### Master's programs

# Programs

The Department offers Master's programs in both Mathematics and Statistics. The Master's programs are based on a two-year curriculum of study culminating with a comprehensive examination or a thesis. Graduates from these programs are well prepared both for doctoral studies and for employment in academic and non-academic settings.

## Master of Arts

The M.A. program is designed to provide a comprehensive introduction to the fundamental concepts of modern mathematics and is appropriate for students who wish to pursue a career teaching at the community or junior college level or for those who intend to enter a doctoral program. The degree requires 30 semester hours of course work that must include the two-semester introductory courses in algebra, topology, and real analysis and one semester of complex analysis. In addition, students are required to complete one upper level sequence in algebra, topology, differential geometry, differential equations, real or complex analysis. Electives can be chosen from other graduate level courses in mathematics.

## Master of Science in Statistics

The M.S. program in statistics gives students training in
methodology of applied statistics and also provides a solid
foundation in statistical theory. Students' skills in applied
statistics are developed through project oriented courses,
statistical computing emphasizing *S+* and *SAS*, and
faculty supervised experience in the Department's statistical
consulting service. Through the statistical consulting service
students gain first hand experience assisting with the statistical
analysis of problems that come from local institutions such as the
UT College of Medicine and The UT Center for Applied Pharmacology,
and from local industries. The program requires 32 semester hours
of courses. Among the required courses are applications of
statistics, statistical inference, linear statistical models,
multivariate analysis, statistical computing, non-parametric
statistics, categorical data analysis, statistical consulting, and
sample survey methods and theory.

## Master of Science in Applied Mathematics

The M.S. program in Applied Mathematics offers students a rigorous introduction to the fundamental tools of applied mathematics, with particular emphasis on differential equations and numerical analysis. The program requires 30 semester hours of course work that includes year-long courses in real analysis, numerical analysis, and differential equations and a semester course in complex analysis. Elective courses can be chosen from graduate courses in applied areas such as linear, nonlinear and dynamic programming, convex analysis, calculus of variations, applied functional analysis, and optimal control. A recently added Industrial Mathematics track allows students to take six of their elective hours in approved courses in the departments of Physics, Chemistry, Biology, Economics, Engineering, ISOM, Business or Environmental Sciences. A major component of this track is a project report (to serve as a thesis) which contains a solution to a practical "real-life" problem drawn from a company, university department or government unit.

## Master of Science and Education

The M.S.E. degree is offered jointly by the Department of Mathematics and the College of Education and Allied Professions, and is appropriate for secondary school teachers seeking graduate training in Mathematics. At least 18 semester hours of mathematics courses are required which must include algebra, linear algebra, geometry, probability and statistics, logic, and analysis. At least 9 hours of education courses are required.

# Master's Examinations and Theses

All masters programs culminate in a written comprehensive examination or a thesis project.

- The M.A. examination consists of two three-hour exams (one in Real and Complex Analysis and one in Algebra) and a third two-hour exam in one of the areas of Topology, Differential Equations or Probability and Statistics.
- The M.S. (applied math) examination consists of two three-hour exams (one in Real and Complex Analysis and one in Differential Equations).
- The M.S. (statistics) examination consists of two three-hour exams (one in Probability and Statistical Theory and one in Applied Statistics) plus a take-home project.
- The M.S.E examination consists of three 2-hour exams covering areas of mathematics studied by the student.

All of the examinations are generally scheduled a week apart in the student's fourth semester of study. Students in the M.A. and M.S. applied programs who intend to pursue a doctoral degree in the department may also satisfy the M.A. and M.S. exam requirements by passing the corresponding doctoral exam at the M.A. or M.S. level.

The thesis option is available in the M.A. and M.S. (applied mathematics) programs only. Thesis writing and research takes place during the student's second year of study under the supervision of a faculty adviser. Recent master's thesis topics include: "applications of nonlinear programming to optimal control", "exotic containers", "closed geodesics on Jacobi surfaces", and "matroids".