Level of study Second Year
Credit value 20
Semester Students may study either 1, 2 or both.
Pre-requisite modules 23601,23602,22481
Semester 1: In this module, an axiomatic approach to ring theory will lead to the construction of the field of fractions of an integral domain, and will be used to study quotients of polynomial rings that are fields. Finite fields of small prime power will be constructed.
Semester 2: The module also introduces metric spaces as abstract settings for the study of analytical concepts such as convergence and continuity. This generalisation allows one, for example, to regard functions as points of a space and consider various ways in which a function can be the limit of a sequence of functions. The module will include detailed discussion of the structure of the real line, including the countability and density of the rationals.