Research in computationally-based mathematics is a strong feature of the Department. There are active research programs in numerical analysis and scientific computing, together with links to other computational endeavours within the department and throughout the university. The MIR@W Program provides a steady flow of visitors, whose interests lie in computational mathematics, to the department.

Computationally-based research within the department includes work on the analysis and design of algorithms for dynamical systems and stochastic processes, the development of models and methods for fast, interactive simulations of reaction-diffusion partial-differential equations, exploiting methods for large sparse linear systems to compute solutions and bifurcations in discretisations of partial-differential equations involving large numbers of variables, Computational Group Theory and a variety of problems in applied mathematics where intensive simulation is central, such as Mathematical Biology. Interactions outside the department include the Centre for Scientific Computing, the Foundations of Computer Science Research group within Computer Science and a variety of problems in Scientific Computing, such as Computational Fluid Dynamics.