The technological mediation of mathematics and its learning

This paper examines the extent to which mathematical knowledge, and its related pedagogy, is inextricably linked to the tools – physical, virtual, cultural – in which it is expressed. Our goal is to focus on a few exemplars of computational tools, and to describe with some illustrative examples, how mathematical meanings are shaped by their use. We begin with an appraisal of the role of digital technologies, and our rationale for focusing on them. We present four categories of digital tool-use that distinguish their differing potential to shape mathematical cognition. The four categories are: i. dynamic and graphical tools, ii. tools that outsource processing power, iii. new representational infrastructures, and iv. the implications of highbandwidth connectivity on the nature of mathematics activity. In conclusion, we draw out the implications of this analysis for mathematical epistemology and the mathematical meanings students develop. We also underline the central importance of design, both of the tools themselves and the activities in which they are embedded

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

Research and Education in Computational Science and Engineering

Over the past two decades the field of computational science and engineering (CSE) has penetrated both basic and applied research in academia, industry, and laboratories to advance discovery, optimize systems, support decision-makers, and educate the scientific and engineering workforce. Informed by centuries of theory and experiment, CSE performs computational experiments to answer questions that neither theory nor experiment alone is equipped to answer. CSE provides scientists and engineers of all persuasions with algorithmic inventions and software systems that transcend disciplines and scales. Carried on a wave of digital technology, CSE brings the power of parallelism to bear on troves of data. Mathematics-based advanced computing has become a prevalent means of discovery and innovation in essentially all areas of science, engineering, technology, and society; and the CSE community is at the core of this transformation. However, a combination of disruptive developments---including the architectural complexity of extreme-scale computing, the data revolution that engulfs the planet, and the specialization required to follow the applications to new frontiers---is redefining the scope and reach of the CSE endeavor. This report describes the rapid expansion of CSE and the challenges to sustaining its bold advances. The report also presents strategies and directions for CSE research and education for the next decade.Comment: Major revision, to appear in SIAM Revie

Curriculum Guidelines for Undergraduate Programs in Data Science

The Park City Math Institute (PCMI) 2016 Summer Undergraduate Faculty Program met for the purpose of composing guidelines for undergraduate programs in Data Science. The group consisted of 25 undergraduate faculty from a variety of institutions in the U.S., primarily from the disciplines of mathematics, statistics and computer science. These guidelines are meant to provide some structure for institutions planning for or revising a major in Data Science

Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5–6 years, compared to only about one-third in the preceding 5–6 decades.\ud \ud The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function—the Physiome.\ud \ud The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008