Upon completion of this module, a successful student should:
1. have a good working knowledge of several constructions of fields;
2. be able to compute the Galois group of the splitting field of a polynomial;
3. have a good understanding of the Galois correspondence theorem;
4. be able to use the Galois correspondence to obtain the subfield lattice of a Galois extension from the subgroup lattice of the Galois group of that extension and vice versa;
5. be able to use the discriminant of a polynomial as a tool in the classification of its Galois group;
6. be able to compute the fixed fields of subgroups of the Galois group of a field extension;
7. be able to identity normal field extensions;
8. be familiar with a further topic in algebra that relies on Galois theory

Field theory, review of polynomial rings. Field extensions, algebraic closure, splitting fields and normal extensions. Applications including constructions using straight edge and compass. Separable and normal extensions, fixed fields, Artin's Lemma, the Galois correspondence. Additional topics include finite fields, trace and norm, cyclic extensions, solvability by radicals.

Not applicable to this module.

• Group/class feedback, post-assessment

Weekly assignments will be discussed in tutorials, with group feedback given. Individual feedback will be given following the in-class test.