Welcome to our site. I want to tell you a little about the research and philosophy of applied mathematics at Northwestern. We in the ESAM department are concerned with the formulation and solution of mathematics problems arising in engineering and in the natural sciences. The simplest way to describe applied mathematics is to describe what applied mathematicians do.
When confronted with an engineering or scientific problem, the applied mathematician will first either formulate a mathematical model of that problem or determine how to modify a suitable existing model. Most physical problems are just totally intractable when every possible physical effect is taken into account. Thus, all models which are suitable for analysis by applied mathematicians require some degree of simplification together with a precise statement of the underlying assumptions of the model. The ability to abstract a model from a physical problem is one of the essential ingredients of applied mathematics and is one of the key aspects of our graduate program where students are exposed to the principles of modeling from their very first day of classes.
After a suitable mathematical model has been formulated, the next task of the applied mathematician is to solve the equations of the model. Depending on the model the solution can be obtained by applying existing solution techniques or by developing new ones. Furthermore, some models can be solved by analytical means while other models require a combination of analytical and numerical methods. Solution procedures are another essential ingredient of applied mathematics and a key aspect of our graduate program, which includes courses in both analytical and numerical techniques.
The final task in analyzing a model is to compare with experimental or observational data. Often mathematical analysis of models reveals new and unexpected phenomena necessitating additional experimental investigations. Experiments can also reveal the need for modifications of the model, e.g., an extension to incorporate other phenomena in the model, or they can lead to a more extensive study, e.g., using large scale computation, to uncover other properties of the solution. At Northwestern, applied mathematics is coupled very tightly to engineering and science departments, and many of the faculty have ongoing research collaborations with experimentalists.
It is often the case that applied mathematics can also serve as a unifying approach to different science and engineering disciplines. For example, problems in diverse areas often have underlying similarities when formulated mathematically. Thus, what is learned in one discipline may also be used to advantage in a totally different discipline. Similarly, patterns associated with the solution of the models are often similar across a wide range of disciplines. Thus, an offshoot of a mathematical investigation of a problem can be to uncover similarities with phenomena in other application areas. Finally, our applied mathematics program can prepare you to deal with interdisciplinary problems which occur with increasing frequency in today's complex scientific and technological world.
Applied mathematics is a vigorous and growing science. At Northwestern, we have a strong graduate program, stressing both the methodologies and techniques of applied mathematics as well as specific applications. I am glad that you have accessed our website, and encourage you to contact us should you think that you might want to pursue studies in applied mathematics.
