he original vision was to take advantage of the emerging important areas of nonlinear control systems, dynamical systems, and their essential interactions. This has proven to be extremely viable, and the Option remains at the cutting edge of its domain. It has positioned itself as a key player in the development of the theory, computation, and application of complex systems, dynamical systems, ...

We propose certain non-Turing models of computation, but our intent is not to advocate models that surpass the power of Turing Machines (TMs), but to defend the need for models with orthogonal notions of power. We review the nature of models and argue that they are relative to a domain of application and are ill-suited to use outside that domain. Hence we review the presuppositions and context ...

Let G be a finite group, f: G --+ C a function, and p an ir-reducible representation of G. The Fourier transform is defined as j(p) =E SEG f(s)p(s) . Direct computation for all irreducible representations involvesorder IGI2 operations. We derive fast algorithms and develop them for thesymmetric groupSn. There, (n!)2 is reduced to n(n!)a/2, where a is theconstant for matr...

Department of Pure and Applied Mathematics, University of Padova, Italy In this report we present preliminary results of a study on the relationship between informal out-of-school and formal in-school mathematics and the ways each can inform the other in the development of new mathematical knowledge, in this case concerning computation in base 12, 24 or 60. This study is based on a teaching exp...

This study sets out to determine the knowledge of flexible mental computation pre-service elementary mathematics teachers when enrolling at university. Knowledge existing skills could inform teacher educators’ preparation for teaching by determining algorithms that are unable calculate. Such also educators as why calculate algorithms. The produced a domain-specific instrument in form diagnostic...

The advent of inexpensive computing technology has dramatically changed the way many mathematicians do mathematics, and the way many students and teachers learn and teach mathematics. This is an ongoing revolution, and no end is in sight. Among the many different ways that computing technology may be employed in mathematics, one of the most intriguing ones is for interactive and dynamic visuali...

I shall talk generally about experimental and heuristic mathematics and give accessible, primarily symbolic, examples. The emergence of powerful mathematical computing environments like Maple and Matlab, the growing availability of correspondingly powerful (multi-processor) computers and the pervasive presence of the internet allow for research mathematicians, students and teachers, to proceed ...