Mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

Applied mathematical problem solving, modelling, applications, and links to other subjects

The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both in empirical or theoretical research and in the practice of mathematics instruction and mathematics education, concerning (applied) problem solving, modelling, applications and relations to other subjects. In particular, we shall identify and discuss four major trends: a widened spectrum of arguments, an increased globality, an increased unification, and an extended use of computers. In the final part III we shall comment upon some important issues and problems related to our topic.

CV Exemplar and Links

a pdf and word format document which level 1 students can use as an examplar or template for their CV. Also includes links to example CVs and sites which help of creating CVs

notes and links related computer misuse act 1990

collectively edited resource for INFO2009 initially created as a demonstrator

Technical Report Background Reading Guidance and Links

Handout which contains a set of links to a variety of background resources associated with the topics for a technical report coursework. Resources are clustered into three overview areas, but contain links which be used to address each of the six questions scenarios.

The creative teaching and learning resource book.

Es un recurso integral pues presenta técnicas de enseñanza eficaces que pueden utilizar los profesores de todas las materias en las lecciones diarias de su clase pero, también, incluye experiencias para un aprendizaje efectivo que involucra a los estudiantes y aumenta su motivación. Todas estas estrategias de enseñanza y aprendizaje son prácticas y se han probado con éxito en las aulas. Una sección especial se ocupa del desarrollo a nivel personal y profesional de los docentes para mejorar sus habilidades de enseñanza.

Health and social care. Book 1. Level 3. BTEC National.

Recurso preparado para ayudar al alumno en el curso BTEC National, nivel 3 en salud y asistencia social. El programa BTEC, es un programa de estudios que permite obtener una cualificación profesional o laboral. Su contenido se divide en diez unidades, que abarcan temas como: el desarrollo de una comunicación eficaz en salud y asistencia social; igualdad, diversidad y derechos; perspectivas sociológicas y perspectivas psicológicas en salud y asistencia social; anatomía, fisiología y nutrición, y salud, protección y seguridad. Incluye actividades de evaluación en cada unidad que cubren todos los criterios de ésta para ofrecer a los estudiantes la oportunidad de practicar sus tareas y profundizar en el conocimiento y la comprensión de la materia.

Health and social care. Book 2. Level 3. BTEC National.

Recurso preparado para ayudar al alumno en el curso BTEC National, nivel 3 en salud y asistencia social. El programa BTEC, es un programa de estudios que permite obtener una cualificación profesional o laboral. Incluye las siguientes unidades: los valores y la planificación de la atención social; el cuidado de los niños y jóvenes; la protección de los adultos y la promoción de la independencia; salud pública; fisiología del balance de fluidos; desórdenes fisiológicos; aplicación de perspectivas sociológicas a la salud y asistencia social, y promoción de la educación sanitaria. Incluye actividades de evaluación en cada unidad que cubren todos los criterios de ésta para ofrecer a los estudiantes la oportunidad de practicar sus tareas y profundizar en el conocimiento y la comprensión de la materia.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Bistability of the Atlantic overturning circulation in a global climate model and links to ocean freshwater transport

The possibility of a rapid collapse in the strength of the Atlantic meridional overturning circulation (AMOC), with associated impacts on climate, has long been recognized. The suggested basis for this risk is the existence of two stable regimes of the AMOC (‘on’ and ‘off’), and such bistable behaviour has been identified in a range of simplified climate models. However, up to now, no state-of-the-art atmosphere-ocean coupled global climate model (AOGCM) has exhibited such behaviour, leading to the interpretation that the AMOC is more stable than simpler models indicate. Here we demonstrate AMOC bistability in the response to freshwater perturbations in the FAMOUS AOGCM - the most complex AOGCM to exhibit such behaviour to date. The results also support recent suggestions that the direction of the net freshwater transport at the southern boundary of the Atlantic by the AMOC may be a useful physical indicator of the existence of bistability. We also present new estimates for this net freshwater transport by the AMOC from a range of ocean reanalyses which suggest that the Atlantic AMOC is currently in a bistable regime, although with large uncertainties. More accurate observational constraints, and an improved physical understanding of this quantity, could help narrow uncertainty in the future evolution of the AMOC and to assess the risk of a rapid AMOC collapse.

Cyclones causing wind storms in the Mediterranean: characteristics, trends and links to large-scale patterns

A climatology of cyclones with a focus on their relation to wind storm tracks in the Mediterranean region (MR) is presented. Trends in the frequency of cyclones and wind storms, as well as variations associated with the North Atlantic Oscillation (NAO), the East Atlantic/West Russian (EAWR) and the Scandinavian variability pattern (SCAND) are discussed. The study is based on the ERA40 reanalysis dataset. Wind storm tracks are identified by tracking clusters of adjacent grid boxes characterised by extremely high local wind speeds. The wind track is assigned to a cyclone track independently identified with an objective scheme. Areas with high wind activity – quantified by extreme wind tracks – are typically located south of the Golf of Genoa, south of Cyprus, southeast of Sicily and west of the Iberian Peninsula. About 69% of the wind storms are caused by cyclones located in the Mediterranean region, while the remaining 31% can be attributed to North Atlantic or Northern European cyclones. The North Atlantic Oscillation, the East Atlantic/West Russian pattern and the Scandinavian pattern all influence the amount and spatial distribution of wind inducing cyclones and wind events in the MR. The strongest signals exist for the NAO and the EAWR pattern, which are both associated with an increase in the number of organised strong wind events in the eastern MR during their positive phase. On the other hand, the storm numbers decrease over the western MR for the positive phase of the NAO and over the central MR during the positive phase of the EAWR pattern. The positive phase of the Scandinavian pattern is associated with a decrease in the number of winter wind storms over most of the MR. A third of the trends in the number of wind storms and wind producing cyclones during the winter season of the ERA40 period may be attributed to the variability of the North Atlantic Oscillation.