The Department offers the M.S. and Ph.D. degrees in mathematical sciences. The Master's Degree is based on developing breadth as well as depth in the mathematical sciences; it requires two years of course work and culminates with a master's project, taken under the direction of a faculty member. The Ph.D. Degree generally requires at least three years of work beyond the master's degree.
The master's degree program requires breadth of exposure in the mathematical sciences and depth of concentration in one particular area. For breadth, each student selects courses to satisfy certain distributional requirements across the spectrum of mathematical sciences. For depth, each student, in consultation with a faculty adviser, chooses six courses which comprise a meaningful concentration in some specialty within the mathematical sciences. Each student's overall program must contain courses with a significant modeling component. A minimum of 37 credit hours of courses are needed to complete the master's program (twelve three-credit courses plus the one-credit master's project course). Typical M.S. programs total 40 hours.
Entering students are expected to have undergraduate courses in linear algebra, differential equations, a computer language, and statistics. The curriculum includes foundation courses (advanced calculus, modern algebra, probability, and discrete computing courses -- often taken prior to entering the master's program). The breadth requirement consists of six graduate courses: one from each of algebra/combinatorics, applied analysis, computing, operations research, probability and statistics, and financial mathematics plus one additional course in operations research or statistics. In addition, six courses are selected to define an identifiable concentration area. Every student's program is required to include at least one course, possibly chosen from outside the Department of Mathematical Sciences, that emphasizes mathematical modeling. As a means of integrating the student's program of diverse study, a master's project must be completed by the end of the second year. The student makes an oral and written presentation of the master's degree project.
A faculty adviser is assigned to every incoming student prior to preregistration for the first semester of enrollment. Each student chooses an adviser and master's committee during the second semester. There is considerable flexibility to the topic of the master's project work; in some cases it can involve consulting for an external client and may generate financial support for the student.
The doctoral program is similar in structure to the M.S. program in that it contains both breadth and depth components. Including the course work completed for the master's degree, a doctoral program incorporates two courses from each of the major areas of the mathematical sciences (algebra/combinatorics, analysis, computation, operations research, and probability/statistics) as well as other courses in the selected concentration area. A doctoral program generally consists of 60 or more hours of graduate coursework. All students with a B.S. degree who enter the PhD program must complete the MS degree at the end of the second year, following the MS guidelines listed above.
Students are admitted to candidacy for the Ph.D. degree upon successful completion of the preliminary examination and the comprehensive examination. The preliminary examination consists of tests in three areas chosen from algebra, analysis, computation, operations research, statistics, and stochastic processes. Upon completion of the preliminary examination, the student chooses a research committee and adviser, and also submits a plan of study. The comprehensive exam assesses the student's readiness to perform independent research and competency in advanced graduate material. It usually includes a thesis proposal and is administered by the student's advisory committee. A final examination is administered by that committee prior to receipt of the doctoral degree. You must complete the comprehensive exam within two semesters of passing the preliminary exams. Any deviation requires a statement from the advisory committee which must be aprroved by the Graduate Coordinator (in some cases the Graduate Affairs Committee).
The Ph.D. program structures the five areas of the mathematical sciences into three disciplines: applied and computational analysis, discrete mathematics, and statistics and probability. Doctoral research culminating in a dissertation within one of these discipline may range from work having a strong modeling component to work that is primarily theoretical. A student's Ph.D. program must include both a concentration area and a supporting area. Further descriptions of these three areas are given below.
The discipline of applied and computational analysis encompasses the study of dynamical systems (ordinary, integral, partial differential equations), numerical analysis, functional analysis, and harmonic analysis. Research topics within this discipline are closely related to problems that arise in engineering, economics, and the biological sciences. A plan of study within this discipline will emphasize courses in theoretical analysis, dynamical systems, numerical analysis, and physical system modeling.
The discipline of discrete mathematics encompasses algebra, combinatorics/graph theory, computational mathematics, and operations research. Research topics include algebraic structures, algorithms, combinatorial optimization, cryptography, discrete computing, graph theory, mathematical programming, matrix theory, and networks -- emphasizing the interdisciplinary and broad-based nature of this discipline.
The discipline of statistics and probability encompasses mathematical statistics, statistical methodology/data analysis, and stochastic models. These three areas comprise the core upon which research progress in statistical theory and methods is based.