相关论文: Mathematical knowledge: internal, social and cultu…
I point to a deep and unjustly ignored relation between culture and computation. I first establish interpretations of Piaget's and Vygotsky's theories of child development with the language of theoretical computer science. Using these…
Categorization is a fundamental function of minds, with wide ranging implications for the rest of the cognitive system. In humans, categories are shared and communicated between minds, thus requiring explanations at the population level. In…
This article of mathematical education reflects author's experience with job applications and teaching methods and procedures to employ in the American Higher Education. It is organized as a standard questionnaire.
In the article, we would like to take part in a discussion over the problem of ethnomathematics, which has been under way for several years. We would like to express our opinion, our ideas concerning this problem and suggest our point of…
People learn whenever and wherever possible, and whatever they like or encounter--Mathematics, Drama, Art, Languages, Physics, Philosophy, and so on. With the bursting of knowledge, evaluation of one's understanding of conceptual knowledge…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
Over the last decades, a class of important mathematical results have required an ever increasing amount of human effort to carry out. For some, the help of computers is now indispensable. We analyze the implications of this trend towards…
Due to the shift of civilization from the Industrial Age to the Information Age, mathematical literacy has become a necessity in the twenty-first century. However, in order to learn and contribute to the mathematical community, one has to…
In this article I reflect upon the problems connected with writing women in mathematics into Wikipedia. I discuss some of the current projects and efforts aimed at increasing the visibility of women in mathematics on Wikipedia. I present…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to…
Mathematical methods of analysis of data and of predicting growth are discussed. The starting point is the analysis of the growth rates, which can be expressed as a function of time or as a function of the size of the growing entity.…
Some reflections on the role in the development of Mathematics of our unconscious perception of the world and just as unconscious organizing pulsions for those perceptions.
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
Based on a variety of philosophical approaches and my own work for decades in pure and applied mathematics teaching and research, I explain my view upon the basic difficulties of acquiring the Mathematical Experience (in the sense of P.J.…
We present an overview of how certain computational tools currently interact with mathematical practice, and reflect on the implications for research mathematics in the short to medium term, as the field navigates the emerging age of AI and…
This paper provides some reflections on the field of mathematical software on the occasion of John Rice's 65th birthday. I describe some of the common themes of research in this field and recall some significant events in its evolution.…
This paper presents a comprehensive survey of various established mathematical models pertaining to Somitogenesis, a biological process. The study begins by revisiting and replicating the findings from prominent research papers in this…