Analysis and probability
Equations – functional, differential, partial differential – are used to describe and study many important processes in all areas of research and everyday life. These processes and application areas range from biology, for example in cell division, to economics such as in price fluctuations, to physics in the production of electricity by a wind farm.
Many everyday processes exhibit stochastic (or random) behaviour in at least some of their characteristics. Cells may be subject to varying conditions; prices depend on changing market environments which are in turn subject to changes due to exogenous events, and winds are highly dependent on weather patterns. This leads to the need to study stochastic processes.
Rapid advances in technology bring with them the need to explore new systems. The spread of an epidemic through a population, the structure of a social network and the movement of information in it; the evolution of parameters of a machine-learning algorithm, the quality of signal in a 5G network – these are all examples of processes one can model by a set of equations on some variables.
Studying the behaviour of solutions of functional equations, with or without a stochastic component, presents challenging fundamental problems in mathematics but leads to impact in a vast range of application areas. In most cases, explicit solutions are not known, and one needs to study their asymptotics (limiting behaviours) approximations, and their properties in some limiting regimes. Our experts are working on these and numerous analytical problems.
Mathematical Sciences are at the core of technological progress, driving innovations in artificial intelligence, data security, and computational modelling that shape critical sectors like finance, healthcare, and engineering. At the School of Mathematical and Computer Sciences (MACS), Heriot-Watt University brings together experts in mathematics, actuarial science, statistics, and computer science to tackle global challenges through interdisciplinary research.
By collaborating with industry and academic partners, MACS plays a pivotal role in supporting Heriot-Watt’s globally renowned research institutes, including The National Robotarium, The Lyell Centre for Earth and Marine Sciences and Technology, The Global Research Institute in Health and Care Technologies, and iNetZ+ Global Research Institute for Net Zero and Beyond. This ensures that MACS research has both theoretical significance and real-world impact, contributing to the university’s mission of advancing global innovation and societal benefit.