Inhalt der Dissertation ist der Einfluß, den die von Alfred Tarski formulierte mathematische Logik auf die Entstehung der drei Computerkonzepte des Konrad Zuse hatte.

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Die vorliegende Dissertation stellt die experimentelle Bestimmung von grundlegenden thermodynamischen und kinetischen Stoffdaten im System Lithium-Silicium vor. Ausgehend von der Synthese qualitativ hochwertiger Lithiumsilicide wurden Wärmekapazitäten über einen großen Temperaturbereich (2-873 K) bestimmt, die aufgrund der Ergebnisse bei tiefen Temperaturen die Ermittlung weiterer Parameter wie beispielsweise der Standardentropien bzw. der Bildungsentropien der Lithiumsilicide ermöglichte. Die Eigenschaft der Silicide, mit Wasserstoff Verbindungen einzugehen, führte zudem zur Ausdehnung der Untersuchungen auf das System Li-Si-H. Aus der Erweiterung resultierte neben der formalkinetischen Beschreibung ablaufender Gleichgewichtsreaktionen die Bestimmung von Bildungsenthalpien der Silicide. Auf Grundlage der experimentell bestimmten Stoffgrößen (Cp, S°, ∆BH°), die für theoretische und praxisrelevante Berechnungen sehr verlässliche Stoffdaten darstellen, wurden thermodynamische Modellierungen im stofflichen System durchgeführt.

Most of people have fatal attitude to Mathematics: some of them are capable to learn it form nature, but the others are not. So is their fate – to suffer from it for the whole of life… But it is a rude though natural mistake, as it results from means of mathematical education and its content. Most of parents and teachers are directed on these aspects both in kindergarten and at primary school. Of course, parents are different. Nevertheless so many parents can’t possibly but speak about achievements of their children. Some start making their own children learn better by the example of success of the others. They make their children learn long chains of figures with no understanding. It is even more sad to see how a mom asks her 4-year old son: “How much is two plus three?..’ But he replies just because he learned the answer but not calculated. Not only parents but also kindergarten tutors don’t want to understand that drilling for arithmetic has no sense. For a specialist it would take two days only…But teach him how to think logically – is a goal demanding from him, reached by different means.

Modern Internet technologies open new possibilities in a wide spectrum of traditional methods, used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay in their schools or universities in different cities and even different countries and try to solve as many mathematical problems as possible and then submit their solutions to organizers through the Internet. Simple Internet technologies supply audio and video connection between participants and organizers in a time of the competitions.

On the basis of experiences and studies developed in the last ten years, the contribution aims to discuss some different peculiarities between Cooperative Learning and Peer Tutoring models in Mathematics lesson. These models are specific interpretations of a way of conducting Mathematics lessons which requires the activity of students, their personal participation in the construction of knowledge. In the description of the two teaching-learning models, the analysis will deal in particular with the social aspects these models involve. Describing these two modalities of cooperation, also the importance of the care for the choice of suitable mathematical tasks and for different pedagogical setting they require will appear clearly. The issues described, together with the analogies and differences between the two models, could contribute to suggest more adequate didactical projects for teachers and deeper studies about students’ collaboration based models for researchers.

Certainly one of the most powerful and important modeling languages of our time is the Calculus. But research consistently shows that students do not understand how the variables in calculus-based mathematical models relate to aspects of the systems that those models are supposed to represent. Because of this, students never access the true power of calculus: its suitability to model a wide variety of real-world systems across domains. In this paper, we describe the motivation and theoretical foundations for the DeltaTick and HotLink Replay applications, an effort to address these difficulties by a) enabling students to model a wide variety of systems in the world that change over time by defining the behaviors of that system, and b) making explicit how a system\'s behavior relates to the mathematical trends that behavior creates. These applications employ the visualization and codification of behavior rules within the NetLogo agent-based modeling environment (Wilensky, 1999), rather than mathematical symbols, as their primary building blocks. As such, they provide an alternative to traditional mathematical techniques for exploring and solving advanced modeling problems, as well as exploring the major underlying concepts of calculus.

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