Students are admitted to the PhD program provisionally; in order to continue as PhD candidates, they must pass a proficiency examination over undergraduate material. Each student will be tested over the following topics, depending on his or her area of concentration:
The purpose of the proficiency examination is to ensure that incoming students have the necessary background knowledge and mathematical maturity to be able to take and benefit from graduate level courses. If students do not have this background, then they must immediately acquire it (by taking the relevant undergraduate courses and preparing for the proficiency examination). Another purpose for the proficiency examination is to make sure that students ``have what it takes'' to complete a PhD. If a student cannot (because of lack of desire or ability) pass an exam over undergraduate mathematics, then that student probably does not belong in the PhD program.