1 Dario Nardi, University of California Los Angeles, Program in Computing, Math Sciences 6363, Los Angeles, CA 90095 [email protected] Abstract—Systems concepts like non-linearity and feedback are relevant in many fields, but interactive software to demonstrate these concepts are uncommon. Three mini-applications are discussed. These applications are relatively simple in programming and desi...

The term isomorphism literally means equality or sameness (iso) of form (morphism). In mathematics an isomorphism between two systems requires a one-toone correspondence between their elements (that is, each element of one system corresponds to one and only one element of the other system, and conversely), which also preserves structures. Referring to isomorphism as one of the most important an...

In this paper theory from population biology is combined with stochastic differential equations. The aim is to compare previously studied deterministic population models with corresponding stochastic population models. As an illustrative example the models are applied to a classical dataset (Gause, 1934). The first half of the paper gives a brief review of the theoretical background needed in o...

Through reporting on an initiative in South Africa that aimed to provide epistemological access to teachers and learners of mathematics (and science) through translating mathematical concepts into two indigenous languages, this paper argues for the urgent development of mathematical registers in indigenous languages for mathematics and science. The pilot research reported on in this paper indic...

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms (object-to-object morphisms between objects of different categories) that parses an adjunction into two separate parts (left and right representations of heterom...

This first chapter is mostly informal. The rest of this book has no dependency on this chapter, save the definitions in §7 concerning asymptotic notations. Hence a light reading may be sufficient. We recommend re-reading this chapter after finishing the rest of the book, when many of the remarks here may take on more concrete meaning. An appendix collects useful mathematical concepts that are u...

This study of the learning of vectors is situated in the intersection of embodied theory relating to physical phenomena, and process-object encapsulation of actions as mathematical concepts. We consider the subtle effects of different contexts such as vector as displacement or force, and focus on the need to create a concept of vector that has greater flexibility. Our approach refocuses the dev...

According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, [Formula: see text]. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-par...

Voting in the EU-Council – a brief sketch At least since the EU-summit in Nice in December 2000 there has been an intensive discussion about the voting procedure in the EU-Council. The Treaty of Nice contains a very complicated procedure which consists of three voting criteria. A proposal is accepted by the Council if: 1) the (simple) majority of states support the proposal 2) the proposal rece...

For the majority of spatiotemporal applications, we assume that the modeled world is precise and bound. This simplification seems unnecessary crude for many environments handling spatial and temporal extents, such as navigational applications. In this work, we explore fuzziness and uncertainty, which we subsume under the term indeterminacy, in the spatiotemporal context. We first show how the f...