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.

The first international workshop on the role and impact of mathematics in medicine: a collective account

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for inter- disciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining

Conjecture, proof, and sense in Wittgenstein's philosophy of mathematics

One of the key tenets in Wittgenstein’s philosophy of mathematics is that a mathematical proposition gets its meaning from its proof. This seems to have the paradoxical consequence that a mathematical conjecture has no meaning, or at least not the same meaning that it will have once a proof has been found. Hence, it would appear that a conjecture can never be proven true: for what is proven true must ipso facto be a different proposition from what was only conjectured. Moreover, it would appear impossible that the same mathematical proposition be proven in different ways. — I will consider some of Wittgenstein’s remarks on these issues, and attempt to reconstruct his position in a way that makes it appear less paradoxical.

The MaPS project: mapping teacher conceptions of musical development

The chapter starts from the premise that an historically- and institutionally-formed orientation to music education at primary level in European countries privileges a nineteenth century Western European music aesthetic, with its focus on formal characteristics such as melody and rhythm. While there is a move towards a multi-faceted understanding of musical ability, a discrete intelligence and willingness to accept musical styles or 'open-earedness', there remains a paucity of documented evidence of this in research at primary school level. To date there has been no study undertaken which has the potential to provide policy makers and practitioners with insights into the degree of homogeneity or universality in conceptions of musical ability within this educational sector. Against this background, a study was set up to explore the following research questions: 1. What conceptions of musical ability do primary teachers hold a) of themselves and; b) of their pupils? 2. To what extent are these conceptions informed by Western classical practices? A mixed methods approach was used which included survey questionnaire and semi-structured interview. Questionnaires have been sent to all classroom teachers in a random sample of primary schools in the South East of England. This was followed up with a series of semi-structured interviews with a sub-sample of respondents. The main ideas are concerned with the attitudes, beliefs and working theories held by teachers in contemporary primary school settings. By mapping the extent to which a knowledge base for teaching can be resistant to change in schools, we can problematise primary schools as sites for diversity and migration of cultural ideas. Alongside this, we can use the findings from the study undertaken in an English context as a starting point for further investigation into conceptions of music, musical ability and assessment held by practitioners in a variety of primary school contexts elsewhere in Europe; our emphasis here will be on the development of shared understanding in terms of policies and practices in music education. Within this broader framework, our study can have a significant impact internationally, with potential to inform future policy making, curriculum planning and practice.

Environmental justice and conceptions of the green economy

Green economy has become one of the most fashionable terms in global environmental public policy discussions and forums. Despite this popularity, and its being selected as one of the organizing themes of the United Nations Rio+20 Conference in Brazil, June 2012, its prospects as an effective mobilization tool for global environmental sustainability scholarship and practice remains unclear. A major reason for this is that much like its precursor concepts such as environmental sustainability and sustainable development, green economy is a woolly concept which lends itself to many interpretations. Hence, rather than resolve long-standing controversies, green economy merely reinvigorates existing debates over the visions, actors and policies best suited to secure a more sustainable future for all. In this review article, we aim to fill an important gap in scholarship by suggesting various ways in which green economy may be organized and synthesized as a concept, and especially in terms of its relationship with the idea of social and environmental justice. Accordingly, we offer a systemization of possible interpretations of green economy mapped onto a synthesis of existing typologies of environmental justice. This classification provides the context for future analysis of which, and how, various notions of green economy link with various conceptions of justice.

Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.