PhD Program


The Department of Mathematics offers 2 PhD degrees, one in Mathematics and one in Applied Mathematics. Applicants for admission to either PhD program are expected to have preparation comparable to the undergraduate major at Berkeley in Mathematics or in Applied Mathematics. These majors consist of 2 full years of lower-division work (covering calculus, linear algebra, differential equations, and multivariable calculus), followed by 8 one-semester courses including real analysis, complex analysis, abstract algebra, and linear algebra. These eight courses may include some mathematically based courses in other departments, e.g., physics, engineering, computer science, or economics.

Applicants for admission are considered by the Department's Graduate Admissions and Appointments Committees. The number of students that can be admitted each year is determined by the Graduate Division and by departmental resources. In making admissions decisions, the Committee considers, among other things, grades in mathematics courses, level of mathematical preparation, letters of recommendation, and GRE scores.

Experience has shown that the score on the Mathematics Subject GRE is a partial indicator of preparation for Berkeley's PhD program. A score below the 80th percentile suggests inadequate preparation and must be balanced by other evidence if a favorable admission decision is to be reached.

Degree Requirements

In outline, to qualify for the PhD in either Mathematics or Applied Mathematics, the candidate must meet the following requirements.

  1. During the first year in the PhD program:

    1. take at least 4 courses, 2 or more of which are graduate courses in mathematics;

    2. and pass the six-hour written Preliminary Examination covering primarily undergraduate material. (The exam is given just before the beginning of each semester, and the student must pass it within their first 3 semesters.)

  2. Pass a three-hour, oral Qualifying Examination emphasizing, but not exclusively restricted to, the area of specialization. The Qualifying Examination must be attempted within two years of entering the program.

  3. Complete a seminar, giving a talk of at least one hour duration.

  4. Write a dissertation embodying the results of original research and acceptable to a properly constituted dissertation committee.

  5. Meet the University residence requirement of two years or four semesters.

The detailed regulations of the PhD program are as follows:

Course Requirements

During the first year in the PhD. program, the student must enroll in at least 4 courses. At least 2 of these must be graduate courses in mathematics. Exceptions can be granted by the student's Graduate Advisor.

Preliminary Examination

The Preliminary Examination consists of 6 hours of written work given over a two-day period. Most of the examination covers material, mainly in analysis and algebra, that should be part of a well-prepared student's undergraduate training. The Preliminary Examination is offered twice a year---during the week before classes start in both the Fall and Spring Semesters. A student may repeat the examination twice. A student who does not pass the Preliminary Examination within 13 months of the date of entry into the PhD program will not be permitted to remain in the program past the third semester. In exceptional cases, a fourth try may be granted upon appeal to Committee Omega.

Qualifying Examination

To arrange for the Qualifying Examination, a student must first settle on an area of concentration, and a prospective Dissertation Supervisor, someone who agrees to supervise the dissertation if the examination is passed. With the aid of the prospective supervisor, the student forms an examination committee of 4 members, at least 2 of which must be members of the Department. The Graduate Division requires that at least one committee member be from outside the Department and that the committee chair be someone other than the Dissertation Supervisor. The syllabus of the examination is to be worked out jointly by the committee and the student, but before final approval it is to be circulated to all faculty members of the appropriate Sections. The Qualifying Examination must cover material falling in at least 3 subject areas and these must be listed on the application to take the examination. Moreover, the material covered must fall within more than one Section of the Department. Sample syllabi can be seen in 910 Evans Hall.

The student must attempt the Qualifying Examination within twenty-five months of entering the PhD program. If a student does not pass on the first attempt, then, on the recommendation of the student's examining committee, and subject to the approval of the Graduate Division, the student may repeat the examination once. The examining committee must be the same, and the re-examination must be held within thirty months of the student's entrance into the PhD program.

For a student to pass the Qualifying Examination, at least one identified member of the subject area group must be willing to accept the candidate as a dissertation student, if asked. The student must obtain an official Dissertation Supervisor within one semester after passing the Qualifying Examination or leave the PhD program. For more detailed rules and advice concerning the Qualifying Examination, consult the Graduate Advisor in Room 910 Evans Hall.