Mathematics

Algebra

Module code: G5096
Level 5
15 credits in autumn teaching
Teaching method: Lecture, Workshop
Assessment modes: Unseen examination, Coursework

Topics covered on this module include:

  • definition of a group, examples, abelian groups, subgroups, cosets, Lagrange's theorem, cyclic groups
  • the symmetric group S_n and conjugacy
  • homomorphisms, normal subgroups and quotient groups
  • definition of a ring, examples, polynomial rings, ideals and homomorphisms
  • definition of a field and construction of extensions.

Module learning outcomes

  • Understand the structure of a finite group.
  • Understand permutations.
  • Understand quotient groups
  • Understand and illustrate the difinitions of a ring and a field.