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.
Three 1 hour lectures and one 1 hour tutorial per week.
One 2 hour exam, homework assignments (100%)
Students are advised to take MATH2968 before attempting this unit.
MATH2922 or MATH2961
Credit average or greater in 12 credit points of Intermediate MathematicsProhibitions
MATH3062 or MATH3902 or MATH3002