Algebra (Ord) (U01638)

? Credit Points : 20 ? SCQF Level : 9 ? Acronym : MAT-3-AlgO

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.

For this Ordinary version there is more emphasis on the technical, rather than conceptual elements, which will be reflected by a different examination.

Entry Requirements

? Pre-requisites : MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM or MAT-2-am3, MAT-2-mm3, MAT-2-am4, MAT-2-mm4 or MAT-2-mi3, MAT-2-mi4

? Prohibited combinations : MAT-3-AlgS1, MAT-3-Alg, MAT-3-ALgS1O

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Ordinary), (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
07/01/2008	11:10	12:00	Lecture Theatre A, JCMB	KB

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

The following are the learning objectives for the Honours version, MAT-3-Alg :

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.