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Details of Grant 

EPSRC Reference: EP/L016516/1
Title: EPSRC Centre for Doctoral Training in Analysis (Cambridge Centre for Analysis)
Principal Investigator: Norris, Professor J
Other Investigators:
Peake, Professor N
Researcher Co-Investigators:
Project Partners:
BP EADS L-3 TRL Technology
MathWorks Microsoft Schlumberger
Waymont Consulting Limited
Department: Pure Maths and Mathematical Statistics
Organisation: University of Cambridge
Scheme: Centre for Doctoral Training
Starts: 01 May 2014 Ends: 31 October 2022 Value (£): 3,239,837
EPSRC Research Topic Classifications:
Mathematical Analysis
EPSRC Industrial Sector Classifications:
Electronics Energy
Aerospace, Defence and Marine Information Technologies
Related Grants:
Panel History:
Panel DatePanel NameOutcome
23 Oct 2013 EPSRC CDT 2013 Interviews Panel E Announced
Summary on Grant Application Form
Our proposal builds on the successful start made by Cambridge Centre for Analysis (CCA), a current EPSRC Centre for Doctoral Training. We propose to develop further our activity in two important and rapidly evolving areas of analysis, namely mathematics of information and statistics of complex systems.

Beginning with Newton, for whom the development of calculus and the mathematical understanding of bodies in motion were closely intertwined, the mathematics used to describe real phenomena consistently involves notions of continuity, rate of change, average value, and basic challenges such as the relationship between discrete and continuum objects. This is the domain of analysis, encompassing modelling by partial differential equations and by random processes, and the mathematical theory which guides effective computation for such models.

The centrality of mathematical analysis in the relationship between mathematics and its applications has been acknowledged by successive International Reviews of Mathematics, as has the need to increase the capacity of UK PhD training in analysis. Mathematical Analysis and its Applications is an EPSRC Priority Area.

Beyond the established and important uses of analysis in modelling physical phenomena, digital technology has created new areas where mathematical analysis, in guiding the extraction of knowledge from massive discrete systems, plays an essential role. These include the fields of high-dimensional statistics and the mathematics of information, including compressed sensing. In each of these, one is looking for a reliable means to interpret massive high-dimensional data. Already several CCA students are working in these areas. Big Data is one of the Eight Great Technologies championed by the Minister for Universities and Science. Statistics and Data to Knowledge are EPSRC Priority Areas.

We propose a first year training programme based on our current successful model, now expanded by two further core courses, one in Statistics of Complex Systems and one in Mathematics of Information. These new courses will be paired with postgraduate level courses from the existing Cambridge Masters' (MASt), which students can use to consolidate their understanding. The core courses themselves are based on supervised student team assignments leading to student presentations. The other main components of the first year are research mini-projects (often the route to a PhD project) and an industry workshop. Years two to four are devoted mainly to the PhD thesis.

First year training establishes a collaborative ethos in the cohort and, by mixing students with different prior skills, encourages cross-fertilization of ideas across the different threads of analysis. This is sustained in later years through a programme of seminars, workshops and training in transferable skills. The students appreciate that their collective understanding of a given problem using different skills will often exceed each individual's understanding. This makes cohort-based training especially valuable in analysis.



We already expose all our students to the role of mathematics and the opportunities for mathematicians in industry and society, and we encourage first-hand engagement with applications through mini-projects, industrial seminars and study weeks, and, for some, PhD projects with industrial partners. The development of core skills and eventually the ability to generate new ideas is the hardest and crucial part of training as a research mathematician. This is necessarily our overriding task, in which we seek synergy and inspiration from user engagement. In the new CDT, our network of industrial connections will be further enhanced, along with our collaborations with Cambridge engineering colleagues, and our links with the Smith Institute for Industrial Mathematics.
Key Findings
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Potential use in non-academic contexts
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Organisation Website: http://www.cam.ac.uk