Limits and continuity are the central concepts of calculus in one and several variables. These concepts can be extended to quite general situations. The simplest of these is when there is some way of measuring the distance between two objects. Some of the most important examples of these `metric spaces' occur as sets of functions, so this course looks at ways in which one might say that a sequence of functions converges. Taking these ideas one step further, we look at convergence which does not come from a generalized distance function. These are the ideas of point set topology. The course will include topics such as countability, continuity, uniform convergence, compactness and connectedness. This is not a `computational' course, but rather one in which you will develop your ability to think abstractly, precisely and creatively.

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