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.

Modelling Denial of Service Attacks on JFK with Meadow's Cost-Based Framework

We present the first detailed application of Meadows’s cost-based modelling framework to the analysis of JFK, an Internet key agreement protocol. The analysis identifies two denial of service attacks against the protocol that are possible when an attacker is willing to reveal the source IP address. The first attack was identified through direct application of a cost-based modelling framework, while the second was only identified after considering coordinated attackers. Finally, we demonstrate how the inclusion of client puzzles in the protocol can improve denial of service resistance against both identified attacks.