# Doctoral Program Overview

The Department of Mathematics offers three Ph.D. specializations (Applied Mathematics, Pure Mathematics, and Mathematics Education). The Ph.D. degree is meant to prepare a mathematician for a career in college instruction, university research, or industrial research. The Ph.D. degree is the highest earned degree and consequently its recipients are expected to have significant breadth in mathematical knowledge, as well as research skills in a particular area. In order to prepare students for positions where instructional duties and research in mathematics education are of primary importance the Department offers a Ph.D. with specialization in Mathematics Education.

## General Requirements (i.e. requirements independent of specialization) of the doctoral program:

- 90 hours of course work beyond a Bachelor's degree or 60 hours of course work beyond the Master's degree
- 15 hours of core course work (core courses vary with degree specialization)
- Completing a preliminary research project
- Passing a qualifying exam
- Writing a dissertation
- A graduate GPA of at least 3.0.

## Requirements for each of the three specializations:

For a more detailed explanation of these general requirements, see Requirements and Timetable for Ph.D. in Mathematics.

The Mathematics Department at Oklahoma State University has granted over 200 doctoral degrees. Graduates of the doctoral programs have been highly successful in academic and industrial careers. Most of these graduates have become professors at colleges or universities, and some have gone on to distinguished careers in academic administration. Others have chosen to pursue research careers with either industrial or government concerns.

The doctoral degree program has been designed to produce graduates who have advanced pure mathematics, applied mathematics and/or mathematics education and who are capable of contributing further developments through careers in academia and industry. A set of core courses is required in order to achieve consummate degree of breadth in each of the three specializations. The selection of core courses has sufficient overlap so as not to delay students who wish some time before committing themselves to any particular one of the Ph.D. specializations. The preliminary research project provides a mathematical research experience at an early stage of the Ph.D. program. The qualifying exam determines the student's readiness to write a dissertation. The dissertation itself is of integral importance to all doctoral degrees. It is the culmination of a major research project and exhibits the student's expertise in a very specific field of study. The Ph.D. dissertation is an original piece of significant mathematical research or research in mathematics education.

Beginning students in Applied Mathematics concentrate on gaining general knowledge in the core areas of complex analysis, real analysis, differential equations and numerical and computational mathematics. Those in Pure Mathematics concentrate on complex analysis, real analysis, algebra and topology. Students in Mathematics Education are required to take courses in at least three of the 6 above areas, or two of the above and statistics.

All doctoral students must complete an advanced course in linear algebra.

As students progress, they take more specific topics courses and attend seminars to gain greater understanding of particular research areas. The actual course sequences taken by a doctoral candidate may vary greatly depending on his/her preparation and goals. The next step is to gain specific knowledge about an area of interest which might lead to a dissertation topic. Under the direction of a faculty member, the doctoral student will carry out his/her preliminary research project, continue with topics courses, and become actively involved in research seminars. When the student has gained the background to begin research directed at a dissertation, a qualifying exam is administered by his/her advisory committee. This exam determines if the student is ready to conduct the necessary research. Upon completion of the qualifying exam, the student devotes a major portion of his/her time to research for a dissertation.