What is it like to study analysis in the MAST programme?
For the first year, you have a number of what you could call core courses, which are useful not just for your own specialization but for the wider MAST programme. We teach, for instance, Complex Analysis and Real and Fourier Analysis. You then have more specialized courses that build on what you were taught in your first year. Analysis’ teaching methods are very traditional for mathematics, with most courses taught on a blackboard. Blackboards are used because, in my perspective, a teacher must think and slow down with the material when they’re writing, while a projector encourages the opposite. The structure of courses in the programme can depend on the size of the course and the teacher, though there is also a focus on exercises.
Who are the studies suitable for?
Many of the available courses are common core courses between the study tracks, and you can decide in your second year what you want to graduate with. It is also common practice to change fields of study during the programme. However, we have a focus on a general background of mathematics, with studies, for instance, in differentiability of functions and continuity. There is a slight emphasis on the theoretical side, but once you have done the basic courses you can very easily do more applied mathematics. A lot of classical subareas are also taught, since analysis has a long tradition and many of its concepts can emerge again after decades of perceived irrelevance – for instance, metric space for topological data analysis on internet traffic.
What kind of career paths do studies in analysis open up?
There are many places that our graduates can go. You can, for instance, end up in postgraduate studies, where we have a lot of people who do research in geometric, harmonical, or functional analysis. There are also the more applied sectors like banks, insurance companies, financial maths, high school teaching, or even the IT-industry.
What do you find most interesting about this field of research?
What fascinated me and brought me into analysis was the idea that you could have infinitely dimensional linear spaces that are not just the calculus of one or two variables. This concept is very natural for time-dependent physical processes and has served as a background for quantum mechanics. My favorite course is actually the two core courses in Functional Analysis, as the concepts it teaches are what brought me into the work I do today. I’ve been involved in teaching and building the Functional Analysis courses.