# Masters Program

**Aim of the MA Program**

The purpose is to offer students who hold the AB degree in mathematics
(or related fields) an opportunity to broaden their knowledge in the
several fields of mathematics and its applications by providing further
courses at the upper-division and beginning graduate levels. The
program is designed to prepare graduates for teaching at the high school
and junior college levels or for careers in business, industry, or
government. The MA program is not intended primarily as preparation for
the PhD program. Adequately prepared students whose ultimate objective
is the PhD are advised to apply directly to the PhD program. However,
students who apply to the PhD program and are not accepted may be
considered for the MA program. They may apply to transfer later from
the MA to the PhD program if their record during their first year is
sufficiently strong. Graduate Student Instructorships and other forms
of departmental support are typically offered only to students in the
PhD program.

**Prerequisites**

To enter the MA program, a student should have an AB degree in
mathematics or a related field. Exceptions can be made at the
discretion of the departmental Committee on Graduate Admissions and the
Graduate Division. The student should have completed a minimum of 4
courses, each with a content equivalent to a one-semester upper-division
mathematics course at Berkeley, distributed as follows: one in algebra,
one in analysis, and one from each of 2 different fields from the
following list: geometry, foundations, numerical analysis, computer
science, statistics, one or 2 fields of applied mathematics. These
courses must have a fair amount of mathematical sophistication.
Students who are admitted without having the prescribed 4 courses must
make up the entrance deficiency at the beginning of their studies here,
and these make-up courses will not be counted toward the MA degree.

**Degree Requirements**

General University requirements for the MA degree are given in the Berkeley Academic Guide.
In particular, there is a two-semester academic residence requirement,
a restriction on transfer credit from other institutions, and a choice
between two plans:

*Plan I* requires at least 20 semester units of upper-division and
graduate courses and a thesis. At least 8 of these units must be in
graduate courses (200 series). These 8 units are normally taken in the
Department of Mathematics at Berkeley. In special cases, upon
recommendation of the Graduate Adviser and approval of the Dean of the
Graduate Division, some of the 8 graduate units may be taken in other
departments.

*Plan II* requires at least 24 semester units of upper-division and
graduate courses, followed by a comprehensive final examination, the MA
examination. At least 12 of these units must be in graduate courses
(200 series). These 12 units are normally taken in the Department of
Mathematics at Berkeley. In special cases, upon recommendation of the
Graduate Advisor and approval of the Dean of the Graduate Division, some
of the 12 graduate units may be taken in other departments. All
courses fulfilling the above unit requirements must have significant
mathematical content. In general, MA students are encouraged to take
some courses outside the Department of Mathematics. In many jobs, at
least some acquaintance with statistics and computer science is
essential; and, for some students, courses in such fields as
engineering, biological or physical sciences, or economics are highly
desirable.

A breadth requirement consisting of at least one course in each of three
fields must be met by all students. Fields include: algebra, analysis,
geometry, foundations, history of mathematics, numerical analysis,
probability and statistics, computer science, and various other fields
of applied mathematics. The last category specifically covers courses in
a variety of departments, and the Graduate Advisor may allow more than
one such course to count toward the breadth requirement. A depth
requirement consisting of a coherent program of three courses all in one
of the above fields, at least two of these courses being at the
graduate level, must be met. Students interested in a field of applied
mathematics are encouraged to take some of these courses outside the
department.

**The MA Examination**

The MA examination is a two-hour examination consisting of:

- a 45-minute prepared talk on an advanced topic in the student's
field of concentration, followed by 15 minutes of discussion of the
subject of the talk;

- then 2 half-hour oral examinations, each covering very basic material in one of the fields cited above. (The student selects the 2 fields for the examination.)