Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.

Extending conceptual models for Web based applications

The next phase envisioned for the World Wide Web is automated ad-hoc interaction between intelligent agents, web services, databases and semantic web enabled applications. Although at present this appears to be a distant objective, there are practical steps that can be taken to advance the vision. We propose an extension to classical conceptual models to allow the definition of application components in terms of public standards and explicit semantics, thus building into web-based applications, the foundation for shared understanding and interoperability. The use of external definitions and the need to store outsourced type information internally, brings to light the issue of object identity in a global environment, where object instances may be identified by multiple externally controlled identification schemes. We illustrate how traditional conceptual models may be augmented to recognise and deal with multiple identities.

Improving the Flexibility of Active Grids through Web Services

Active Grids are a form of grid infrastructure where the grid network is active and programmable. These grids directly support applications with value added services such as data migration, compression, adaptation and monitoring. Services such as these are particularly important for eResearch applications which by their very nature are performance critical and data intensive. We propose an architecture for improving the flexibility of Active Grids through web services. These enable Active Grid services to be easily and flexibly configured, monitored and deployed from practically any platform or application. The architecture is called WeSPNI ('Web Services based on Programmable Networks Infrastructure'). We present the architecture together with some early experimental results on using web services to monitor data movement in an active grid.