Computational and Applied Mathematics

Computational mathematics focuses on approximate solutions and reliable estimates of accuracy for mathematical problems arising in science, engineering, and industry. One pillar of research is numerical Analysis–the field of mathematics in which the convergence of numerical approximations are studied and robust error estimates derived. The other pillar is the practical and efficient implementation of numerical algorithms on computers, which not only exploits skills in general-purpose programming languages (C, Fortran, Python, etc.) but also benefits from working knowledge in several areas of computer science. Nearly every branch of modern science and engineering relies upon computational mathematics as a fundamental tool of verification and discovery.

Applied mathematics in the traditional sense of applied analysis remains one of the most vibrant research fields of modern mathematics. This includes areas such as ordinary differential equations (dynamical systems), partial differential equations (applied functional analysis), asymptotic analysis, and stochastic differential and partial differential equations. Many of the most challenging problems of the 21st century, such as climate, environmental and medical sciences, depend upon advancing knowledge in these fields. Engineering and industry are client applications, as well as inspirations, for much modern research. While closely linked to scientific modelling, applied mathematics maintains, at the same time, diverse connections with pure mathematics, including differential geometry, Lie algebras, harmonic analysis, functional analysis, probability theory, stochastic analysis, and many others.