Applied Mathematical and Computational Sciences (AMCS) at The University of Iowa is a broad-based interdisciplinary Ph.D. program for students desiring to study mathematics and a companion science so that they can apply their mathematical skills to significant scientific problems. The main goal of the program is to nurture applied mathematicians with sufficient professional experience and versatility to meet the research, teaching, and industrial needs of our technology-based society.
The University of Iowa has become a center for the computational sciences. Because of expertise in fields such as numerical analysis, mathematical programming, parallel and vector processing, hydraulics and fluid mechanics, heat transfer, dynamic simulation of mechanical systems, optimization in management sciences and industrial engineering, discrete event simulation, robotics, atmospheric and environmental studies, climate/chemistry modeling, geographical decision making, theoretical and plasma physics, and pharmacological and biological modeling, the computational sciences are now an important part of the program. There is a demand for mathematical scientists who are trained to use a computational sciences approach in relevant problems. Our 65 faculty in 17 different departments are working on exciting research projects and are eager to train students. The diversity of the areas of application is manifest in the descriptions provided by the faculty associated with the program in the AMCS Faculty Personal Pages.
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.
While building a base in the Mathematical Sciences, students acquire skills in another area of their own interest, chosen from the behavioral, biological, business, engineering, medical, physical, or social science areas. Most students concentrate on applied mathematics such as differential equations, numerical analysis or optimization, but a few students have used statistics as their mathematical science base.
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.