Quantifying change, with a key role played by fundamental notions of continuity and approximation.
Mathematical analysis is concerned with quantifying change, with a key role played by fundamental notions of continuity and approximation. This research area includes, for example:
- Fourier and harmonic analysis
- operator theory
- ordinary and partial differential equations
- probability theory
- stochastic analysis
- applications of analysis.
Mathematical analysis has links with all other areas of pure and applied mathematics.
The UK is strong across all areas of mathematical analysis and we aim to maintain this world-leading position. This strategy recognises the research area’s many intradisciplinary links to all fields of mathematics and strong links to other disciplines, which will help it contribute strongly to the EPSRC outcomes. It also considers how best to support the people pipeline, given the major investment in relevant centres for doctoral training (CDTs).
High quality research
We aim to maintain high-quality research across the breadth of mathematical analysis to sustain support for core areas and drive developments in key challenges.
Encourage novel interactions
We aim to encourage novel interactions between mathematical analysis and application areas, particularly research relating strongly to EPSRC outcomes. There are many opportunities to engage with research challenges related to EPSRC ambitions, as a result of this area’s underpinning nature and links to all areas of mathematics, for example:
- mathematical biology
- mathematical physics
- continuum mechanics
- non-linear systems
- numerical modelling
- statistics and applied probability
- data science.
Support for early career analysts
Another aim is to increase support for early career analysts and so build capacity across the breadth of the area, to respond to growing demand for broad mathematical analysis skills. This recognises the relatively large number of well trained analysts in the UK delivered by investment in three CDTs. We wish to maintain this momentum and build on the greater connectedness of analysis, both in the UK and internationally.