Program Overview

Program Overview

The 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. 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.

Fields of Expertise

• Numerical Analysis
• Scientific Computing
• Machine Learning
• Operations Research
• Optimization
• Stochastic Processes
• Mathematical Biology
• Atmospheric Chemistry and Modeling
• Plasma Physics
• Inverse Problems

Program Structure

The program cooperates with the Department of Mathematics, and many of the courses taken by students are in the Department of Mathematics. Most students in the program have teaching assistantships in the Department of Mathematics.

Current Students

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 26 students enrolled in the program.

Comprehensive Exams

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
• in the particular area of the student's specialization

Research Topics

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
• chaotic dynamics in physics

Faculty and Research

The University of Iowa has become a center for the computational sciences, with 62 faculty in 16 different departments working on exciting research projects and eager to train students. The diversity of the areas of application is manifest in the descriptions provided by the faculty associated with the program. 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.