Mathematical analysis and its applications
Mathematical analysis is concerned with quantifying change, continuity and approximation. This area provides a significant input into all other areas of mathematics, both pure and applied. Given the central role of this area within mathematical sciences and the shortage of UK academics in many areas of analysis, there is a need to grow the next generation of UK researchers.
The report of the EPSRC Pure Mathematics workshop considered there to be insufficient UK activity in mathematical analysis compared with international norms; training was identified as a particular issue. It was commented that there are many opportunities for increased links to other areas of the mathematical sciences. The International Review of Mathematical Sciences 2010 also noted that analysis was under-represented in the UK with a notable shortage of UK-trained talent.
Centres should cover a breadth of mathematical analysis ranging from pure to applied. Centres should engage with other areas of the mathematical sciences, and academic and non-academic users as appropriate so that students understand the context and potential impact of their research, and are able to facilitate two-way knowledge exchange.