Stanford University

PhD Qualifying Exams

To qualify for the Ph.D. in Mathematics, students must pass two examinations: one in algebra and one in real analysis. The exams each consist of two parts. Students are given three hours for each part.

Topics Covered on the Exams:

Algebra Syllabus

Real Analysis Syllabus

Past Qualifying Exams

Timeline for Completion

Students must pass both qualifying exams by the autumn of their second year. Ordinarily first-year students take courses in algebra and real analysis throughout the year to prepare them for the 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 Autumn.

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 autumn. 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.

Exam Schedule

Unless otherwise noted, the exams will be held each year according to the following schedule:

Autumn Quarter: The exams are held during the week prior to the first week of the quarter.
Spring Quarter: The exams are held during the first week of the quarter.

Algebra: Tuesday, 9:30am-12:30pm and 2:00-5:00pm
Real Analysis: Friday, 9:30am-12:30pm and 2:00-5:00pm

For the start date of the current or future years’ quarters please see the Academic Calendar

Upcoming Exam Dates

Autumn 2022

Algebra: Tuesday, September 20th, 9:30am-12:30pm and 2:00-5:00pm
Location: TBA

Real Analysis: Friday, September 23rd, 9:30am-12:30pm and 2:00-5:00pm
Location: TBA