The main aim of the course is to get across the basic language of
mathematics. In particular we do prove things. The material is to a
large extent the same as `calculus' which is to say the analysis of
functions of a real variable. However we do this through the
fundamental concept of a metric space; it will take about half the
semester to get this sorted out. In the second half of the semester we
go back and examine the notions that you already `know' of
differentiability of functions and integration.