The Qualifying Exam

The qualifying exam is part of the process used by the Mathematics Department to satisfy the Graduate School Requirements for the Master of Arts and Master of Science Degrees. This examination consists of two parts: written exams in basic analysis and linear algebra, and oral exams on two graduate level topics.

Written exams in undergraduate analysis and linear algebra are administered in August (just before fall classes begin), January (just before spring classes begin) and May of the student's first year.

The results of the August exam can sometimes be used a guide for selecting appropriate courses in the fall semester. Students who do not pass the August exam should work to become more prepared to retake the exam either through coursework or faculty mentoring.

Students are normally expected to pass both the basic analysis and linear algebra written exams by May of their first year.

For more details, consult either the basic analysis syllabus and the linear algebra syllabus. The repository of questions from past exams at the UC-Berkeley Math Dept may be helpful.

The oral qualifying exam is a two-hour examination before a committee of three members of the graduate faculty. It is usually taken towards the end^* of the first year of graduate study. It must be taken and passed before the beginning of the spring semester of the second year of study. The oral qualifying examination may not be taken before the student has passed the written qualifying examinations.

The purpose of the oral examination is to determine if the student is making adequate progress towards the Ph.D. There are five possible outcomes of the oral qualifying exam:

• A student who passes at the Ph.D. level will continue to work towards the Ph.D. by taking further courses and concentrating on more specialized material in preparation for the next exam, the preliminary exam.
• A student who fails the first attempt at the oral qualifying examination may be given a chance to retake the examination one more time to continue working towards the Ph.D.
• A student may fail the examination at the Ph.D. level but pass the examination at the Masters (i.e., M.A.) level. Such a student will be allowed to continue to complete the 10 3-unit courses required for the Masters degree (no later than the end of the spring semester of the second year), but must leave the Mathematics graduate program after that.
• A student may fail the examination but be allowed to retake the examination at the Masters level.
• It is possible to fail the exam completely and to be asked to leave the program without obtaining a degree.

The two graduate level topics for the oral qualifying exam are chosen from the following list of seven.

• Algebra
• Complex Analysis
• Differential Equations
• Differential Geometry and Topology
• Probability and Stochastic Processes
• Real Analysis
• Scientific Computing

After choosing the graduate level topics, the student asks the Director of Graduate Studies to appoint a committee. For some of the topics, the student must prepare a syllabus to be approved by the Director of Graduate Studies and the chair of the committee. The amount of material covered on each topic corresponds roughly to the content of a one semester introductory graduate level course.

While preparing to take the exam, the student is encouraged to discuss the material of the exam with the members of the committee. Many of the oral questions probe the student's ability to apply the general theory to specific examples.

^* Note that the oral qualifying exam must be taken during a semester for which the student is registered. Thus it may be before the last day of final exams of the spring semester. It may also be taken after the summer session starts (which is around 12 days later) so long as the student is registered for the summer session.

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