Applied mathematics focuses on the creation and study of mathematical and computational tools broadly applicable in science and engineering, and on their use in solving challenging problems in these and related fields.
From ecological modeling to electromagnetic theory, from robotics to meteorology, areas of investigation in Applied Mathematics are diverse.
Such applications can occur in any field of human endeavor. Most commonly known are those in science, economics or engineering, where, for example, Einstein invented the general theory of relativity by applying methods from differential geometry to the structure of space and time; Arrow probed the limits of democracy as an institution by calculating the probabilities that decisions cannot be reached on purely rational terms; Black, Sholes and Merton wrote down a fundamental formula for the price of an option, by applying the theory of random walks to the stock market; Shannon characterized an information source in mathematical terms, and in so doing laid the quantitative basis for modern information technology.
The interdisciplinary setting at Harvard provides an ideal environment for applied mathematics, with activities occurring both within and at the boundaries of many different fields, using a variety of mathematical and computational tools.
Researchers aim to:
- understand the mathematical concepts and techniques used to analyze, explain, or predict information (whether it relates to scientific and engineering measurements or the less precise data that describe certain aspects of our social, economic or ecological environment);
- study relations between models and observations; and
- examine the mathematical foundations and limitations of models and techniques and develop extensions.