**The purpose of the M.A. program in Mathematics** is to offer students who hold a Bachelor's degree in mathematics an opportunity to broaden their knowledge in several areas of mathematics and its applications. This program will prepare a student for teaching at junior colleges or for careers in business, government, or industry. An inadequately prepared Ph.D. applicant may be admitted to the M.A. program with the possibility of transferring later to the Ph.D. program if he or she makes sufficient progress.

## Prerequisites:

To enter the M.A. program a student should have a strong Bachelor's degree in mathematics. The student should have had training at the junior/senior level in courses requiring reading and writing proofs, preferably including at least one course from at least two of the areas modern algebra, topology, and real analysis. Additional courses in pure and applied mathematics, probability, statistics, physics, and computer science are desirable.

## University M.A. Program Requirements:

The M.A. program in mathematics is offered under two plans: (1) **M.A. with thesis**, and (2) **M.A. without thesis**. The general requirements by the University include 24 credit hours of course work (exclusive of thesis), of which at least 12 hours must be in courses available only to graduate students; a 3.0 average or better on all course work; and at least one year's residency. For additional requirements concerning transfer credit, submission of program of study, admission to candidacy, and regulations concerning Master's comps and preparation of theses: see the current Graduate Bulletin, or consult the Graduate school.

## Departmental M.A. requirements are as follows:

- Candidates for the
**M.A. degree with thesi**s are required to take 30 credit hours of mathematics-related course work, and to write a thesis. The course work must include 9 hours in 8000-level courses, and 3 hours of MATH 7300. It is desirable that the thesis should present original research. However, the thesis may be expository in nature in which case it should be a synthesis of several research articles and books. The thesis must be read and approved by a committee of three members including the thesis advisor. - Candidates for the
**M.A. degree without thesis**are required to take at least 33 credit hours of mathematics-related course work, including 12 hours in 8000-level courses. Candidates are also required to take comprehensive examinations in three areas as specified below.

A student's progress towards an M.A. degree is supervised by a 3-person Master's committee, formed at the beginning of his or her graduate career. The student's faculty advisor chooses this committee, and is its chair.

**Graduate courses** are offered at two levels. In rough terms, courses numbered 6000-6900 are pitched at the Master's level and courses numbered 8000-8980 are pitched at the Ph.D. level. As a general rule, 6000-level courses and 8000-level courses carry 3 hours of credit per semester. (Most graduate courses meet 3 hours a week.) A list of courses is given below. In order to encourage breadth of study at the M.A. level, the department's course offerings have been divided into groups. Normally, a student selects three courses per semester at the 6000-level (groups A, B, C or D) the first year. A second year student normally selects at least two courses per semester at the 8000-level (groups E, F or G). A first year student with pervious course work at the 6000-level may substitute 8000-level courses.

A. | 6100-10-20 | Real Analysis, Lebesgue Integration, Multivariable Analysis, Complex Analysis |

B. | 6000-10-50-80 | Algebra |

6400-50 | Number Theory | |

A. 6100-10-20 Real Analysis, Lebesgue Integration, Multivariable Analysis, Complex Analysis

B. 6000-10-50-80 Algebra

6400-50 Number Theory

6300 Algebraic Geometry

C. 6200 Topology

6220 Differential Topology

6250 Differential Geometry

D. 6500-10 Numerical Analysis

6600 Probability

6630-70-90 Algorithms, Combinatorics, Graph Theory

6700-20-80 Applied Mathematics, Differential Equations

E. 8100-10 Real Analysis

8150-60 Complex Analysis

8170-80 Functional Analysis

8190 Lie Groups

F. 8000-10-20 Algebra, Finite Groups, Commutative Algebra

8080 Lie Algebras

8200-10-20 Algebraic Topology, Topology of Manifolds, Homotopy

8300-10-20 Algebraic Geometry, Schemes, Curves

8250-60 Differential Geometry

8400-10 Number Theory

G. 8500-10-20 Numerical Analysis

8600-20-30 Probability

8700-10 Applied Mathematics

8740-50-70 Differential Equations

**The three comprehensive M.A. exams** taken by students in the M.A. non-thesis program must be chosen from three different areas among (1) Analysis areas A and E, (2) Algebra areas B and F, (3) Topology areas C and F, and (4) Applied areas D and G. At least one exam must cover an 8000-level sequence. Master's comps are two hours in length, and must initially be taken in a one-week period, ordinarily at the end of the candidate's second year of study. The examiner marks the exam and makes a pass/fail recommendation, but success is ultimately determined by the student's committee; if the student's work is not satisfactory the committee may recommend

"fail" or administer another exam.

Students transferring from the Ph.D. to the M.A. non-thesis program are given credit for Master's comps if they have passed two or more Ph.D. Quals.