On the rank of semimodules over semirings

In this paper we investigate conditions on a semiring $S$ such that there are semimodules over $S$ with bases of different length. This includes and generalizes corresponding results on rings, in particular one due to P. Dubreil

Domain-Specific Knowledge and Memory Performance: A Comparison of High- and Low-Aptitude Children

Two studies compared memory performance and text comprehension of groups that were equivalent on domain-specific knowledge but differed in overall aptitude, to investigate whether prior knowledge about a particular domain or overall aptitude level was more important when the task was to acquire and use new information in the domain of interest. Both studies dealt with third-, fifth-, and seventh-grade soccer experts' and novices' memory and comprehension of a story dealing with a soccer game. Several measures of memory performance, memory monitoring, and text comprehension were used. Levels of soccer knowledge and of overall aptitude were varied in a factorial design. Neither study detected significant differences between high-aptitude and low-aptitude experts, regardless of their ages. Low aptitude experts outperformed high-aptitude novices on all memory and comprehension measures. The results indicate that domain-specific knowledge can compensate for low overall aptitude on domain-related cognitive tasks

Was ist Mathematik (Zusammenfassung)

Natürlich wollte der Verfasser auf die Frage: "Was ist Mathematik?" keine definitive oder gar allgemein akzeptierte Antwort geben. Vielmehr ging es ihm darum, aus seiner Sicht gewisse Grundzüge der Mathematik in ihrer historischen Entwicklung darzustellen und dabei herauszuarbeiten, welche Rolle die jeweiligen Auffassungen über die Mathematik in der Geschichte der Philosophie gespielt haben