The MACSI summer school: a case study in outreach in mathematics

To encourage the study of mathematics in Ireland, the Mathematics Applications Consortium for Science and Industry (MACSI) organizes a summer school once a year. The different aspects of this summer school are presented. Students are selected depending on their motivation, academic abilities, gender and geographical origins. Instruction and supervision is provided by academics, post-doctoral fellows and post-graduate students. The teaching programme evolves every year and reflects the interests of the people involved. Feedback from participants has been almost uniformly positive. Students favour interactive sessions and enjoy the residential aspect of the summer school. Food and accommodation are however the most costly aspects of this summer school. In this respect the support of Science Foundation Ireland has been invaluable.     

Mathematical modelling of social obesity epidemic in the region of Valencia,Spain

In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic.

We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general strategies to reverse the increasing trend of obesity are suggested.

The obese population in the region of Valencia is increasing (11.6% in 2000 and 13.48% in 2005) and the future is worrisome. Our model predicts that 15.52% of the population in Valencia will be obese by 2011. Model sensitivity analysis suggests that obesity prevention strategies (healthy advertising campaigns) are more effective than obesity treatment strategies (physical activity) involving the obese and overweight subpopulation in controlling the increase of adulthood obesity in the region of Valencia.     

Mathematical modelling of the patent ductus arteriosus (PDA)

The heart is one of the most important and vital body organs, which is responsible for pumping blood to different body tissues. Abnormalities in each part of heart can lead to lack of proper blood circulation. The arterial duct is one of the most important parts of embryonic cycles which may provide the possibility of a relationship between the aorta and the pulmonary artery. The failure of this duct to close after birth causes the abnormality called patent ductus arteriosus (PDA). In this article, we propose a novel model for accurate simulation of PDA abnormality in the human heart. The model is obtained by exploiting the mathematical relation between hemodynamic parameters of heart, including pressure, blood, volume and flow. The proposed model is verified using clinical data.     

Mathematics achievement in the secondary high school context of STEM and non‐STEM schools

The purpose of this study is to compare students’ mathematics achievement growth rate in Texas science, technology, engineering, and mathematics (T‐STEM) academies to students’ mathematics achievement growth rate in traditional public high schools. Forty‐six schools, 23 of which were T‐STEM academies and 23 of which were matched non‐STEM schools, were included in this study. A hierarchical linear modeling method was conducted. The result of the present study revealed that there was no difference in students’ mathematics achievement growth rate in T‐STEM academies compared to students’ mathematics achievement growth rate in comparison schools. However, in terms of ethnicity, the results indicated that African American and Hispanic students in T‐STEM academies outperformed African American and Hispanic students in comparison schools on their mathematics growth rate.     

Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and span. The objective is to evaluate this didactic proposal by determining the level of match between the hypothetical learning trajectory (HLT) designed in this study with the actual learning trajectory in the second experimental cycle of an investigation design-based research more extensive. The results show a high level of match between the trajectories in more than half of the conjectures, which gives evidence that the HLT has supported, in many cases, the achievement of the learning objective, and that additionally mathematical modelling contributes to the construction of these linear algebra concepts.     

Mathematical Modeling for Preservice Teachers: A Problem from Anesthesiology

The study reported in this article deals with the observed actions of prospective Swedish mathematics teachers as they were working with a modeling situation. These prospective teachers were preparing to teach in Grades 4 to9 or in the gymnasium (Grades 10 to 12) and were students in a course in mathematical modeling. The larger study of which this study was a part focused on these students' understanding of modeling and how they related mathematical models to the real world. This article also attempts to illustrate how mathematics is intertwined with many other subjects, in this case medicine. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mathematical modelling of the stochastic mechanical properties of wood and its extensibility at small scales

This paper investigates the relation between the uncertain mechanical properties of wood and its extensibility at the ultrastructural scale. A statistical approximation to the output of a multi-scale constitutive model is adopted to predict the extensibility of wood in the presence of parametric uncertainty. By means of this procedure, a very large number of computationally intensive fully-coupled multi-scale simulations are avoided. Following this approach, four different micromechanical parameters are chosen to assess their influence on the extensibility of the material under tensile loading conditions. These are the degree of cellulose crystallinity, the ultimate strain and Young’s modulus of the hemicellulose–lignin matrix, and the thickness of the amorphous cellulose layer which covers the periodic crystalline portions of cellulose. We believe that a better understanding of the mechanisms of deformation and extensibility in wood and in natural materials can pave the way for the development of new strategies to design more advanced materials in engineering structures.     

Exploring informal mathematical products of low achievers at the secondary school level

This article examines the notion of informal mathematical products, in the specific context of teaching mathematics to low achieving students at the secondary school level. The complex and relative nature of this notion is illustrated and some of its characteristics are suggested. These include the use of ad-hoc strategies, mental calculations, idiosyncratic ideas, everyday rather than mathematical language, non-symbolic explanations, visual justifications and common-sense based reasoning. The main argument raised in the article concerns the challenge of valuing informal mathematical products, created by low achievers, and using them within the mathematics classroom as means for advancing such students. The data draws from several research and design projects conducted in Israel since 1991. Selected examples of students’ products, gathered from low-track mathematics classrooms involved in these projects, are presented and analyzed. The analyses highlight various features of such products, and portray the possible gains of teaching approaches that legitimize, and build onwards from, informal products of low achievers.     

半导体与超晶格的数学模型及其分析Ⅰ:模型

本文论及半导体与超晶格的数学模型方法的一些新近发展动态。介绍了半导体与超晶格的一些背景材料并给出了半导体宏观模型间的层次框架。超晶格中载流子传输的SHE扩散模型也被观察。     

Mathematical modelling for keyhole surgery simulations: a biomechanical model for spleen tissue

There is growing interest in the potential for computer simulationsto provide good training materials for abdominal endoscopicor ‘keyhole’ surgery. This paper describes a preliminarystudy of the mechanical properties of abdominal (spleen) tissue.We show how experimental force–displacement data can beused to derive a biomechanical model for the tissue as an incompressible,homogeneous, isotropic nonlinear elastic material with an exponentialstress–strain law. We also show how the model can be usedto predict the response of the tissue to a surgical probe. Thisinvolves solving a complicated nonlinear constrained boundary-valueproblem, and there is a good fit between the computed solutionand experimental data.     

Crust density in bread baking: Mathematical modelling and numerical solutions

A model for the formation of a “crust” during bread baking is presented. The crust is the outermost part of the loaf where the final bread density is significantly higher than in the “crumb”, the interior of the loaf. The model is based on a collapse mechanism, whereby raised pressures due to thermal expansion and water evaporation squash bubbles in the bread as the dough sets and fractures; the latter process allows vapour within bubbles to escape.     

大学数学创新教育实施过程的探讨

从创新教育的理念出发,结合大学数学教育的现状,探讨了大学数学创新教育实施过程中的实现手段,分析了数学创新教育中的层次化、学生思想培养、习惯、文化等核心问题.     

Empirically supporting school STEM culture—The creation and validation of the STEM Culture Assessment Tool (STEM‐CAT)

School STEM Culture—an aspect of culture within a school community—is defined as the beliefs, values, practices, and resources in STEM fields as perceived by students, parents, teachers, and administrators and counselors within a school. This study validates the STEM Culture Assessment Tool (STEM‐CAT), an instrument intended to advance the use of the School STEM Culture construct within the research community. Internal consistency was determined through the use of Cronbach's alpha and factor analyses, and the instrument was found to be a reliable measure of School STEM Culture. The instrument can be used in future research to quantify School STEM Culture to determine if interventions change the culture of a school to further STEM education.     

《数学物理方法》课程教改的探索与实践

随着我国科学技术的快速发展,对于理工科学生在数学基础和数学素养方面的要求越来越高.数学物理方法课程综合应用了各个数学分支的内容,是提升理工科本科学生应用数学能力的重要基础课程.本文以课程作用、课程安排以及教学内容的梳理改进为主线,介绍数学物理方法课程教改的思考与实践.     

Application of autoregressive modelling for the analysis of clinical and other biological data

This paper deals with the application of autoregressive (AR) modelling for the analysis of biological data including clinical laboratory data. In the first part of the paper, we discuss the necessity of feedback analysis in the field of biochemistry. In order to enable this, relative power contribution analysis was introduced. Next, we utilized the two types of impulse response curves of the open and closed loop systems for elucidating the structure of the metabolic networks under study. Time series data obtained from 31 chronic hemodialysis patients observed for periods of 3 to 7 years were analyzed by these procedures. The results of the analysis were rather uniform among the patients and suggested the consistency of this approach in identifying the dynamical system of individual patients. An example of data set is included in the paper.     

将数学实验的思想和方法融入大学数学教学

大学数学教学中应注重理论联系实际,注重数学思想和方法的讲授,强调应用案例中融入数学实验思想的新教学方法.改革课堂教学方法,探索新的教学模式,加强学生的实践性教学环节,培养学生的应用和创新能力.最后,本文给出了几个例子显示了数学实验与大学数学教学结合的效果.     

慢速饮酒血液中酒精含量的数学模型

描述的是在一定时间内慢慢地匀速喝完一定数量酒的问题,并建立了相应的数学模型.同时也建立了快速饮酒的数学模型,以及证明了在各次饮酒后的某时刻酒精含量的可叠加性.     

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method, Part 1: Mathematical modelling

A methodology is proposed for the efficient determination of gradient information, when performing gradient based optimisation of an off-road vehicle’s suspension system. The methodology is applied to a computationally expensive, non-linear vehicle model, that exhibits severe numerical noise. A recreational off-road vehicle is modelled in MSC.ADAMS, and coupled to MATLAB for the execution of the optimisation. The successive approximation method, Dynamic-Q, is used for the optimisation of the spring and damper characteristics. Optimisation is performed for both ride comfort and handling. The determination of the objective function value is performed using computationally expensive numerical simulations.This paper proposes a non-linear pitch-plane model, to be used for the gradient information, when optimising ride comfort. When optimising for handling, a non-linear four wheel model, that includes roll, is used. The gradients of the objective function and constraint functions are obtained through the use of central finite differences, within Dynamic-Q, via numerical simulation using the proposed simplified models. The importance of correctly scaling these simplified models is emphasised. The models are validated against experimental results. The simplified vehicle models exhibit significantly less numerical noise than the full vehicle simulation model, and solve in significantly less computational time.     

Mathematical modelling in university education. An experiment at the University of Oldenburg

This paper suggests that mathematics teacher educators should listen carefully to what their students are saying. More specifically, it demonstrates how from one pre-teacher's non-traditional geometric representation of a unit fraction, a variety of learning environments that lead to the enrichment of mathematics for teaching can be developed. The paper shows how new knowledge may be generated through an attempt to validate an intuitive idea; in other words, how the quest for rigour may serve as a catalyst for the growth of mathematical concepts in the context of K-16 mathematics.