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.

Let's Dance: A Language for Service Behavior Modeling

In Service-Oriented Architectures (SOAs), software systems are decomposed into independent units, namely services, that interact with one another through message exchanges. To promote reuse and evolvability, these interactions are explicitly described right from the early phases of the development lifecycle. Up to now, emphasis has been placed on capturing structural aspects of service interactions. Gradually though, the description of behavioral dependencies between service interactions is gaining increasing attention as a means to push forward the SOA vision. This paper deals with the description of these behavioral dependencies during the analysis and design phases. The paper outlines a set of requirements that a language for modeling service interactions at this level should fulfill, and proposes a language whose design is driven by these requirements.