# PhD Program

**Admission to the 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 offered by other
departments, e.g., Physics, Engineering, Computer Science, or Economics.

Applicants for admission are considered by the department's Graduate
Admissions Committee. The number of students that can
be admitted each year is determined by the Graduate Division. In making admissions decisions, the committee
conducts a comprehensive review taking into consideration letters of recommendation, level of mathematics preparation, performance in courses, broader impacts (community contributions), research experience, etc.

**Degree Requirements**

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

- During the first year in the PhD program:

- Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics

- Pass the six-hour written Preliminary Examination
covering calculus, real analysis, complex analysis, linear algebra, and abstract algebra; students must pass the prelim before the start of their second year in the program (within three semesters of starting the program).

- Take at least 4 courses, 2 or more of which are graduate courses offered by the Department of Mathematics
- 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.

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

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

- 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 offered by the Department of Mathematics. Exceptions can be granted by the Vice Chair for Graduate Studies.

**Preliminary Examination**

The Preliminary Examination consists of 6 hours (total) of written work given
over a two-day period (3 hours/day). Exam questions are given in calculus, real analysis, complex analysis, linear algebra and abstract algebra. The Preliminary Examination is
offered twice a year during the first week of the fall and spring semesters.

**Qualifying Examination**

To arrange the Qualifying Examination, a student must first settle
on an area of concentration, and a prospective Dissertation Advisor (Dissertation Chair),
someone who agrees to supervise the dissertation if the examination is
passed. With the aid of the prospective advisor, the student forms
an examination committee of 4 members, at least 2 of which must be
members of the Mathematics Department. The Graduate Division requires that at least
one committee member be from outside the Mathematics Department and that the
committee chair be someone other than the Dissertation Chair. 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 research 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 reviewed online or 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.