The course content may vary from year to year. But each year we will select subjects that show a rich mathematical structure. The areas will also be selected in order to represent different mathematical methods and approaches; for example the axiomatic method, constructive methods, algebraic methods in geometry and topology.
Typically, the course will include a mix of algebra (eg, solution of polynomial equations or unsolvability of classic problems such as angle trisection), analysis (e.g. the question “for which functions do the fundamental theorem of calculus hold?”), topology (e.g. “what two-dimensional surfaces are possible?”) or geometry (e.g. non-Euclidean geometry).
The content of the course should be seen as the abstract ideas behind mathematics rather than the topics covered in the course.