Rings, Fields and Galois Theory (Adv) (MATH3962)


This unit of study investigates the modern mathematical theory that was originally developed for the purpose of studying polynomial equations. The philosophy is that it should be possible to factorize any polynomial into a product of linear factors by working over a "large enough" field (such as the field of all complex numbers). Viewed like this, the problem of solving polynomial equations leads naturally to the problem of understanding extensions of fields. This in turn leads into the area of mathematics known as Galois theory.

The basic theoretical tool needed for this program is the concept of a ring, which generalizes the concept of a field. The course begins with examples of rings, and associated concepts such as subrings, ring homomorphisms, ideals and quotient rings. These tools are then applied to study quotient rings of polynomial rings. The final part of the course deals with the basics of Galois theory, which gives a way of understanding field extensions.

Our courses that offer this unit of study

Further unit of study information


Three 1 hour lectures and one 1 hour tutorial per week.


One 2 hour exam, homework assignments (100%)

Faculty/department permission required?


Unit of study rules

Prerequisites and assumed knowledge

Credit average or greater in 12 credit points of Intermediate Mathematics



MATH3062 or MATH3902 or MATH3002

Study this unit outside a degree

Non-award/non-degree study


Cross-institutional study
