The course description in the handbook lists four topics:
The first two follow on directly from MATH2320 and MATH2405; the fourth is essentially the infinite dimensional version of Euclidean space.
The third will be new, and will take up the majority of the course. Measure theory is a topic fraught with technical difficulties, and one needs some appreciation as to why all the effort is really necessary. Because of this, much of the early lectures will be concerned with a broad view of the subject, motivating examples, and the like. To start with at least, two lectures a week will be on measure theory, the third will be on one of the other topics, which will run end to end starting with metric spaces.
The formal prerequisite for the course is at least a credit in MATH2320, though it is often the level of mathematical sophistication rather than specific content that is required. However, for the measure theory it is essential that you be familiar with the theory of Riemann integration (MATH1116) and ideas of several variable calculus (MATH2405).
Assessment will be by three assignments during the semester and one at the end, together with an "essay" on a topic of individual choice relevant to the measure theory material. Further details are given in the handout. Here is a list of reference books for measure theory.
Office hours (when I guarantee to be available) will de decided once lecture times are fixed.
Lecture Notes will be available shortly after each lecture:
Measure Theory:
Metric spaces:
Hilbert Spaces:
Inverse function theorem:
Here are the assignments:
You may contact me by email here.
Last modified: January, 2004