Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Simultaneous observations of reconnection pulses at Cluster and their effects on the cusp aurora seen at Chinese Yellow River Station

While the Cluster spacecraft were located near the high-latitude magnetopause, between 10:10 and 10:40 UT on 16 January 2004, three typical flux transfer event (FTE) signatures were observed. During this interval, simultaneous and conjugated all-sky camera measurements, recorded at Yellow River Station, Svalbard, are available at 630.0 and 557.7nm that show poleward-moving auroral forms (PMAFs), consistent with magnetic reconnection at dayside magnetopause. Simultaneous FTEs seen at the magnetopause mainly move northward, but having duskward (eastward) and tailward velocity components, roughly consistent with the observed direction of motion of the PMAFs in all-sky images. Between the PMAFs meridional keograms, extracted from the all-sky images, show intervals of lower intensity aurora which migrate equatorward just before the PMAFs intensify. This is strong evidence for an equatorward eroding and poleward moving open-closed boundary (OCB) associated with a variable magnetopause reconnection rate under variable IMF conditions. From the durations of the PMAFs we infer that the evolution time of FTEs is 5-11 minutes from its origin on magnetopause to its addition to the polar cap.

Models, mathematics and meaning in interdisciplinary research

Interdisciplinary research presents particular challenges for unambiguous communication. Frequently, the meanings of words differ markedly between disciplines, leading to apparent consensus masking fundamental misunderstandings. Researchers can agree on the need for models, but conceive of models fundamentally differently. While mathematics is frequently seen as an elitist language reinforcing disciplinary distinctions, both mathematics and modelling can also offer scope to bridge disciplinary epistemological divisions and create common ground on which very different disciplines can meet. This paper reflects on the role and scope for mathematics and modelling to present a common epistemological space in interdisciplinary research spanning the social, natural and engineering sciences.

Uneven playing field or falling standards? Chinese students' competence in English.

This paper explores student and teacher perspectives of challenges relating to the levels of competence in English of Chinese students studying overseas from the perspective of critical pedagogy. It draws on two complementary studies undertaken by colleagues at the University of Reading. The first—a research seminar attended by representatives from a wide range of UK universities—presents the views of teachers and administrators; the second draws on four case studies of the language learning of Chinese postgraduate students during their first year of study in the UK, and offers the student voice. Interview and focus group data highlight the limitations of current tests of English used as part of the requirements for university admission. In particular, university teachers expressed uncertainty about whether the acceptance of levels of written English which fall far short of native-speaker competence is an ill-advised lowering of standards or a necessary and pragmatic response to the realities of an otherwise uneven playing field. In spite of this ambivalence, there is evidence of a growing willingness on the part of university teachers and support staff to find solutions to the language issues facing Chinese students, some of which require a more strategic institutional approach, while others rely on greater flexibility on the part of individuals. Although the studies reported in this paper were based on British universities, the findings will also be of interest to those involved in tertiary education in other English-speaking countries which are currently attracting large numbers of Chinese students.