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We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume-Emery-Griffith model. The theorems consist of scaling limits for the total spin. The model depends on the inverse temperature β and the interaction strength K. The rates of convergence results are obtained as (β,K) converges along appropriate sequences (βn,Kn) to points belonging to various subsets of the phase diagram which include a curve of second-order points and a tricritical point. We apply Stein's method for normal and non-normal approximation avoiding the use of transforms and supplying bounds, such as those of Berry-Esseen quality, on approximation error. We observe an additional phase transition phenomenon in the sense that depending on how fast Kn and βn are converging to points in various subsets of the phase diagram, different rates of convergences to one and the same limiting distribution occur.
When it comes to university-level mathematics in engineering education it is getting harder and harder to bridge the gap between the requirements of the curriculum and the actual math skills of first-year students. Often students fail to realise that they lack elementary math skills. Lecturers intend to help them to learn what they have not learned at school. But obstacles like for example lapses in their concentration while working on exercises or playing down their problems can make it difficult to bridge existing gaps.
In order to increase the concentration while solving problems that deal with elementary mathematics students could communicate in a foreign language. By doing so, they have to understand the subject matter in order to talk about it. The Bonn-Rhein-Sieg University of Applied Science tries to launch a project that examines how dealing with these mathematical problems in a foreign language can support students acquiring fundamental mathematical skill. For this purpose the university is seeking for an international partnership. Via virtual communications students from both universities work in teams in English on mathematical problems. The research question if foreign language teaching can advance the acquisition of knowledge is the focus of interest.
Mathematische Vorkurse werden zur Vorbereitung auf das Studium allen Studienanfängerinnen und Studienanfängern der Ingenieurmathematik dringend empfohlen, aber leider fällt es immer schwerer, die Lücke zwischen den Erwartungen an die Vorkenntnisse der Studierenden und dem tatsächlichen Rüstwerkzeug der Studienanfänger/innen zu schließen. In diesem Artikel wird die Projektidee vorgestellt, im Rahmen einer Zusammenarbeit mit dem internationalen ROLE-Projekt einen mathematischen Vorkurs durch zusätzliche Elemente aus dem Bereich der Open Educational Resources sinnvoll zu ergänzen, um eine Binnendifferenzierung zu ermöglichen und den Studierenden zu erleichtern, sich in den Lehrstoff individuell einzuarbeiten.