The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. We question the validity of this metaphor, and make the case that engineers do in fact use mathematics as more than a set of passive tools—that mathematical models for phenomena depend critically on the settings in which they are used, and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and we think it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways

Reuse through rapid development

The general issue of reuse of digital resources, called Learning Objects (LOs), in education is discussed here. Ideas are drawn from software engineering which has long grappled with the reuse problem. Arguments are presented for rapid development methodologies and a corresponding method for generation of online mathematics question banks is described

The mathematical components of engineering expertise: the relationship between doing and understanding mathematics

this paper are extracts from our interviews with engineers.) Where, then, is the complex mathematics that certainly exists in modern engineering? Throughout all aspects of engineering design, computer software has an overwhelming presence. Also, in the particular firm that we visited, there a small number of analytical specialists (a few per cent of the professional engineers employed) who act as consultants for the mathematical/analytical problems which the general design engineers cannot readily solve. (In general in structural engineering, such specialist work is often carried out by external consultants, eg. academic researchers

Concurrent system design: Applied mathematics & modeling in software engineering education

A hallmark of engineering design is the use of models to explore the consequences of design decisions. Sometimes these models are physical prototypes or informal drawings, but the sine qua non of contemporary practice is the use of formal, mathematical models of system structure and behavior. Whether circuit models in electrical engineering, heat-transfer models in mechanical engineering, or queuing theory models in industrial engineering, mathematics makes it possible to perform rigorous analysis that is the cornerstone of modern engineering. Until recently, such modeling was impractical for software systems. Informal models abounded, such as those created in UML1, but rigorous models from which one could derive significant properties were either so rudimentary or so tedious to use that it was difficult to justify the incremental benefit in other than the most critical of systems. In part this is a reflection of the relative immaturity of software engineering, but it also reflects a key distinction between software and traditional engineering: whereas the latter builds on numerical computation and continuous functions, software is more appropriately modeled using logic, set theory, and other aspects of discrete mathematics. Most of the models stress relationships between software components, and numerical computation is the exception rather than the norm. Recent advances in both theory and application have made it possible to model significant aspects of software behavior precisely, and to use tools to help analyze the resulting properties2,3,4. In this paper, we focus on a course developed by James Vallino and since taught and modified by Michael Lutz, to present formal modeling to our software engineering students at RIT. Our overall goals were three-fold: To acquaint our students with modern modeling tools, to connect the courses they take in discrete mathematics to real applications, and to persuade them that mathematics has much to offer to the engineering of quality software

Determining the quality of mathematical software using reference data sets

This paper describes a methodology for evaluating the numerical accuracy of software that performs mathematical calculations. The authors explain how this methodology extends the concept of metrological traceability, which is fundamental to measurement, to include software quality. Overviews of two European Union-funded projects are also presented. The first project developed an infrastructure to allow software to be verified by testing, via the internet, using reference data sets. The primary focus of the project was software used within systems that make physical measurements. The second project, currently underway, explores using this infrastructure to verify mathematical software used within general scientific and engineering disciplines. Publications on using reference data sets for the verification of mathematical software are usually intended for a readership specialising in measurement science or mathematics. This paper is aimed at a more general readership, in particular software quality specialists and computer scientists. Further engagement with experts in these disciplines will be helpful to the continued development of this application of software quality

Experiences with alloy in undergraduate formal methods

At the core of all engineering endeavors is the modeling of proposed system designs and the use of these models to determine system properties. While some models are physical, the vast majority use mathematics to both describe and analyze the consequences of design decisions. In the case of traditional engineering disciplines, most models are based on continuous mathematics, e.g., calculus and differential equations. The situation is quite different in software engineering, however, where the applicable models are more likely to be drawn from discrete mathematics, logic, and set theory. The term of art for such modeling approaches is formal methods

Strategies for teaching engineering mathematics

This thesis is an account of experiments into the teaching of mathematics to engineering undergraduates which have been conducted over twenty years against a background of changing intake ability, varying output requirements and increasing restrictions on the formal contact time available. The aim has been to improve the efficiency of the teaching-learning process. The main areas of experimentation have been the integration in the syllabus of numerical and analytical methods, the incorporation of case studies into the curriculum and the use of micro-based software to enhance the teaching process. Special attention is paid to courses in Mathematical Engineering and their position in the spectrum of engineering disciplines. A core curriculum in mathematics for undergraduate engineers is proposed and details are provided of its implementation. The roles of case studies and micro-based software are highlighted. The provision of a mathematics learning resource centre is considered a necessary feature of the implementation of the proposed course. Finally, suggestions for further research are made

A Review On The Comparative Roles Of Mathematical Softwares In Fostering Scientific And Mathematical Research

Mathematical software tools used in science, research and engineering have a developmental trend. Various subdivisions for mathematical software applications are available in the aforementioned areas but the research intent or problem under study, determines the choice of software required for mathematical analyses. Since these software applications have their limitations, the features present in one type are often augmented or complemented by revised versions of the original versions in order to increase their abilities to multi-task. For example, the dynamic mathematics software was designed with integrated advantages of different types of existing mathematics software as an improved version for understanding numerical related problems for advanced mathematical content (advanced simulation). In recent times, science institutions have adopted the use of computer codes in solving mathematics related problems. The treatment of complex numerical analysis with the aid of mathematical software is currently used in all branches of physical, biological and social sciences. However, the programming language for mathematics related software varies with their functionalities. Many invaluable researches have been compromised within the confines of unacceptable but expedient standards because of insufficient understanding of the valuable services the available variety of mathematical software could offer. In the developing countries, some mathematical software like Matlab and MathCAD are very common. A comparative review for some mathematical software was embarked upon in order to understand the advantages and limitations of some of the available mathematical software

Could it be possible to replace DERIVE with MAXIMA?

In recent years, a considerable number of teachers in Spain have been using DERIVE to teach math subjects in High Schools and Universities. This software has been used by the authors of this work as a support tool in Mathematics courses for Engineering. Since Texas Instruments does not support DERIVE, we were faced with finding an alternative software product, and considering the possibility of using a public-domain software such as MAXIMA. Here we make a comparative study of DERIVE and MAXIMA as support tools for a Calculus course for first year Engineering students