haha actually you are quite right, what I meant was that good applied maths/stats students would have no problem; pure maths students with some training in PDE's and probability would cope fine as well.
I can't find a word more appropriate than "yucky" to describe measure theory
you won't need that for advanced option pricing, but for interest rate modelling, there are a few more technicalities to take care of, so some analysis background would be beneficial. There is no harm leaving that last though.
Most of the students taking the courses are applied/stats honours. There were a few postgrad research students as well. There was one MIT student on the first day, but he got scared away. There is a maths foundation course for MIT students before they take these financial courses, but most of them were already in deep trouble handling the foundation course (some of them couldn't even do integration by parts). So the focus would be on the maths rather than computing.