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.

Innovative use of vodcast (Video-Podcast) to enrich learning experience in structures laboratory

Students may have difficulty in understanding some of the complex concepts which they have been taught in the general areas of science and engineering. Whilst practical work such as a laboratory based examination of the performance of structures has an important role in knowledge construction this does have some limitations. Blended learning supports different learning styles, hence further benefits knowledge building. This research involves an empirical study of how vodcasts (video-podcasts) can be used to enrich learning experience in the structural properties of materials laboratory of an undergraduate course. Students were given the opportunity of downloading and viewing the vodcasts on the theory before and after the experimental work. It is the choice of the students when (before or after, before and after) and how many times they would like to view the vodcasts. In blended learning, the combination of face-to-face teaching, vodcasts, printed materials, practical experiments, writing reports and instructors’ feedbacks benefits different learning styles of the learners. For the preparation of the practical, the students were informed about the availability of the vodcasts prior to the practical session. After the practical work, students submitted an individual laboratory report for the assessment of the structures laboratory. The data collection consisted of a questionnaire completed by the students, follow-up semi-structured interviews and the practical reports submitted by them for assessment. The results from the questionnaire were analysed quantitatively, whilst the data from the assessment reports were analysed qualitatively. The analysis shows that most of the students who have not fully grasped the theory after the practical, managed to gain the required knowledge by viewing the vodcasts. According to their feedbacks, the students felt that they have control over how to use the material and to view it as many times as they wish. Some students who have understood the theory may choose to view it once or not at all. Their understanding was demonstrated by their explanations in their reports, and was illustrated by the approach they took to explicate the results of their experimental work. The research findings are valuable to instructors who design, develop and deliver different types of blended learning, and are beneficial to learners who try different blended approaches. Recommendations were made on the role of the innovative application of vodcasts in the knowledge construction for structures laboratory and to guide future work in this area of research.

Blended learning approach to include the innovative use of vodcasts (video-podcasts) to enrich students learning experience in structures laboratory

Students may have difficulty in understanding some of the complex concepts which they have been taught in the general areas of science and engineering. Whilst practical work such as a laboratory based examination of the performance of structures has an important role in knowledge construction this does have some limitations. Blended learning supports different learning styles, hence further benefits knowledge building. This research involves the empirical studies of how an innovative use of vodcasts (video-podcasts) can enrich learning experience in the structural properties of materials laboratory of an undergraduate course. Students were given the opportunity of downloading and viewing the vodcasts on the theory before and after the experimental work. It is the choice of the students when (before or after, before and after) and how many times they would like to view the vodcasts. In blended learning, the combination of face-to-face teaching, vodcasts, printed materials, practical experiments, writing reports and instructors’ feedbacks benefits different learning styles of the learners. For the preparation of the practical laboratory work, the students were informed about the availability of the vodcasts prior to the practical session. After the practical work, students submit an individual laboratory report for the assessment of the structures laboratory. The data collection consists of a questionnaire completed by the students, and the practical reports submitted by them for assessment. The results from the questionnaire were analysed quantitatively, whilst the data from the assessment reports were analysed qualitatively. The analysis shows that students who have not fully grasped the theory after the practical were successful in gaining the required knowledge by viewing the vodcasts. Some students who have understood the theory may choose to view it once or not at all. Their understanding was demonstrated by the quality of their explanations in their reports. This is illustrated by the approach they took to explicate the results of their experimental work, for example, they can explain how to calculate the Young’s Modulus properly and provided the correct value for it. The research findings are valuable to instructors who design, develop and deliver different types of blended learning, and beneficial to learners who try different blended approaches. Recommendations were made on the role of the innovative application of vodcasts in the knowledge construction for structures laboratory and to guide future work in this area of research.

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.

Science learning and graphic symbols: an exploration of early years teachers’ views and use of graphic symbols when teaching science

The study investigated early years teachers’ understanding and use of graphic symbols, defined as the visual representation(s) used to communicate one or more “linguistic” concepts, which can be used to facilitate science learning. The study was conducted in Cyprus where six early years teachers were observed and interviewed. The results indicate that the teachers had a good understanding of the role of symbols, but demonstrated a lack of understanding in regards to graphic symbols specifically. None of the teachers employed them in their observed science lesson, although some of them claimed that they did so. Findings suggest a gap in participants’ acquaintance with the terminology regarding different types of symbols and a lack of awareness about the use and availability of graphic symbols for the support of learning. There is a need to inform and train early years teachers about graphic symbols and their potential applications in supporting children’s learning.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

Abstracts of communications: Proceedings of the thirty-nineth meeting of the Agricultural Research Modellers' Group

This group, which is concerned with the applications of mathematics to agricultural science, was formed in 1970 and has since met at approximately yearly intervals in London for one-day meetings. The thirty-ninth meeting of the group, chaired by Professor N. Crout of the University of Nottingham, was held in the Kohn Centre at the Royal Society, 6 Carlton House Terrace, London on Friday, 30 March 2007 when the following papers were read.