Program Overview

The ACMS program is structured into a core and a set of options. The same set of core courses is required for all options (with some exceptions). Students declaring an ACMS major need to choose an option at that time. Options come in two varieties: associated with a particular application domain, or with a particular area of specialization in the mathematical sciences.

Options associated with an applications domain

Biological and Life Sciences. Application of mathematical modeling and computation is paving the way for great strides in our understanding of basic biological phenomena. Training in the mathematical sciences is becoming essential for modern research in a wide variety of biological and medical disciplines, including developmental biology, genetics and genomics, ecological modeling, physiology, and biomechanics. The Biological and Life Sciences option focuses on basic techniques of mathematical modeling and computation that are employed in these disciplines. It is also ideal as a second major for students in the Biological and Life Sciences.

Mathematical Economics. Mathematical and statistical models are becoming increasingly important as tools for prediction and analysis in the business world. Students choosing the Mathematical Economics option will acquire a solid foundation in applied and computational mathematics as well as a grounding in economic theory. It is also ideal as a second major for students in Economics who want more mathematical training, especially those preparing for graduate school, since the academic field of Economics relies heavily on mathematical and statistical modeling.

Social and Behavioral Sciences. Solving complex problems in the social and behavioral sciences requires sophisticated approaches to gathering and analyzing large amounts of data. Creating mathematical models useful in prediction and analysis relies on a broad range of mathematical techniques including graph theoretical analysis, Markov chains and other stochastic processes, or differential equations. The Social and Behavioral Sciences option provides a foundation in commonly-used statistical and computational techniques followed by flexibility in pursuing different sets of advanced courses. It is also ideal as a second major for students in social sciences who want to obtain more background in quantitative methods and mathematical techniques.

Engineering and Physical Sciences. Mathematical models form the basis for much of our understanding of the physical world and are used to predict and analyze complex phenomena. Theoretical and computational linear algebra, Fourier analysis, and differential equations are particularly important since they are essential in modeling mechanical systems, heat transfer, fluid dynamics, and wave motion of all kinds (electromagnetic, sound, seismic, water waves, etc.). The Engineering and Physical Sciences option exposes students to these classical areas of applied mathematics. It is also ideal as a second major for students in engineering or a physical science.


Options associated with a specialization in the mathematical sciences

Discrete Math and Algorithms. This option gives students a broad background in mathematics and computation with special emphasis on discrete mathematics and its application to optimization and algorithm design. It is particularly well suited for students who are interested in mathematical aspects of Computer Science, or who wish to pursue an ACMS / CSE double major.

Operations Research. Operations research is concerned with system modeling and optimal decision making in a deterministic or stochastic setting. Such problems frequently arise in the context of resource management, portfolio selection, logistics planning, vehicle routing, scheduling, and inventory control. The Operations Research option provides a foundation in the mathematical tools of operations research, particularly optimization and stochastic modeling.

Scientific Computing and Numerical Analysis. Computer simulation is heavily used in science and engineering as a tool in analysis, visualization, and design. Complex mathematical models can give very accurate prediction of real-world phenomena, but typically lead to equations that can only be solved with the aid of a computer. The Scientific Computing and Numerical Analysis option focuses on the design, mathematical analysis, and efficient implementation of numerical algorithms for such problems.

Statistics. Statistics is concerned with methods for the acquisition, management, exploration, and use of information, in order to learn from experience and to make decisions under uncertainty. Statistical methodology is applied throughout the physical and social sciences, engineering, and business. Indeed, it provides the basis for the evaluation and exploration for much of our empirical knowledge of physical and social phenomena. The Statistics option is designed to introduce students to theory, methodology, and applications of statistics. It is ideally suited as a second major for students with a primary focus in the biological sciences, earth sciences, social sciences, engineering, or management science.