Global ETD Search

21	Teaching for the objectification of the Pythagorean Theorem Spyrou, Panagiotis, Moutsios-Rentzos, Andreas, Triantafyllou, Dimos 09 May 2012 (has links) This study concerns a teaching design with the purpose to facilitate the students’ objectification of the Pythagorean Theorem. Twelve 14-year old students (N=12) participated in the study before the theorem was introduced to them at school. The design incorporated ideas from the ‘embodied mind’ framework, history and realistic mathematics, linking ‘embodied verticality’ with ‘perpendicularity’. The qualitative analyses suggested that the participants were led to the conquest of the ‘first level of objectification’ (through numbers) of the Pythagorean Theorem, showing also evidence of appropriate ‘fore-conceptions’ of the ‘second level of objectification’ (through proof) of the theorem. The triangle the sides of which are associated with the Basic Triple (3,4,5) served as a primary instrument for the students’ objectification, mainly, by facilitating their ‘generic abstraction’ of the Pythagorean Triples. info:eu-repo/classification/ddc/510 ddc:510
22	Some Initiatives in Calculus Teaching Abramovitz, Buma, Berezina, Miryam, Berman, Abraham, Shvartsman, Ludmila 10 April 2012 (has links) (PDF) In our experience of teaching Calculus to engineering undergraduates we have had to grapple with many different problems. A major hurdle has been students’ inability to appreciate the importance of the theory. In their view the theoretical part of mathematics is separate from the computing part. In general, students also believe that they can pass their exams even though they do not have a real understanding of the theory behind the problems they are required to solve. In an effort to surmount these difficulties we tried to find ways to make students better understand the theoretical part of Calculus. This paper describes our experience of teaching Calculus. It reports on the continuation of our previous research. Mathematisches Denken SLM Methoden Annahmen und Folgerungen aus einem Satz Annahme formulieren Aufgaben Mathematical Thinking SLM Method Assumptions and Conclusions of a Theorem Formulation of a Conjecture Assignments ddc:510 rvk:SD 2009
23	How do rabbits help to integrate teaching of mathematics and informatics? Andžāns, Agnis, Rācene, Laila 11 April 2012 (has links) (PDF) Many countries are reporting of difficulties in exact education at schools: mathematics, informatics, physics etc. Various methods are proposed to awaken and preserve students’ interest in these disciplines. Among them, the simplification, accent on applications, avoiding of argumentation (especially in mathematics) etc. must be mentioned. As one of reasons for these approaches the growing amount of knowledge/skills to be acquired at school is often mentioned. In this paper we consider one of the possibilities to integrate partially teaching of important chapters of discrete mathematics and informatics not reducing the high educational standards. The approach is based on the identification and mastering general combinatorial principles underlying many topics in both disciplines. A special attention in the paper is given to the so-called “pigeonhole principle” and its generalizations. In folklore, this principle is usually formulated in the following way: “if there are n + 1 rabbits in n cages, you can find a cage with at least two rabbits in it“. Examples of appearances of this principle both in mathematics and in computer science are considered. Problemlösen Moderne Elementarmathematik Satz von Ramsey Graphentheorie Diskrete Mathematik problem solving modern elementary mathematics Ramsey theorem graph theory discrete mathematics ddc:510 rvk:SD 2009
24	Synthese als Modus der Prozessualität bei Schubert: Sein spezifisches Wiederholungsprinzip im langsamen Satz Takamatsu, Yusuke 29 October 2020 (has links) In contrast to Beethoven’s music, Schubert’s music has been described through the concept of “a-finality” (Fischer 1983), employing the same elements repeatedly. In this sense, Schubert’s music seems incompatible with the kind of “processual” thinking which is typical for Beethoven’s music. This paper addresses such incompatibility through a comparison of the slow movements of Schubert’s piano sonata D 840 with those of Beethoven’s piano sonata No. 8 (op. 13) which is one of the possible precursors for D 840. The second movement of D 840 features an ABABA structure in which the themes of the first part A and the first part B become integrated into the second part A. This kind of integration differs fundamentally from the design of Beethoven’s op. 13, insofar as the two themes are combined while they also maintain their initial form. This mode of combination suggests Schubert’s own type of synthetic or “processual” thinking. info:eu-repo/classification/ddc/780 ddc:780
25	How do rabbits help to integrate teaching of mathematics andinformatics? Andžāns, Agnis, Rācene, Laila 11 April 2012 (has links) Many countries are reporting of difficulties in exact education at schools: mathematics, informatics, physics etc. Various methods are proposed to awaken and preserve students’ interest in these disciplines. Among them, the simplification, accent on applications, avoiding of argumentation (especially in mathematics) etc. must be mentioned. As one of reasons for these approaches the growing amount of knowledge/skills to be acquired at school is often mentioned. In this paper we consider one of the possibilities to integrate partially teaching of important chapters of discrete mathematics and informatics not reducing the high educational standards. The approach is based on the identification and mastering general combinatorial principles underlying many topics in both disciplines. A special attention in the paper is given to the so-called “pigeonhole principle” and its generalizations. In folklore, this principle is usually formulated in the following way: “if there are n + 1 rabbits in n cages, you can find a cage with at least two rabbits in it“. Examples of appearances of this principle both in mathematics and in computer science are considered. info:eu-repo/classification/ddc/510 ddc:510
26	Complementation and Inclusion of Weighted Automata on Infinite Trees: Revised Version Borgwardt, Stefan, Peñaloza, Rafael 16 June 2022 (has links) Weighted automata can be seen as a natural generalization of finite state automata to more complex algebraic structures. The standard reasoning tasks for unweighted automata can also be generalized to the weighted setting. In this report we study the problems of intersection, complementation, and inclusion for weighted automata on infinite trees and show that they are not harder complexity-wise than reasoning with unweighted automata. We also present explicit methods for solving these problems optimally. info:eu-repo/classification/ddc/004 ddc:004
27	Optimierung in normierten Räumen Mehlitz, Patrick 10 August 2013 (has links) (PDF) Die Arbeit abstrahiert bekannte Konzepte der endlichdimensionalen Optimierung im Hinblick auf deren Anwendung in Banachräumen. Hierfür werden zunächst grundlegende Elemente der Funktionalanalysis wie schwache Konvergenz, Dualräume und Reflexivität vorgestellt. Anschließend erfolgt eine kurze Einführung in die Thematik der Fréchet-Differenzierbarkeit und eine Abstraktion des Begriffs der partiellen Ordnungsrelation in normierten Räumen. Nach der Formulierung eines allgemeinen Existenzsatzes für globale Optimallösungen von abstrakten Optimierungsaufgaben werden notwendige Optimalitätsbedingungen vom Karush-Kuhn-Tucker-Typ hergeleitet. Abschließend wird eine hinreichende Optimalitätsbedingung vom Karush-Kuhn-Tucker-Typ unter verallgemeinerten Konvexitätsvoraussetzungen verifiziert. normierter Raum Banachraum Optimierung Satz von Weierstraß KKT-Bedingungen optimale Steuerung normed space Banachspace optimization Weierstraß-theorem KKT-conditions optimal control ddc:510 Normierter Raum Funktionalanalysis Fréchet-Differenzierbarkeit Optimierung Banach-Raum Optimale Kontrolle Karush-Kuhn-Tucker-Bedingungen
28	Zauberworte Schröder, Gesine 21 September 2016 (has links) Ausgehend von einem ‚Close Reading’ der ersten Durchführung aus dem langsamen Satz von Johann Nepomuk Davids dritter Symphonie diskutiert der Beitrag Kontrapunktlehrwerke der 1930- und frühen 1940er-Jahre, um von dort her das Spielfeld von ‚Linearität' abzustecken, eines Begriffs, der aus der Theorie der Bildenden Kunst Mitte der 1910er-Jahre in musikgeschichtliche Diskurse wanderte, um sich um 1940 mit kämpferischem Ton zu rüsten. info:eu-repo/classification/ddc/780 ddc:780
29	Some Initiatives in Calculus Teaching Abramovitz, Buma, Berezina, Miryam, Berman, Abraham, Shvartsman, Ludmila 10 April 2012 (has links) In our experience of teaching Calculus to engineering undergraduates we have had to grapple with many different problems. A major hurdle has been students’ inability to appreciate the importance of the theory. In their view the theoretical part of mathematics is separate from the computing part. In general, students also believe that they can pass their exams even though they do not have a real understanding of the theory behind the problems they are required to solve. In an effort to surmount these difficulties we tried to find ways to make students better understand the theoretical part of Calculus. This paper describes our experience of teaching Calculus. It reports on the continuation of our previous research. info:eu-repo/classification/ddc/510 ddc:510
30	The Bruckner Challenge: In- and Outward Dialogues in The Third Symphony’s Slow Movements Venegas, Gabriel Ignacio 23 October 2023 (has links) No description available. info:eu-repo/classification/ddc/780 ddc:780

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