There are two types of qualifying exam: the Basic exam and the Area exams. The Basic exam is designed to be passed by well-trained students before they commence study at UCLA. It examines fundamental topics of the undergraduate mathematics curriculum. The Area exams are graduate level exams. For each Area exam there is a preparatory course sequence. There are Area exams in Algebra, Analysis, Applied Differential Equations, Numerical Analysis, Geometry /Topology, and Logic. Students may attempt any number of examinations in each examination period.
MA students must pass the Basic Exam only. PhD students must pass the Basic exam and two Area exams. MA students must pass the Basic by the beginning of the sixth quarter of study. PhD students must pass the Basic by the fourth quarter of graduate study. A PhD student must pass the one Area examination by the sixth quarter. A PhD student must pass the second Area examination by the seventh quarter of graduate study.
The exams are offered in the Fall and in the Spring, usually just before the beginning of those quarters. Precise dates and times are posted well in advance of the exams. Students must sign-up for the exams in the Graduate Office. Each exam lasts 4 hours. Copies of past exams may be downloaded from our website by clicking here: Download Exams. However, it is strongly recommended that students prepare for exams by studying their syllabi theme by theme, and by doing numerous exercises other than those on old exams. Experience shows that study organized around working old exams is not as efficacious as thematically organized study.
Each exam is written and graded by a committee created for that purpose. The Graduate Studies Committee approves exam results (passing or failing), taking into account recommendations of the examination committee. Shortly after the Graduate Studies Committee’s decision, students are notified of their exam results. Students are reminded that the grading of exams is a complex matter, and that final result (Pass or Fail) is not usually determined by the total score of all work on all problems. Students should read and follow carefully the instructions of an exam.
Graded exams are kept in the Graduate Office for six months and then destroyed. They may be examined in the Graduate Office during this time. After the results of the exams are announced, there is a one week appeal period during which students may petition, in writing, to a Qual Committee for regrading of problems. Appeals must be submitted via the Graduate Office. The Qual Committee will respond, usually in writing, to any appeal within one week.
Currently, most UCLA PhD students pass all their exams on schedule. However, the few students who fail to pass exams by the required deadlines are deemed not to be making Satisfactory Progress. Each such student is discussed individually by the Graduate Studies Committee at a meeting shortly after the above period of appeals is over. Students who have missed a deadline, or otherwise failed to make Satisfactory Progress, will receive a letter from the Graduate Vice Chair indicating any action that was taken, and detailing any schedule for performance that must be satisfied in order to continue in the program. Only in unusual circumstances will a PhD student who is more than six months behind the schedule of Satisfactory Progress be permitted to remain in the PhD program. Students who are facing negative actions are encouraged to write to GSC, and to speak to the Graduate Vice Chair, before GSC meets, to explain any extenuating circumstances that could positively influence it.
Here follow the syllabi for the Examinations. Each examination may test on any of the topics of its syllabus.