Algebraic Structures
MODULE CODE
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Module Aims
Aim 1
To introduce some of the most important structures in modern algebra.
Module Content
Extensions of Q: Subfields of C, extensions of Q, algebraic over Q, minimum polynomials and irreducibility over Q, extensions of Q as vector spaces, structure of simple algebraic extensions of Q.
Groups: subgroups, generating set, cyclic groups, normal subgroups, factor groups, isomorphisms,
direct products, classifying groups
Rings: Subrings, ideals, factor rings (including modulo n), isomorphisms.
Learning Outcomes
On successful completion of this module, a student will be able to:
Teaching Methods
The direct contact will consist of lectures. During these lectures theory will be introduced and developed. Examples will be demonstrated throughout the module during these lectures. The lectures will also contain assisted problem solving. Regular non-assessed work sheets will be provided.
Assessment Methods
The module is assessed through 2 assignments and a written examination
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Compulsory
Optional
