Aims and objectives
===================
This page is dedicated to the memory of the footling nonsense we had
to go through to pander to the requirements of the last Teaching
Quality Assessment.
Aims:
The course will discuss the problem of solutions of polynomial equations
both in explicit terms and in terms of abstract algebraic structures.
The course demonstrates the tools of abstract algebra (linear algebra,
group theory, rings and ideals) as applied to a meaningful problem.
Objectives:
By the end of the module the student should understand
1. The relation between roots and coefficients of a polynomial:
elementary symmetric functions; complex roots of unity; and solutions
by radicals of cubic and quartic equations.
2. The characteristic of a field and the prime subfield.
3. Factorisation and ideal theory in the polynomial ring $k[x]$;
the structure of a primitive field extension.
4. Field extensions and characterisation of finite normal extensions
as splitting fields.
5. The structure and construction of finite fields.
6. Counting field homomorphisms; the Galois group and the Galois
correspondence.
7. Radical field extensions.
8. Soluble groups and solubility by radicals of equations.