To qualify for the Ph.D. in the Stanford University Mathematics Department, students must pass three examinations: one in real analysis, one in complex analysis, and one in algebra. The real analysis and algebra exams each consist of two parts. The complex analysis exam has only one part. Students are given three hours for each part.
Students must pass all three exams by the fall of their second year. Ordinarily much of the first year of graduate school is devoted to taking courses to prepare for the qualifying exams. Students take the exams in the spring of the first year. 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 any or all of the three 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 any or all of the exams.
Students who are interested in applied mathematics have the optioin of replacing the complex analysis and algebra exams by an exam on partial differential equations (corresponding to Math 220) and an exam on numerical methods for PDEs (corresponding to Computer Science 237 B, C). These exams are three hours each and are also given twice a year: in the spring and in the fall. Students can work in an applied area even if they take the standard math qualifying exams.
Click here to see qualifying exams from recent years.
Click here to see the dates of the upcoming qualifying exams.