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.

Inspecting the teaching of singing in the teacher training colleges of England, Wales and Scotland 1883-1899

This paper investigates the links between the teaching of singing, training and inspection during the late Victorian era. It utilises as a primary source the annual inspection reports of the music inspector, Sir John Stainer. More specifically it focuses upon the musical background of the students in the training colleges of England, Wales and Scotland, the methods employed to teach sight singing and voice production, the vocal repertoire and preparation for the teaching of singing in schools. Finally, some comparison is made with the present day and the relationship between the teaching of singing, training and inspection.

The role of drama in the teaching of speaking and listening as the basis for social capital

This paper explores how the concept of 'social capital' relates to the teaching of speaking and listening. The argument draws on Bourdieu's notion that a common language is an illusion but posits that an understanding of the grammar of speech can be productive in the development of both an understanding of what constitutes effective speech and the development of competence in speaking. It is argued that applying structuralist notions of written grammar is an inadequate approach to understanding speech acts or enhancing the creative use of speech. An analysis is made of how typical features of speech relate to dramatic dialogue and how the meaning of what is said is contingent upon aural and visual signifiers. On this basis a competent speaker is seen as being one who produces expressions appropriate for a range of situations by intentionally employing such signifiers. The paper draws on research into the way drama teachers make explicit reference to and use of semiotics and dramatic effectiveness in order to improve students' performance and by so doing empower them to increase their social capital. Ultimately, it is concluded that helping students identify, analyse and employ the aural, visual and verbal grammar of spoken English is not an adjunct to the subject of drama, but an intrinsic part of understanding the art form. What is called for is a re-appraisal by drama teachers of their own understanding of concepts relating to speech acts in order to enhance this area of their work.

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.

Contested and contesting identities: minority languages vs. the teaching of 'world' languages within the global cultural economy

This paper juxtaposes postmodernist discourses on language, identity and cultural power with historical forms of language inequalities grounded in the nation-state. The discussion is presented in three sections. The first section focuses on the mixed legacies of language-state relations within the pluralist nation-state, colonial and postcolonial language policies. The second section examines the concept of linguistic minority rights beyond the nation-state. This incorporates discussion of transmigration, the breaking up of previous power blocs in Eastern Europe and the role of language in the articulation of emergent 'ethnic' nationalisms. The third section examines the concept of multilingualism within the interactive cultural landscape defined by 'informationalism'. Discussing the collective impact of these variables on the shaping of new cultural, economic and political inequalities, the paper highlights the tensions in which the concept of linguistic minority rights exists in the world today.