SERS-barcoded colloidal gold NP assemblies as imaging agents for use in biodiagnostics

There is a growing need for new biodiagnostics that combine high throughput with enhanced spatial resolution and sensitivity. Gold nanoparticle (NP) assemblies with sub-10 nm particle spacing have the benefits of improving detection sensitivity via Surface enhanced Raman scattering (SERS) and being of potential use in biomedicine due to their colloidal stability. A promising and versatile approach to form solution-stable NP assemblies involves the use of multi-branched molecular linkers which allows tailoring of the assembly size, hot-spot density and interparticle distance. We have shown that linkers with multiple anchoring end-groups can be successfully employed as a linker to assemble gold NPs into dimers, linear NP chains and clustered NP assemblies. These NP assemblies with diameters of 30-120 nm are stable in solution and perform better as SERS substrates compared with single gold NPs, due to an increased hot-spot density. Thus, tailored gold NP assemblies are potential candidates for use as biomedical imaging agents. We observed that the hot-spot density and in-turn the SERS enhancement is a function of the linker polymer concentration and polymer architecture. New deep Raman techniques like Spatially Offset Raman Spectroscopy (SORS) have emerged that allow detection from beneath diffusely scattering opaque materials, including biological media such as animal tissue. We have been able to demonstrate that the gold NP assemblies could be detected from within both proteinaceous and high lipid containing animal tissue by employing a SORS technique with a backscattered geometry.

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.