements

? Pre-requisites : Passes at C or better in MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM

? Prohibited combinations : MAT-3-AlgS1, MAT-3-AlgO, MAT-3-ALgS1O, similar courses from Mathematics 3 (Hons) prior to 2004-05

Variants

? This course has variants for part year visiting students, as follows

Algebra (VS1) (Semester 1 (Blocks 1-2))
Algebra (VS2) (Semester 2 (Blocks 3-4))

Subject Areas

Home subject area

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

Delivery Information

? Normal year taken : 3rd year

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

? Contact Teaching Time : 3 hour(s) per week for 22 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
15/09/2006	14:00	15:00	Lecture Theatre 6301, JCMB	KB	Course Registration Meeting

All of the following classes

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

? Additional Class Information : Supervision: one hour per week (shared with other 'core' courses), at a time to be arranged with Supervisor.

Summary of Intended Learning Outcomes

1. Ability to do elementary calculations in finite-dimensional vector spaces over general fields.
2. Some understanding of quotient constructions in linear algebra and group theory.
3. Ability to classify symmetric bilinear and quadratic forms and to use the results.
4. Familiarity with the basic ideas of classification of endomorphisms of vector spaces.
5. Familiarity with the singular-value decomposition and its applications.
6. An understanding of the basic ideas of the linear algebra arising in discretization of differential equations.
7. A basic understanding of the Fast Fourier Transform.
8. Ability to calculate in several different sorts of group.
9. Familiarity with the language and ideas of group actions.