Bachelor of Science
Master of Science
Doctor of Philosophy
Research Activities
University Catalog

Bachelor of Science Degree Program

During the first two years, mathematics majors share many courses with other students. The mathematics curriculum includes courses with extensive theoretical content, as well as applied courses from related departments. Students can choose electives that will enable them to apply mathematics to engineering, the physical sciences, biological sciences, environmental studies, social sciences and business applications. Mathematics graduates who have successfully completed the program are prepared to pursue graduate work or take their place in industry along with engineers and scientists.

Degree Requirements

Required Courses

Mathematics

Computer Science

Communication and Humanities Core

Science

Electives

Note: Upper-division math courses may be offered in alternate years. Positioning of electives is unrestricted.

Elective Restrictions Choices of electives are subject to approval by the student's advisor. Math electives must include at least one proof-based course in addition to the required courses in discrete math and analysis. Examples of suitable courses include MTH 4015 Abstract Algebra and MTH 4105 Topology, MTH 4801 Advanced Geometry.

Applied area electives must be taken from a single area of application. Typically, this means from a single department or program other than mathematics. Any science or engineering program can be chosen. Suitably chosen management courses (courses with math prerequisites) can also be taken.

At least 30 elective credits must be at the 3000+ level.

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Master of Science Degree Program

The master's degree program in mathematics is designed to produce mathematicians with competence in analysis who have breadth and versatility in mathematics and its applications in related fields. To this end, students entering the master's program in mathematics are required to select an applied field in which they wish to develop some expertise and to complete six credits toward the degree from approved courses outside the math curriculum. In addition, the master's program is organized so that students will have the freedom to select some of their mathematics electives to develop their own special interests and to complement their choice of applied field. The flexibility in the elective part of the curriculum allows some students the opportunity to achieve a breadth of experience in mathematics and its uses in physical and engineering sciences, computer science or operations research. At the same time, it will allow other students to achieve more knowledge in a particular area in which they may wish to develop expertise. In either case, the program is organized to help students obtain an appropriate background for industrial employment or to pursue further graduate studies toward the doctoral degree. In either case, students will benefit from the range of options that are available in the mathematics master's program.

Students are encouraged to consider which combinations of elective mathematics courses are appropriate for their choice of applied specialization and to discuss the program with their advisors as soon as graduate study begins.

Admission Requirements
Applicants should have the equivalent of an undergraduate major in mathematics and must have completed undergraduate courses in differential equations and statistics, and have proficiency in FORTRAN or C. (Programming languages are noncredit courses for graduate mathematics students.)

Applications from graduates with undergraduate majors in the physical sciences or graduate students seeking a second master's degree are welcome. In such cases, however, it may be necessary for applicants to take courses in addition to the 36-credit degree requirement in those subjects where their backgrounds are deficient.

Degree Requirements
The master of science degree in mathematics requires a minimum of 36 credit hours of work beyond the bachelor's degree. For the thesis option, six hours of thesis are required. The thesis should demonstrate the candidate's abilities in the areas of reading and understanding mathematical literature, independent learning and written expression. Theses that combine mathematics with its applications in a related field are encouraged. A Nonthesis Option candidate must successfully complete an oral comprehensive examination.

Curriculum

Core Areas

Elective Courses

Twelve credit hours are to be devoted to elective courses in mathematics or in other scientific or engineering courses with a high degree of mathematical content. Six credit hours of electives can be devoted to writing a thesis. The selection of elective courses must have the faculty advisor's approval.

Applied Field

Six credit hours are to be devoted to the applied field requirement. This requirement consists of courses outside the mathematics program. The applied field courses must be at the 5000-level or above. The selection of applied field courses must have the faculty advisor's approval. Normally, only those subjects involving an appropriate degree of mathematical content are approved as applied field courses in a mathematics program.

Master's Thesis

Six credit hours of electives may be devoted to writing a thesis. The thesis is expected to be completed in two terms. The master's thesis in mathematics is expected to be a thorough investigation of a well-defined problem.

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Doctor of Philosophy Degree Program

The doctoral program in mathematics is designed to produce a mathematician with a broad background in analysis and a strong field of specialization in either nonlinear analysis, applied analysis, or numerical analysis and scientific computing. This combination of training will prepare the student for a career in a variety of areas, such as government or industrial research, or academic research and teaching. Doctoral graduates have the necessary experience in areas of application to be able to work successfully with other members of multidisciplinary research teams. Graduates also have the critical ability to think independently and analytically. They are able to make significant contributions to knowledge in their chosen fields of inquiry.

A preliminary program of study should be prepared by the student and advisor during the first semester of graduate studies. The final doctoral program of study must be approved by the student's advisory committee and program chair.

Admission Requirements
Applicants for the doctoral program in mathematics usually have a bachelor's or master's degree in mathematics. However, applications are also invited from graduates in physical and engineering sciences. In these cases, necessary undergraduate courses have to be taken to remove deficiencies before the student enters the doctoral program. In evaluating international applicants, due consideration is given to academic standards in the country in which the graduate studies were performed. Graduate teaching assistants carry on a variety of teaching assignments and in view of this, evidence of good English- speaking skills is an important criterion in processing the applications. For admission, a student should have a superior academic record and letters of recommendation. Preference will be given to applicants who have good scores in the Graduate Record Examination.

General admission requirements and the process for applying are presented in the Graduate Information and Regulations section of this catalog.

Degree Requirements
The degree of doctor of philosophy (Ph.D.) will be conferred primarily in recognition of the breadth of scientific accomplishment and of the power to investigate scientific problems independently, rather than for the completion of a definite course of studies. Although demanding a strong mathematical orientation, the doctoral program in mathematics does not fall within the traditional boundaries of a single academic unit and the scope is quite broad. Consequently, every course in a student's program of study is evaluated not only as to content, but also the way in which it complements other courses and furnishes breadth and depth to the program. The work should consist of advanced studies and scientific research that lead to a significant contribution and knowledge of a particular area.

Each student must 1) pass a preliminary examination or equivalent on the core courses; 2) complete an approved program of studies; 3) pass the comprehensive examination (usually oral); 4) complete a program of significant original research work; and 5) defend the dissertation concerning the research work completed.

General degree requirements are presented in the Graduate Information and Regulations section of this catalog.

Curriculum
After a bachelor's degree in mathematical sciences, a minimum of 81 credit hours is required for the doctoral program as detailed below:

Core Areas (30 credit hours)

Areas of Specialization (21-27 credit hours)

Nonlinear Analysis
Stochastic Analysis
Optimization
Numerical Analysis and Scientific Computing
Statistics

Considerable flexibility is allowed in the selection of courses in core areas and areas of specialization. Selected course offerings from the mathematics department and other areas of science and engineering may be taken to fulfill the requirements.

Doctoral Dissertation
The dissertation consists of 24-30 credit hours of work and is expected to be completed within two years. The doctoral dissertation is expected to represent original research in mathematics. It may present new theoretical developments or new areas of application or both. The dissertation should contain results that constitute a significant contribution to the literature of the field of investigation. These results should be worthy of publication in an established technical journal.

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Research Activities

Active areas of research in the mathematics program include methods of nonlinear analysis, qualitative and quantitative properties of nonlinear evolution equations, including differential equations with delay, integro-differential equations and stochastic differential equations, spectral theory of operators, reaction-diffusion equations, approximation theory, applied statistics, sequential analysis, mathematical programming, combinatorial optimization, operations research, queueing theory, stochastic processes, mathematical modeling, neural networks, numerical and computational mathematics with emphasis on numerical methods for ordinary and partial differential equations, numerical algorithms and parallel processing.

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