We can characterize what applied mathematicians should learn by examining what they do. Mathematical scientists who identify themselves primarily as applied mathematicians function in complementary dual roles in varying proportions. Department Website Department Undergraduate Page
First, they develop, implement, and study mathematical, statistical, and computational techniques broadly applicable in various fields. Second, they bring mathematical modeling skills to bear on particular scientific problems through judicious approximations to obtain novel insights and predictions when the underlying phenomena are thought to be relatively simple and well understood, or through the creation of conceptual frameworks for quantitative reasoning and measurement when the underlying phenomena are complicated and less well understood. In their methodological role, applied mathematicians may function temporarily as mathematicians, statisticians, or computer scientists; in their phenomenological role, they may function temporarily as physicists, chemists, biologists, economists, engineers, and the like. In both roles, they must possess relevant knowledge, technical mastery, and educated taste; clearly this necessitates specialization.
Ideally, applied mathematicians demonstrate over time substantive involvement with both the mathematical and scientific aspects of their dual roles. Inside academia, their activities are usually carried out in collaboration with students or colleagues; outside academia, they often serve as part of a multidisciplinary team tackling complex problems under time and resource constraints. In either context, a premium is placed on outstanding ability to communicate with fellow technical professionals. Applied mathematics is inherently interdisciplinary, in motivation and in operation. This vision informs the design of the concentration.
The Applied Mathematics concentration involves a broad undergraduate education in the mathematical sciences, especially in those subjects that have proved vital to an understanding of the world around us, and in some specific area where mathematical methods have been substantively applied. The goal is to acquire experience at a mature level, consistent with the nature of a Harvard undergraduate education. Generally, students select the concentration because they like to use mathematics to solve real-world problems. Some want a deeper involvement with an area of application than may be provided within a mathematics, statistics, or computer science concentration. Others want a more mathematically-oriented approach to an area of application than that normally provided within the corresponding concentration; mathematical economics is a prime example. Yet others want a special program not otherwise available, usually involving an area of application in which mathematical modeling is less common.