Week 1: Symmetric operations and groups: definition of group, standard examples.
Week 2: Subgroups (including cyclic subgroups): structure, generators, properties.
Week 3: Permutation groups: definition of symmetric groups, basic properties.
Week 4: Group isomorphisms; Direct product constructions, Cosets.
Week 5: Lagrange’s Theorem; The Orbit-Stabiliser Theorem; Burnside's Theorem; Normal subgroups and factor groups
Week 6: Group homomorphisms; Finite abelian groups; Cauchy's theorem
Week 7: Rings and integral domains: definition, examples, properties
Week 8: Ideals, factor rings and ring homomorphisms: definition, kernels
Week 9: Polynomial rings and factorisation: structure and operations, tests for irreducibility.
Week 10: Vector spaces (including extension fields): basis for field.
Week 11: Field extensions (including algebraic extensions): construction, factorisation of polynomials.
Week 12: Finite fields: construction, uniqueness, properties.