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# Graduate Study

In 1992, the program name was changed from Applied Mathematical Sciences to Applied Mathematical and Computational Sciences, which better describes the current nature of the program. Some aspect of the computational sciences has been a part of the dissertation research of nearly all recent graduates. Although it is a separate, independent academic unit in the Graduate College, the program cooperates with the Department of Mathematics. Many of the courses taken by students are in the Department of Mathematics, and most students in the program have teaching assistantships in the Department of Mathematics.

The AMCS program differs from other Ph.D. programs because it is flexible and individualized and because it requires study in both a science and a mathematical science. It is not designed to replace existing departmental Ph.D. programs at The University of Iowa. For example, individuals interested primarily in mathematical aspects of applicable mathematics should apply to the graduate program in the Department of Mathematics, which has many faculty members interested in ordinary and partial differential equations, numerical analysis, optimization, mathematical physics, and biomathematics. Students interested primarily in a science may fit into another departmental Ph.D. program since many of these programs involve some aspects of applied mathematics, statistics, or computer science.

The program is suitable for those who are capable of graduate study in both a mathematical science and another science and who want to do dissertation research on a problem in the scientific area which involves the use of graduate-level mathematics.

Currently, there are about 35 students enrolled in the program. This small size means that students have more direct contact with faculty members. Each student's faculty committee helps plan a program consistent with the student's background, interests, and goals, which should develop expertise in methods of application of mathematics, build a good foundation in related topics of theoretical mathematics, and provide sufficient knowledge in a particular science so the student can use mathematical techniques in that science.

Each student takes comprehensive examinations in three areas: in a theoretical foundation area, in the applied mathematics that is useful in the student's chosen field, and in the particular area of the student's specialization. Each student's dissertation research should include the activities of a mathematical scientist. For example, this could involve formulation of a model, quantitative analysis of the model, and interpretation of the results.

Research topics of students have included geometric programming and entropy optimization problems, the computational finite analytic method for three-dimensional fluid mechanics problems, the effects of monetary policy on economic optimization problems, global optimization problems in manufacturing management, efficient algorithms for computer-aided design problems, effective numerical algorithms for mechanical systems simulation, a modified finite analytic method to solve concavity flow problems, computational exterior flow problems in fluid mechanics, digital signal processing, neural networks, computer-aided simulation of automobile performance, optimization in robotic trajectory design, and chaotic dynamics in physics.