How difficult is mathematics PhD qualifying exams? - Quora.
The written PhD qualifying exam, also called the PhD Comprehensive Examination, is administered twice yearly, during the two weeks just prior to the start of the Spring semester (January exam) and Fall semester (August exam). The qualifying exam is offered in six separate sections, out of which students need to pass three.
Qualifying Exams The Department of Mathematics provides the following examinations for study purposes. Please consult the Graduate Student Handbook for the most current passing requirements. As of January 2010, changes to the Qualifying Exam System have taken effect.
GGAM Qualifying Exam Guidelines. As expressed by the Dean of Graduate Studies, the Doctoral Qualifying Examination is not only a major benchmark in the student's career, but a point at which the faculty must reflect with wisdom on the student's general qualifications for a respected position as an educator or leader as well as the student's preparation in a special area of study.
PhD Qualifying Examinations (comprehensive examinations) are arranged and administered by a Doctoral Comprehensive Board of five faculty members of the Institute who are assigned for a three-year term by recommendation of the chair of the program and approval of the Institute. The Board sets up examination juries in order to prepare exams in varied fields, and administer and evaluate these exams.
Applied Mathematics. The Mathematics Department offers an Applied Mathematics Option for the qualifying exams that are required for all PhD students in Mathematics. The description from the 1999-2000 Stanford Bulletin (page 460) is as follows.
Every student planning to earn the PhD in Applied Mathematics must pass the two Joint Program Examinations. One exam covers real analysis. The other exam covers linear algebra and numerical linear algebra. Each exam is three and one half hours long.
Here are the detailed syllabi for the Qualifying Examinations. Algebra Qualifying Examination syllabus; Analysis Qualifying Examination syllabus.