MA 460: Topics in Analysis

Kurt Bryan, Spring 2011-12

What will this course be about?

This course will take Real Analysis to the next level. Nonetheless, it has a much less "epsilon-delta" feel to it than Reals I. It is in many ways essential material for people going to grad school, and it also forms the theoretical backbone of most modern applied math in the physical sciences and engineering, especially numerical work and simulation. We'll start with some basic info on metric, normed, and inner product spaces; it's sort of like linear algebra, but with infinitely many dimensions. Then we'll cover Lebesgue integration, which is the modern approach to integration. We'll talk about "Hilbert" spaces and operators on Hilbert spaces, an extension of the idea of matrices or linear mappings in linear algebra. Finally, we'll take a look at application of this stuff to Quantum Mechanics! No physics background needed!

This course will have a proof-writing component---not quite as intense as real analysis, but every assignment will have some proofs, as well as some more routine computations. The course work will consist of homework assignments (about one per week) and a couple of take home exams.