To qualify for the Ph.D. in the Stanford University Mathematics Department, students must pass two examinations: one in real analysis and one in algebra. The real analysis and algebra exams each consist of two parts. Students are given three hours for each part.
Students must pass both exams by the fall of their second year. Ordinarily first-year students take courses in real analysis and algebra throughout the year to prepare them for the qualifying exams. The exams are then taken at the beginning of Spring Quarter. A student who does not pass one or more of the exams at that time is given a second chance in the following fall.
Because some students have already taken graduate courses as undergraduates, incoming graduate students are allowed to take either or both of the exams in the fall. If they pass any of the exams, they thereby fulfill the requirement in those subjects. However, they are in no way penalized for failing either of the exams.
In addition to the qualifying exams, during the first year students must satisfactorily complete one of a choice of three courses sequences. The choices are:
Click here to see qualifying exams from recent years.
Click here to see the dates of the upcoming qualifying exams.