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.
|Academic unit||Mathematics and Statistics Academic Operations|
|Unit name||Rings, Fields and Galois Theory (Adv)|
|Semester 1, 2022|
|Attendance mode||Normal day|
|MATH3062 or MATH4062|
|MATH2961 or MATH2922 or a mark of 65 or greater in (MATH2061 or MATH2022)|
|Available to study abroad and exchange students||