The theory of rings and fields holds the key to questions which frustrated mathematicians for hundreds of years, including the impossibility of squaring a circle or trisecting an angle with ruler and compass or finding a formula for solving quintic equations. It also forms the basis for algebraic aspects of number theory, with applications to encryption. Topics covered in the course will include subrings, ideals, quotient rings, integral domains, fields of fractions, factorization in various special types of rings, Gaussian and algebraic integers, extension fields, splitting fields and Galois theory.

Note: Students wishing to enrol in Level III Higher Pure Mathematics courses should consult with the Pure Mathematics Department before enrolling.