Browse Hierarchy MTH745P: Further Topics in Algebra

This is a course in modern abstract algebra, with a focus on Galois theory. This is a beautiful subject which uses group theory to study the symmetries and solutions of polynomial equations. We begin by building up some necessary tools from the theory of rings and fields, and go on to develop the notions of field extension and Galois group. Towards the end of the module we will be able to prove several remarkable results such as the impossibility of certain ruler-and-compass constructions, and the impossibility of creating a general formula for the solution of quintic polynomials. The latter of these was famously proved by the French revolutionary Évariste Galois shortly before his death in a duel at the age of 20.