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## Highlights of the Doctoral (Ph.D.) Program

The following highlights of a doctoral program are described in more detail in the sections on departmental requirements for the Ph.D. degree, with specializations in Applied Mathematics, Pure Mathematics and Mathematics Education. For general requirements and a timetable, look here. A chronology showing steps and assessment of progress is available here.

A doctoral degree in mathematics has several main requirements.

- 90 hours of course work beyond a Bachelor's degree or 60 hours of course work beyond the Master's degree
- 24 hours of core course work (core courses vary with degree specialization)
- Passing written comprehensive exams in three areas or in two areas with a minor thesis
- Completing a language requirement (varies with degree specialization)
- Passing a qualifying exam
- Writing a dissertation

The Department of Mathematics offers three Ph.D. specializations (Applied Mathematics, Pure Mathematics and Specialization in 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.

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 Department is exceptionally well equipped to provide doctoral education. The degree program has been designed to give maximum benefit to the students. A core of courses is required in each of the various 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 faculty at Oklahoma State is highly recognized for its accomplishments both in research and in mathematics education.

The comprehensive exams are meant to test students on breadth in mathematics. They cover material from several general areas. 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. 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 will vary greatly depending on the preparation received in their Master's work. After the core courses have been completed students take their comprehensive exams. Students have the option of taking two comprehensive exams and completing a minor thesis. 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 continue with topics courses, work on outside readings, and become actively involved in seminars. When the student has gained the background to begin serious research for 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.

For more information please contact the math department at (405) 744-5688 or email at graddir@mathdept.okstate.edu.