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...

This report presents a condensed summary on foundations of gauge theory and its application to mecanics. In particular, we will see how the involved mathematical concepts allow to describe the reorientation of a free falling cat in a coordinate free (and nearly calculation free) manner.

What a study of the historical development of mathematical concepts can offer teaching is still being debated. This study examines use of a combination of the historical development of number systems and modelling, with concrete materials as a way of deepening students’ understanding of positional notation. It looks at place value in different number bases as a way of enhancing students’ unders...

Spatial autocorrelation plays an important role in geographical analysis; however, there is still room for improvement of this method. The formula for Moran's index is complicated, and several basic problems remain to be solved. Therefore, I will reconstruct its mathematical framework using mathematical derivation based on linear algebra and present four simple approaches to calculating Moran's...

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...

Historically, all basic mathematical concepts of control theory were first stated and developed in continuous time, and subsequently reformed for discrete time, motivated by the growing role of digital computations and computer use. Although a majority of notions and results for continuousand discrete-time systems are almost identical, these two branches of the control science have been develop...