Kinematics and dynamics motion planning by polar piecewise interpolation and geometric considerations

The importance of numerical methods in science and engineering [Chapra, S.C., and R.P. Canale, “Numerical Methods for Engineers,” McGraw-Hill, 6th Ed., 2010] was long recognised and considered a fundamental factor in improving productivity and reducing production costs. The ability to model flexible systems and describe their trajectories [Gasparetto A., Boscariol P., Lanzutti A., Vidoni R., Trajectory planning in Robotics, Mathematics in Computer Science 6 (2012), pp. 269–279] involves usually the study of nonlinear coupled partial differential equations. Since their exact solutions are not normally feasible in practice, computational methods [V. Kumar, M. Zefran, J.P. Ostrowski, Motion Planning and Control of Robots, Handbook of Industrial Robotics, 2nd Edition, J. Wiley and Sons (2007), pp. 295–315] can be considered

Next steps in implementing Kaput's research programme

We explore some key constructs and research themes initiated by Jim Kaput, and attempt to illuminate them further with reference to our own research. These 'design principles' focus on the evolution of digital representations since the early nineties, and we attempt to take forward our collective understanding of the cognitive and cultural affordances they offer. There are two main organising ideas for the paper. The first centres around Kaput's notion of outsourcing of processing power, and explores the implications of this for mathematical learning. We argue that a key component for design is to create visible, transparent views of outsourcing, a transparency without which there may be as many pitfalls as opportunities for mathematical learning. The second organising idea is that of communication, a key notion for Kaput, and the importance of designing for communication in ways that recognise the mutual influence of tools for communication and for mathematical expression

Improving The Quality Of The Mathematics Education: The Malaysian Experience

Improving the quality of teaching and learning of mathematics has always been a major concern of mathematics educators. The four recurring and inter-related issues often raised in the development of a mathematics curriculum are: “What type of mathematics ought to be taught?”, “Why do we need to teach mathematics?”, “How should mathematics curriculum be planned and arranged?” and “ How can teacher ensure that what is transmitted to the pupils is as planned in the curriculum?”.The relatively brief history of mathematics education in Malaysia can be said to have developed in three distinct phases. In the first phase, the traditional approach, which emphasized mainly on basic skills (predominantly computational), was the focus of the national syllabus. In the late 70’s, in consonance with the world-wide educational reform, the modern mathematics program (MMP) was introduced in schools. Understanding of basic concepts rather than attaining computational efficiency was the underlying theme of the syllabus. Finally, in the late 80’s the mathematics curriculum was further revised. It is part of the national educational reform that saw the introduction of the national integrated curriculum (KBSM) both at the primary and secondary levels. This mathematics curriculum, which has undergone several minor changes periodically, is presently implemented in schools. The curriculum also emphasizes on the importance of context in problem solving. These three syllabi, as in any other curricular development, can be seen to have evolved from changing perspectives on the content, psychological and pedagogical considerations in teaching and learning of mathematics. In this paper, I will trace the development of the Malaysian mathematics curriculum from the psychological, content and pedagogical perspectives in relation to the recurring issues. I will argue that the development has in many ways attempted to make mathematics more meaningful and thus friendlier for students both at the primary and secondary levels. There has been also a marked improvement on the quality of mathematics education in Malaysi

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context