Handbook

This is a third-year course aimed at students completing a mathematics major or program. It is assumed that students are familiar with single and several variable calculus as taught in first and second-year mathematics courses.

The central concepts of calculus are limits and continuity. 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 generalised distance function. These are the ideas of point set topology. The course includes topics such as countability, continuity, uniform convergence and compactness, as well as normed vector spaces, which are the central object of study in functional analysis.

This is not a computational course; throughout the emphasis will be on ideas, concepts, and proofs rather than calculations and formulas.

The course consists of 4 hours of lectures per week and 1 hour of tutorial.