Teamwork: computational science and applied mathematics

Computational science and engineering, or CSE, is a relatively new and rapidly evolving field of study. It draws heavily on other fields, often using interdisciplinary teams of mathematicians and computer scientists working with scientists and engineers to solve problems requiring multiple areas of expertise. In this paper four examples of computational science in action illustrate the relation between CSE and the distinct but complementary disciplines it draws upon, focusing in particular on mathematics. Each example illustrates the need for interdisciplinary work. The training necessary for success in computational science, not surprisingly, is somewhat different from that traditionally prescribed by single academic disciplines. The use of the term applied mathematics is a little arbitrary. Some, applied mathematicians working in areas such as fluid dynamics are unconnected with applications, while the work of some core mathematicians in areas such as string theory and number theory makes fundamental contributions in applied areas such as mathematical physics and cryptography. We take applied mathematics to be that part of mathematics used in science and engineering.