The following document was circulated within the research community in spring 1996.
As part of its continuing support for the health of both IT and Computer Science and Mathematics, the EPSRC is considering developing a programme to foster and improve the links between the two disciplines.
A steady pull-through of new research in mathematics is considered to be essential for the sustained development of Information Science, and ultimately its success in supporting the engineering and application of Information Technology in industry and commerce. For Mathematics too, there are advantages to strengthening links with the IT community. Recognition of the underpinning role and the relevance of much of pure mathematics for IT can provide a strong drive for mathematical research, not restricted to narrowly defined or directed programmes.
Initial consultation by EPSRC and the London Mathematical Society (LMS) has suggested that there are many pressing opportunities for bringing the communities together in a joint programme, driven by both industrial and scientific need, and for laying the groundwork for substantial collaboration in future generations. This document is intended to serve as the basis for further consultation with the two communities on the requirement, direction, and priorities for a possible EPSRC programme to stimulate and direct inter-disciplinary links in areas of research, training and information exchange.
This proposed programme is broadly modelled on the successful LOGFIT initiative mounted by the former Science and Engineering Research Council, which was responsible for encouraging mathematical logicians and their students to address their skills to problems arising in IT.
In recent years, questions in information science and engineering have provided the spur for much of the new work in the relevant areas of pure mathematics, which in turn has led to real technological advance. For example:
the transputer and the Z specification language have won Queen's awards to industry, and depend on advances in language semantics;
CAD and computer algebra systems are widely used and depend on basic research in geometry and algebra;
modern data security techniques depend on fundamental work in group and number theory;
analysis of the behaviour of complex networks relies on understanding of dynamical and stochastic systems.
Applied mathematics has a long tradition of interaction with computer science, through the development of numerical procedures. Here we are concerned with the interplay between pure mathematics and computer science, which has traditionally centred around areas in logic, category theory and discrete mathematics. In recent years new connections between mathematics and computer science have emerged from such unexpected quarters as algebraic topology, differential geometry, dynamical systems and operator algebras.
These new developments hold the promise of bringing new insights and powerful mathematical tools to bear on problems in computing, and are already attracting the attention of the industrial community through work at the Hewlett Packard Basic Research Institute of the Mathematical Sciences at Bristol. At the same time such problems have opened new avenues of exploration for pure mathematicians.
By way of example, the January 1994 issue of the IEEE Transactions has articles on interactive communication, cellular telephone systems, detection, random sequences, convolutional codes, public-key cryptosystems and authentication. The mathematical areas concerned include probability theory, finite group theory, finite fields, algebraic geometry, linear algebra, and polynomial rings.
The aims of the proposed programme are:
to develop a climate in which new links between mathematics and information science can flourish so as to stimulate and support high quality research in both fields;
to provide the training needed to enable high quality research students to move into these new areas;
to ensure that the wider community is aware of recent developments and trained in the contemporary scientific and mathematical techniques to understand and implement them;
to enable senior scientists of high quality in mathematics and computer science to work in collaboration, and to develop research programmes in new areas complementary to their own.
This is seen as a science led programme; however, an initial consultation suggests that the following descriptions are suggestive of mathematical areas and applications in which new developments are either already appearing, or are strategically important:
discrete mathematical structures, algorithms and combinatorics;
mathematical foundations of computer languages (including ordered structures, game theory, knowledge theory, domain theory, etc.);
complexity, including communicating systems;
computational geometry and computer vision (including the mathematics of Virtual Reality);
mathematics of artificial intelligence (including planning, scheduling, mathematics of reasoning) and neural computing;
networks and telecommunications (including digitalisation, signal processing, routing, cryptography, information security - involving graph theory, error correcting codes, etc.).
This list is by no means exhaustive, and other areas identified by the community may be added in the future.
One aim of Mathfit is to create a climate in which new connections can emerge supporting new applications and industries. In this way, appropriate mathematical support may be provided for IT initiatives in line with Foresight and in pursuit of EPSRC's mission, while at the same time stimulating the emergence of new initiatives from the academic resources of the country.
An EPSRC mechanism is proposed, which would be co-ordinated jointly by the Mathematics and IT & Computer Science Programmes of EPSRC. Programme managers would draw on the advice of the two communities for guidance and peer review as appropriate. The programme will make full use of the mechanisms available under EPSRC in order to achieve the above aims. These may include:
Supporting a series of workshops and summer schools aimed at EPSRC funded research students, academics and industrialists in mathematics, computer science and engineering. Such meetings are considered to be exceptionally good value for the low cost of supporting EPSRC student participation. They serve to establish new cross-disciplinary communities and develop the expertise for courses to be run in home institutions to benefit future generations of students, eventually being reflected in the undergraduate curriculum.
Encouraging the transfer of personnel between institutions and departments for periods to establish collaborative research programmes across disciplinary lines. Existing mechanisms, such as the Visiting Fellowship Scheme, provide one model for this.
Encouraging research grant proposals within the 'conditional responsive' grants mode. This would mean that certain conditions would be imposed upon proposals (such as requiring collaborative proposals from different disciplines), to ensure that the priority areas are targeted and the objectives of the programme are advanced, but the actual research direction of a particular proposal would still be determined by the proposes themselves. Steps will need to be taken to ensure that the interdisciplinary nature of the programme does not disadvantage proposals, which will still be in competition with other proposals received in the responsive mode. The new mechanism of project studentships associated with research grant proposals may also prove of particular value here.
There is a wealth of talent and expertise in mathematics in the UK, and a continual stream of gifted students renewing that talent and potential. While the mathematics of physical processes and materials is well-established in the undergraduate curriculum, this is not the case for those aspects of pure mathematics that is increasingly applied in the discrete world of IT today. This initiative is intended as support for those mathematical areas that have not traditionally been seen as directly applicable to technology and engineering but which are now beginning to demonstrate significant relevance.
It is proposed that this programme should run for 3 years in the first instance, but there is considerable scope to strengthen these links and to establish them as a permanent and thriving aspect of mathematical and computational research in the UK, a situation which would be of great import for the foundations of present and future information technologies.
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