# Graduate Program

## Graduate Study in Computational and Applied Mathematics

The master's and doctoral programs in computational and applied mathematics offered by the Department of Mathematics and Statistics are designed to produce applied mathematicians and statisticians who can meet the growing demand for analytical and computational skills in traditional scientific and multidisciplinary fields. Students in the program can choose to pursue an option in either applied mathematics or statistics/biostatistics.

Applied mathematics is the application of mathematics to the solution of non-mathematical problems. Such problems may originate in math-oriented fields (physics, chemistry, and engineering) as well as in such areas as geology, oceanography, meteorology, biology, ecology, environmental health, economics, actuarial science, business (operations and market research), banking, and medicine. Students will learn to use methods of applied mathematics, probability, statistics, biostatistics, numerical analysis, and scientific computing in seeking solutions to such problems. For work in both applied mathematics and statistics, training in an additional field of application is a necessity.

The desire and ability to use mathematics to bring together various disciplines is the unique characteristic of an applied mathematician or statistician. Not only has mathematical modeling and solving of societal and scientific problems increased the demand for applied mathematicians and statisticians, but the flexibility and breadth of knowledge inherent in this discipline make it attractive for those who do not want to become irreversibly specialized.

Old Dominion University is one of the few American institutions offering a program expressly focused in applied mathematics and statistics. There are approximately 22 graduate program faculty members in the Department of Mathematics and Statistics, and current enrollment in the program is about 50 students. Areas of faculty research include analytical and numerical modeling in oceanography and meteorology, computational fluid dynamics and stability theory, elasticity and fracture mechanics, combustion theory, magnetohydrodynamics, mathematical biology, numerical analysis and approximation, applied probability, statistical inference, design of experiments, reliability, multivariate statistics, biostatistics, nonparametric statistics, and applied statistics.

Facilities within the metropolitan area include the Institute for Computer Applications in Science and Engineering (ICASE), located at the NASA/Langley Research Center, and the Center for Pediatric Research, located at the Eastern Virginia Medical School.

**Program Financial Aid.** Graduate assistantships in the Department of Mathematics and Statistics offer stipends ranging from $15,000 to $18,000. The level of award is determined on the basis of previous experience and performance as a graduate assistant and on the student's academic achievement and potential in applied mathematics or statistics. In addition, a number of teaching and research positions are available for financial support of graduate assistants during the summer months (June and July).

**Writing Proficiency.** All students in computational and applied mathematics are expected to demonstrate an acceptable level of writing ability. Writing samples provided in the first 15 hours of core course work will be evaluated by the faculty. Students needing help to remedy their writing deficiencies will be referred to the Writing Center for diagnosis and assistance.

## Master of Science - Computational and Applied Mathematics Major

**Admission**

An applicant to the master's program in computational and applied mathematics should have a bachelor's degree in mathematics, statistics, computer science, or an application area with a strong mathematics component (e.g., physics or engineering). Undergraduate mathematics preparation should include course work in linear algebra, advanced calculus, differential equations, probability, and numerical methods. Undergraduate averages of 2.80 overall (4.00 scale) and 3.00 in the major and related mathematics courses are required.

A student who does not fully meet all requirements for admission as a regular graduate student may be allowed, with permission of the program director, to enroll as a provisional graduate student. Students lacking adequate preparation will be required to make up their deficiencies by taking appropriate undergraduate courses in addition to those specified for the master's program.

A formal application form, official transcripts and two letters of recommendation should be forwarded to the Office of Admissions. It is recommended that applicants supply Graduate Record Examination aptitude scores.

It is recommended that the following material should be mailed directly to the director of the graduate program in computational and applied mathematics, Department of Mathematics and Statistics: a list of all mathematics courses taken and other courses closely allied to the applicant's primary interests in applied math or statistics along with the texts used (titles and authors), chapters studied or topics covered, and grades.

Students may enroll in the program on either a full-time or part-time basis. Courses are offered on a regular basis during the late afternoon and early evening hours, which allows part- time students to obtain master's degrees or post-master's graduate credit.

## Requirements

The M.S. candidate must complete a minimum of 31 credit hours of course work designed to fulfill an option in either applied mathematics or statistics or biostatistics. With approval of the graduate program director, up to six of these credits may be chosen from a field of application (e.g., geology, oceanography, ecosystem analysis, computer science, economics, health sciences, operations research, physics and engineering mechanics) in which the student applies analytical and numerical techniques to another discipline. A Master's Project is required.

All programs of study must be approved by the graduate program director, and substitutions may be made only with his or her approval. Each student will be assigned to a mentor faculty for the duration of the Master's Project.

**Prerequisites.** Prerequisite courses for the Applied Mathematics option are MATH 501, 508, 509, 517, 518 and 522. Prerequisite courses for the Statistics and Biostatistics options are MATH 316, STAT 331, 431, 532, 535 and 537. For any of the options, at most three of the listed 500 level prerequisite courses can be applied towards the 31 credit degree requirement.

**Applied Mathematics Option.** Students are required to take MATH 617, 618, 622, 632, 637, 693 and 5 additional approved courses.

**Statistics Option.** In this option, the required courses are STAT 505, 625, 626, 627, 628, 632, 640 and 12 additional credits of approved graduate course work.

**Biostatistics Option.** In this option, the required core courses are STAT 505, 532, 540, 550, 625, 626, 627 or 628, 632, and two 600-level courses from either the College of Health Sciences or the EVMS offerings in Epidemiology, Community Health, or History of Diseases and three hours of approved electives. It is strongly recommended the Master's Project be carried out at EVMS or any other department engaged in health sciences research.

## Master of Science in Education - Mathematics Major

Refer to the Darden College of Education section of the University catalog.

## Doctor of Philosophy - Computational and Applied Mathematics Major

**Admission**

Applicants who appear to be qualified for study at an advanced graduate level may be admitted to the doctoral program in computational and applied mathematics. These will be students with very strong backgrounds in mathematics, statistics. computer science, or application areas with a mathematics component (e g. physics or engineering).

Students may be admitted directly to the Ph.D. program with either a bachelor's or a master's degree. A grade point average of 3.00 (4.00 scale) in the major and related mathematics courses is required.

Students are required to submit three letters of recommendation and, if the student will not have completed a master's degree by the intended date of admission, GRE aptitude scores.

## Requirements

**Course Requirements.** A minimum of 55 credit hours of course work beyond the bachelor's degree (24 credit hours beyond the master's degree) and exclusive of doctoral dissertation work is required. Each student will be assigned a guidance committee, and together they will plan a complete program of course work designed to meet the student's objectives and to fulfill an option in applied mathematics or statistics/biostatistics. The student is strongly encouraged to select courses in more than one of these option areas and in a field of application whenever such courses contribute appropriately to his or her program. Each program, however, must be directed and approved by the student's guidance committee.

While the individual program will depend on the nature of the student's preparation prior to entering, each participant will ordinarily be required to complete one of the following options:

**Applied Mathematics Option.** The required courses are MATH 605, 617, 618, 622, 637, 638, 693, 817; and one of MATH 803 or 825.

**Statistics/Biostatistics Option.** In this option, the required core courses are: MATH 517, STAT 537, 550, 625, 626, 627, 628, 640, 827, 828. Students who wish to concentrate in Biostatistics must take STAT 540 and at least six credits at the 700-level from either the College of Health Sciences or the EVMS offerings in Epidemiology, Community Health, or History of Diseases.

**Research Skills.** Students are required to achieve proficiency at the advanced graduate level in either mathematics or statistics. This proficiency is validated by passing the Admission to Candidacy Examination.

**Foreign Language.** A foreign language is not required.

**Admission to Candidacy Examination.** At the end of the core mathematics or statistics course work and prior to selecting a dissertation advisor, the student must pass an Admission to Candidacy Examination designed to test scholarly competence and knowledge and to give the examiners a basis for constructive recommendations on subsequent study. The written portion of this examination will be based upon an examination syllabus that will be provided to each student. The outcome of this examination will be reported to the associate vice president for economic development, research and graduate studies as passed, failed, additional work to be completed, or to be re-examined. In the event of a re-examintion, the outcome must be reported as passed or failed. This decision is final. The examination must be passed at least eight months prior to the granting of the degree.

**Dissertation.** A doctoral dissertation representing an achievement in research and a significant contribution to the field is required. Students must register for Research 898 or 899 each semester in which they are doing substantial work on their dissertations. A minimum of 24 hours of such research credit is required.

**Defense of Dissertation. **This examination will be oral and must be completed at least four weeks before the date on which the degree is to be conferred. The dissertation committee members must have the completed dissertation at least two weeks before the date of the oral examination. Under normal circumstances, it is expected that the student will have had a research paper accepted for publication prior to the dissertation defense.