Mathematical motivators: using the history of mathematics to enrich the curriculum

This article provides a summary of the MSOR funded mini project Mathematical Motivators. Mathematics is usually, and of course correctly, presented ‘ready-made’ to students, with techniques and applications presented systematically and in a logical order. However, like any other academic subject, mathematics has a history which is rich in astonishing breakthroughs, false starts, misattributions, confusions and dead-ends. This history gives a narrative and human context which adds colour and context to the discipline

Regional alcohol consumption and alcohol-related mortality in Great Britain: novel insights using retail sales data

Background: Regional differences in population levels of alcohol-related harm exist across Great Britain, but these are not entirely consistent with differences in population levels of alcohol consumption. This incongruence may be due to the use of self-report surveys to estimate consumption. Survey data are subject to various biases and typically produce consumption estimates much lower than those based on objective alcohol sales data. However, sales data have never been used to estimate regional consumption within Great Britain (GB). This ecological study uses alcohol retail sales data to provide novel insights into regional alcohol consumption in GB, and to explore the relationship between alcohol consumption and alcohol-related mortality. Methods: Alcohol sales estimates derived from electronic sales, delivery records and retail outlet sampling were obtained. The volume of pure alcohol sold was used to estimate per adult consumption, by market sector and drink type, across eleven GB regions in 2010–11. Alcohol-related mortality rates were calculated for the same regions and a cross-sectional correlation analysis between consumption and mortality was performed. Results: Per adult consumption in northern England was above the GB average and characterised by high beer sales. A high level of consumption in South West England was driven by on-trade sales of cider and spirits and off-trade wine sales. Scottish regions had substantially higher spirits sales than elsewhere in GB, particularly through the off-trade. London had the lowest per adult consumption, attributable to lower off-trade sales across most drink types. Alcohol-related mortality was generally higher in regions with higher per adult consumption. The relationship was weakened by the South West and Central Scotland regions, which had the highest consumption levels, but discordantly low and very high alcohol-related mortality rates, respectively. Conclusions: This study provides support for the ecological relationship between alcohol-related mortality and alcohol consumption. The synthesis of knowledge from a combination of sales, survey and mortality data, as well as primary research studies, is key to ensuring that regional alcohol consumption, and its relationship with alcohol-related harms, is better understood

Analysis of a Class of Low-Dimensional Models of Mutation and Predation

We consider a class of simple two-dimensional discrete models representative of a system incorporating both mutation and predation. A selection of analytic and numerical results are presented, classifying the dynamic behavior of the system by means of Lyapunov exponents over a biologically-reasonable region of parameter space, and illustrating the occurrence of hyperchaos and a Neimark–Sacker bifurcation producing regions of quasiperiodicity.</jats:p

Do patients who die from an alcohol-related condition ‘drift’ into areas of greater deprivation? Alcohol-related mortality and health selection theory in Scotland

Background: Health selection has been proposed to explain the patterning of alcohol-related mortality by area deprivation. This study investigated whether persons who die from alcohol-related conditions are more likely to experience social drift than those who die from other causes. Methods: Deaths recorded in Scotland (2013, &gt;21 years) were coded as ‘alcohol-related’ or ‘other’ and by deprivation decile of residence at death. Acute hospital admissions data from 1996 to 2012 were used to provide premortality deprivation data. χ² tests estimated the difference between observed and expected alcohol-related deaths by first Scottish Index of Multiple Deprivation (SIMD) decile and type of death. Logistic regression models were fitted using type of death as the outcome of interest and change in SIMD decile as the exposure of interest. Results: Of 47 012 deaths, 1458 were alcohol-related. Upward and downward mobility was observed for both types of death. An estimated 31 more deaths than expected were classified ‘alcohol-related’ among cases whose deprivation score decreased, while 204 more deaths than expected were classified ‘alcohol-related’ among cases whose initial deprivation ranking was in the four most deprived deciles. Becoming more deprived and first deprivation category were both associated with increased odds of type of death being alcohol-related after adjusting for confounders. Conclusion: This study suggests that health selection appears to contribute less to the deprivation gradient in alcohol-related mortality in Scotland than an individual’s initial area deprivation category

Evaluating the impact of the Alcohol Act on off-trade alcohol sales: a natural experiment in Scotland

&lt;b&gt;Background and aims&lt;/b&gt; A ban on multi-buy discounts of off-trade alcohol was introduced as part of the Alcohol Act in Scotland in October 2011. The aim of this study was to assess the impact of this legislation on alcohol sales, which provide the best indicator of population consumption.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Design Setting and Participants&lt;/b&gt; Interrupted time-series regression was used to assess the impact of the Alcohol Act on alcohol sales among off-trade retailers in Scotland. Models accounted for underlying seasonal and secular trends and were adjusted for disposable income, alcohol prices and substitution effects. Data for off-trade retailers in England and Wales combined (EW) provided a control group.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Measurements&lt;/b&gt; Weekly data on the volume of pure alcohol sold by off-trade retailers in Scotland and EW between January 2009 and September 2012.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Findings&lt;/b&gt; The introduction of the legislation was associated with a 2.6% (95% CI -5.3 to 0.2%, P = 0.07) decrease in off-trade alcohol sales in Scotland, but not in EW (-0.5%, -4.6 to 3.9%, P = 0.83). A statistically significant reduction was observed in Scotland when EW sales were adjusted for in the analysis (-1.7%, -3.1 to -0.3%, P = 0.02). The decline in Scotland was driven by reduced off-trade sales of wine (-4.0%, -5.4 to -2.6%, P &#60; 0.001) and pre-mixed beverages (-8.5%, -12.7 to -4.1%, P &#60; 0.001). There were no associated changes in other drink types in Scotland, or in sales of any drink type in EW.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Conclusions&lt;/b&gt; The introduction of the Alcohol Act in Scotland in 2011 was associated with a decrease in total off-trade alcohol sales in Scotland, largely driven by reduced off-trade wine sales

Using history in mathematics teaching - some open education resources for the future

A recent collaborative project produced both audio- and text-based resources on the history of mathematics to support the teaching of mathematics. The benefits of using the history of mathematics as a motivational pedagogic tool in the undergraduate curriculum are discussed, with specific reference to the use of MP3 formats as a technique to support different learning styles and future modes of learning. The deliverables produced by the project are discussed

Integral equations of a cohesive zone model for history-dependent materials and their numerical solution

A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for computing the evolution of the crack and CZ in time is discussed along with some numerical results

The role of migration in a spatial extension of the Webworld eco-evolutionary model

We extend an eco-evolutionary food web model to a spatially-explicit metacommunity model which features migration of populations between multiple local sites on the same time-scale as feeding and reproduction. We study how factors including the implementation and rate of dispersal, properties of the local environments, and the spatial topology of the metacommunity interact to determine the local and global diversity and the degree of synchronisation between local food webs. We investigate the influence of migration on the stability of local networks to perturbation, and simulate a 5 x 5 spatial arrangement of cells, demonstrating that combining adaptive migration and heterogeneous habitats allows distinct food webs to coevolve from the beginning of the simulation. When coupling food webs by diffusion migration after an initial period of isolation, the Webworld model can construct metacommunities of distinct food webs if the local sites have spatially-homogeneous environmental parameters. If the sites have heterogeneous parameters, synchronisation between food webs increases greatly, but this can be o�set by a greater number of sites and less-connected spatial topologies