Topology is considered an advanced field in mathematics, and it might seem off-putting to people with no previous experience in mathematics. The classification theorem, which lies within the field of algebraic topology, is fascinating, but understanding it requires extensive mathematical knowledge. In this manuscript, we present a modular object…

This contribution takes up and discusses topology as a relational approach to better understand and empirically trace policy mobilities in federal education systems. While topology echoes other relational approaches in its simultaneous focus on ongoing change and the "making" of stabilized forms (e.g., policy scales), it also brings…

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately…

Currently, modelling of knowledge and skills in a MOOC and the associated instructional and pedagogical engineering process is a major challenge in order to support designers and facilitate learning. This article explains how visuo-cognitive metaphors of the "metro map" and "travel" make possible the design of connections…

As mathematics educators we want our students to develop a natural curiosity that will lead them on the path toward solving problems in a changing world, in fields that perhaps do not even exist today. Here we present student projects, adaptable for several mid- and upper-level mathematics courses, that require students to formulate their own…

In this essay Elizabeth de Freitas follows Tim Ingold's groundbreaking anthropological work on lines and their cultural and material significance to argue that the line is the engine of theory, be it the drawn line of inscription or mathematical measure, the exclusionary line of delineation, or the undulating generative line of flight. De…

This article uses topological approaches to suggest that education is becoming-topological. Analyses presented in a recent double-issue of "Theory, Culture & Society" are used to demonstrate the utility of topology for education. In particular, the article explains education's topological character through examining the global…

This paper provides an account of the topological and its description of contemporary culture and use as a research methodology, a topological lens, generally, and in education research specifically. Some commentary is proffered on the relationships between the topological and the topographical, between relations and locations. A critical account…

We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…

In the current literature on the university it is generally accepted that processes of digitization play an important role regarding both the daily functioning of the university as an institution and the academics that give shape to it. This article contributes to our understanding of the role that digitization plays in contemporary academic…

This paper traces developments across Stephen J. Ball's policy sociology in education "oeuvre" and considers their implications for doing research on education policy today. It begins with an account of his policy sociology trilogy from the 1990s, which outlined his conception of the policy cycle consisting of the contexts of influence,…

This paper presents a new state-space approach for temporal analysis of electrical circuits. The method systematically obtains the state-space formulation of nondegenerate linear networks without using concepts of topology. It employs nodal/mesh systematic analysis to reduce the number of undesired variables. This approach helps students to…

The phenomenon of AM (animal metaphor) can be discussed based on the class-inclusion model in cognitive linguistics. In this article, we try to prove that this kind of metaphor accords more with this model than with correspondence model of Lakoff. It does not mean that the correspondence model is not valid in this regard, but we argue that…

Starting in the late eighties, with a growing discontent with analytical methods in science and the growing power of computers, researchers began to study complex systems such as living organisms, evolution of genes, biological systems, brain neural networks, epidemics, ecology, economy, social networks, etc. In the early nineties, the research…

Cognitive processes require a functional interaction between specialized multiple, local and remote brain regions. Although these interactions can be strongly altered by an acquired brain injury, brain plasticity allows network reorganization to be principally responsible for recovery. The present work evaluates the impact of brain injury on…