Models of protein linear molecular motors for dynamic nanodevices

Protein molecular motors are natural nano-machines that convert the chemical energy from the hydrolysis of adenosine triphosphate into mechanical work. These efficient machines are central to many biological processes, including cellular motion, muscle contraction and cell division. The remarkable energetic efficiency of the protein molecular motors coupled with their nano-scale has prompted an increasing number of studies focusing on their integration in hybrid micro- and nanodevices, in particular using linear molecular motors. The translation of these tentative devices into technologically and economically feasible ones requires an engineering, design-orientated approach based on a structured formalism, preferably mathematical. This contribution reviews the present state of the art in the modelling of protein linear molecular motors, as relevant to the future design-orientated development of hybrid dynamic nanodevices. © 2009 The Royal Society of Chemistry.

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.

Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.