Assessments in Mathematics, undergraduate degree

In the sequel, we question the validity of multiple choice questionnaires for undergraduate level math courses. Our study is based on courses given in major French universities, to numerous audiences

Bypassing dynamical systems : A simple way to get the box-counting dimension of the graph of the Weierstrass function

In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by~${\cal W}(x)=\displaystyle \sum_{n=0}^{+\infty} \lambda^n\,\cos \left ( 2\, \pi\,N_b^n\,x \right)$, where~$\lambda$ and~$N_b$ are two real numbers such that~\mbox{$0 1$, using a sequence a graphs that approximate the studied one.Comment: arXiv admin note: substantial text overlap with arXiv:1703.06839, arXiv:1703.0337

Why do children have accidents?

Accidental injuries are a major health problem for children in the United Kingdom. A number of factors interact to put children at risk for repeated accidents. Chapter one reviews research that has examined child accident risk factors, with particular focus on temperament and risk-taking. Such evidence can usefully inform the assessment and formulation of child clinical psychologists to enable them to identify those children at increased risk for repeated injury and advise on safety education appropriate to the individual's circumstances. The aim of the first study (chapter two) was to examine the role of behavioural and emotional problems (e.g. Attention Deficit Hyperactivity Disorder, anxiety) in the process of accidental injury. Parents of children who had attended a local Accident and Emergency Department completed measures of behaviour and emotional problems and reported on their child’s accidental injuries. The results indicated no statistically significant relationship between behaviour or emotional problems and rates of accidental injury. Surprisingly, higher levels of hyperactivity were associated with fewer accidents. The reason for this is unclear and requires further investigation. Whilst children are able to identify risk, exploration of children’s understanding of the process of accidental injury is lacking. Using a focus group discussion with 10-11 year old children, the second study explored children's understanding of the role of child- related factors in accidental injury. In relation to their own and others’ accidental injuries, they could describe the role of behaviour and mood as well as the influence of peers and adults. This illustrates the discrepancy between children's knowledge and their ability/willingness to act on that knowledge. The final chapter describes some of the ethical and methodological considerations arising out of the two studies. It goes on to discuss some of the learning experiences encountered during the research process and some of the personal challenges faced by the researcher

Towards new schemes: A Lie-group approach of the CBKDV and its derived equations

The aim of this paper is to propose methods that enable us to build new numerical schemes, which preserve the Lie symmetries of the original differential equations. To this purpose, the compound Burgers-Korteweg-de Vries (\textit{CBKDV}) equation is considered. The particular case of the Burgers equation is taken as a numerical example, and the resulting semi-invariant scheme is exposed