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Wir behandeln nichtkommutative Algebren über Ringen und auf algebraischen Varietäten. Im ersten Teil beschreiben wir ein Kriterium, das angibt, ob und wie weit sich eine gegebene Azumaya-Algebra über dem Funktionenkörper einer algebraischen Varietät als Garbe von Azumaya-Algebren auf die Varietät ausdehnen lässt. Außerdem untersuchen wir die lokale Struktur von Azumaya-Algebren oder allgemeiner von Maximalordnungen, die mit Hilfe des Cyclic-Covering-Tricks von Chan konstruiert werden. Mit dieser Methode lassen sich Maximalordnungen auf algebraischen Flächen konstruieren, die zudem genau über einer gewählten Kurve verzweigen. Im zweiten Teil betrachten wir die nichtassoziativen Oktavenalgebren und allgemeiner auch Kompositionsalgebren über Ringen. Dabei übertragen wir die bekannten Aussagen von Kompositionsalgebren über Körpern auf die Situation von Algebren über Ringen. Wir untersuchen Oktavenalgebren und Maximalordnungen über diskreten Bewertungsringen und verallgemeinern ein Resultat von van der Blij und Springer über die lokale Natur von Maximalordnungen über den rationalen Zahlen und über algebraischen Zahlkörpern auf den Fall von beliebigen noetherschen, ganzabgeschlossenen Integritätsbereichen. Abschließend führen wir eine Definition von Garben von Oktavenalgebren und Garben von Maximalordnungen in Oktavenalgebren über algebraischen Varietäten ein.

Die Dresdner Absolventenstudie beschreibt die Ergebnisse der Befragung von Absolvent/innen der im Titel genannten Fakultät der TU Dresden des im Untertitel angegebenen Abschlusszeitraums zu den Themen Berufseinmündung, Tätigkeitsverlauf, Studienverlauf, retrospektive Studienbewertung und Zukunftsorientierungen. Darüber hinaus werden Kohorten- und Panelvergleiche zu befragten Absolvent/innen früherer Jahrgänge realisiert. Gegenstand sind auch Aspekte im Studium, die mit dem beruflichen Erfolg in Zusammenhang stehen.

This dissertation describes the improvement of signal analysis in ultrasonic microscopy for nondestructive testing. Specimens with many thin layers, like modern electronic components, pose a particular challenge for identifying and localizing defects. In this thesis, new evaluation algorithms have been developed which enable analysis of highly complex layer-stacks. This is achieved by a specific evaluation of multiple reflections, a newly developed iterative reconstruction and deconvolution algorithm, and the use of classification algorithms with a highly optimized simulation algorithm. Deep delaminations inside a 19-layer component can now not only be detected, but also localized. The new analysis methods also enable precise determination of elastic material parameters, sound velocities, thicknesses, and densities of multiple layers. The highly improved precision of determined reflections parameters with deconvolution also provides better and more conclusive results with common analysis methods. / Die vorgelegte Dissertation befasst sich mit der Verbesserung der Signalauswertung für die Ultraschallmikroskopie in der zerstörungsfreien Prüfung. Insbesondere bei Proben mit vielen dünnen Schichten, wie bei modernen Halbleiterbauelementen, ist das Auffinden und die Bestimmung der Lage von Fehlstellen eine große Herausforderung. In dieser Arbeit wurden neue Auswertealgorithmen entwickelt, die eine Analyse hochkomplexer Schichtabfolgen ermöglichen. Erreicht wird dies durch die gezielte Auswertung von Mehrfachreflexionen, einen neu entwickelten iterativen Rekonstruktions- und Entfaltungsalgorithmus und die Nutzung von Klassifikationsalgorithmen im Zusammenspiel mit einem hoch optimierten neu entwickelten Simulationsalgorithmus. Dadurch ist es erstmals möglich, tief liegende Delaminationen in einem 19-schichtigem Halbleiterbauelement nicht nur zu detektieren, sondern auch zu lokalisieren. Die neuen Analysemethoden ermöglichen des Weiteren eine genaue Bestimmung von elastischen Materialparametern, Schallgeschwindigkeiten, Dicken und Dichten mehrschichtiger Proben. Durch die stark verbesserte Genauigkeit der Reflexionsparameterbestimmung mittels Signalentfaltung lassen sich auch mit klassischen Analysemethoden deutlich bessere und aussagekräftigere Ergebnisse erzielen. Aus den Erkenntnissen dieser Dissertation wurde ein Ultraschall-Analyseprogramm entwickelt, das diese komplexen Funktionen auf einer gut bedienbaren Oberfläche bereitstellt und bereits praktisch genutzt wird.

In mathematics curricula teachers often find the more or less implicit request to link the taught subjects to the previous knowledge of the students, for example using word problems from everyday life. But in today’s multicultural and multisocial society teachers can no longer assume that the children they teach have a more or less equal background and thus everyday live can have a very different meaning for different children. Furthermore there is evidence that good previous knowledge in arithmetic can hinder the approach to other mathematical subjects, like algebra. In this paper I want to provide a brief overview on how previous knowledge in arithmetic can affect student\'s access to algebra and therefore present an early algebra teaching project which introduces elementary school children to algebraic notation by measurement in an action-oriented way. Thereby the chosen approach to algebra explicitly does not come back to the student\'s previous arithmetical knowledge but additionally may support non-proficient students in obtaining more insight in the structure of calculations and hence may help them to have more success in solving calculations and word problems.

The major aims of this paper are to: present the background of the mathematics education problem in the Stamford Public School (SPS) district which is common is most U.S cities; explain the need for change in mathematics education; describe the process to systemically transform both the curriculum and instruction of mathematics thereby ensuring that each and every students is prepared for the 21st century, for higher education, and for success in a global society; and provide ways to measure these changes. The K-12 mathematics education reform model presented can be replicated in other cities and for other academic areas.

This paper addresses folding the circle in half and discussing some of over one hundred different mathematical terms and functions generated in that one fold. The simplicity of process in understanding fundamentals of mathematics by folding circles and observing what is generated is unknown because we only draw pictures of circles. Examples are given about observing and exploring relationships in the circle that are appropriate for first, second, third grade level and beyond. The traditional educational ‘parts-towhole’ approach can only be fully realized through the comprehensive frame of Whole-to-parts by folding the circle. Wholemovement of the circle is not only direct; it is the only context inclusive to progressively understanding parts within unity of the Whole.

Language is the learning device and the device which forms the student's knowledge in math, his ability to define concepts, express mathematical ideas and solve mathematical problems. Difficulties in the Language are seen more in word problems, clarity and in the way the text is read by the student have a direct effect on the understanding of the problem and therefore, on its solution, could delay the problem solving process. The connection between language and mathematical achievements has a more distinctive significance regarding the Arab student. This is due to the fact that the language which is used in the schools and in textbooks is classical (traditional) Arabic. It is far different than the language used in everyday conversations with family and friends (the spoken Arabic). Our research examine whether rephrasing word problems can affect the achievements of the Arab students in it. The experimental group received mathematics instruction using learning materials of word problems that were rewritten in a “middle language” closer to the students’ everyday language (spoken Arabic), thus keeping the mathematical level of the problems. The research findings showed that students in the experimental group improved their achievements in word and geometric problems significantly more than students from control group.

The author shares some of the findings of the research he conducted in 2007 on grade 11 mathematics learners in two schools, one experimental and the other one control. In his study, the author claims that an open-ended approach towards teaching and learning of mathematics enhances understanding of mathematics by the learners. The outcomes of the study can be summarised as follows: 1. In the experimental school, where the author intervened by introducing an open-ended approach to teaching mathematics (by means of giving the learners an open-ended approach compliant worksheet to work on throughout the intervention period), the performance of the learners in the post-test was better than that of the learners from the control school. Both schools were of similar performance in the pre-test. The two schools wrote the same pre-test and same post-test. Both schools were following common work schedule. 2. Within the experimental school, post-test performance of the learners in the class where the intervention was monitored throughout the intervention period (thus ensuring compliance of the teacher to the open-ended approach) out-performed those in which monitoring was less frequent. 3. There was no significant difference in performance between learners from the unmonitored experimental class and those from the control class.