Entering graduate students are expected to have taken at least two semesters of undergraduate courses in each of the subjects abstract algebra and real analysis. Semester long courses in general topology and complex analysis are also strongly suggested.

Some students arrive with extra mathematical background, for example, masters level courses, a masters degree in mathematics, or expertise in a specialized area as exemplified in a research project or published paper. Such students have the possibility to get a head start toward qualification and candidacy.