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 General Catalog. 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:

1. 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;
   
   
2. 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.)