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This study aims to embed the history of the central limit theorem within the history of the development of probability theory from its classical to its modern shape, and, more generally, within the corresponding development of mathematics. The history of the central limit theorem is not only expressed in light of "technical" achievement, but is also tied to the intellectual scope of its advancement. The history starts with Laplace's 1810 approximation to distributions of linear combinations of large numbers of independent random variables and its modifications by Poisson, Dirichlet, and Cauchy, and it proceeds up to the discussion of limit theorems in metric spaces by Donsker and Mourier around 1950. This self-contained exposition additionally describes the historical development of analytical probability theory and its tools, such as characteristic functions or moments. The importance of historical connections between the history of analysis and the history of probability theory is demonstrated in great detail. With a thorough discussion of mathematical concepts and ideas of proofs, the reader will be able to understand the mathematical details in light of contemporary development. Special terminology and notations of probability and statistics are used in a modest way and explained in historical context.

Central limit theorem -- History. --- Central limit theorem --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- History --- Central limit theorem. --- Free probability theory. --- Probability theory, Free --- Mathematics. --- History. --- Probabilities. --- Statistics. --- History of Mathematical Sciences. --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Asymptotic distribution (Probability theory) --- Limit theorems (Probability theory) --- Operator algebras --- Selfadjoint operators --- Distribution (Probability theory. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics . --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Annals --- Auxiliary sciences of history --- Math --- Science --- Mathematics - History --- Distribution (Probability theory) --- Statistics

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This ethnographic dictionary is the result of Hans Fischer's long-term fieldwork among the Wampar, who occupy the middle Markham Valley in Morobe Province, Papua New Guinea (PNG). Their language, Dzob Wampar, belongs to the Markham family of the Austronesian languages.

Dictionaries --- Bilingual & multilingual dictionaries --- Usage & grammar guides --- Language: history & general works --- linguistics --- Historical & comparative linguistics --- Austronesia --- Dictionary --- Papua New Guinea --- Markham Languages --- Wampar

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Physics --- Ensenyament de la física --- Study and teaching. --- Aprenentatge de la física --- Ensenyament --- Física

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This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementation of representations should consider design principles for using multiple representations. Investigations regarding their effect on classroom communication as well as on the learning results in all levels of schooling and for different topics of physics are reported. The book is intended for physics educators and their students at universities and for physics teachers in schools to apply multiple representations in physics in a productive way.

Education. --- Science education. --- Teaching. --- Higher education. --- Science Education. --- Higher Education. --- Teaching and Teacher Education. --- Study and Learning Skills. --- Learning & Instruction. --- Physics --- Study and teaching. --- Science --- Education, Higher. --- Study Skills. --- How to study --- Learning, Art of --- Method of study --- Study, Method of --- Study methods --- Life skills --- College students --- Higher education --- Postsecondary education --- Universities and colleges --- Science education --- Scientific education --- Education --- Learning. --- Instruction. --- Learning process --- Comprehension --- Didactics --- Instruction --- Pedagogy --- School teaching --- Schoolteaching --- Instructional systems --- Pedagogical content knowledge --- Training

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Dieser Band präsentiert Ergebnisse des interdisziplinären BMBF-Forschungsprojekts SchriFT I (Schreiben im Fachunterricht unter Einbeziehung des Türkischen). Ausgangspunkt ist die Annahme, dass ein textsortenbasiertes, an sprachlich-kognitiven Handlungen orientiertes Schreiben als Lernmedium dienen kann, um Fachinhalte strukturiert und vertieft zu vermitteln. Zur Prüfung der Zusammenhänge zwischen schriftsprachlichen Fähigkeiten und fachlichem Wissen wurde der Ist-Stand der Schreibfähigkeiten von 1.718 Schülerinnen und Schülern der Jahrgangsstufen 7 & 8 an Gesamtschulen in NRW erhoben (davon 186 aus dem herkunftssprachlichen Unterricht Türkisch). Mit Blick auf das mehrsprachige Repertoire wurden Zusammenhänge zwischen schrift- und allgemeinsprachlichen Fähigkeiten in deutsch- und türkischsprachigen Textprodukten analysiert. Die Ergebnisse deuten darauf hin, dass eine koordinierte Sprachenbildung fächer- und sprachenübergreifende Denk- und Verstehensprozesse anbahnen kann. Am Projekt SchriFT sind Forschende aus den Fächern Deutsch als Zweitsprache, Türkisch, Geschichte, Physik, Politik und Technik beteiligt. Diese Kooperation eröffnet eine multiperspektivische Sicht auf die im Projekt erhobenen Daten sowie die Erstellung fachspezifischer und fachübergreifender Sprachbildungskonzepte. [Die Beiträge] sind in Zeiten, in denen Politische Bildung durch das Gesamtkonzept Politische Bildung an bayerischen Schulen in allen Fächern eine Stärkung erfährt, erhellend und regen zur Reflexion an. - Markus Gloe, in: Forum Politikunterricht 1-2/2020.

Schreibforschung --- Schreibdidaktik --- Sprache im Fach --- Schreiben im Fach --- Sprachbildung --- Mehrsprachigkeit --- Textlinguistik --- Vergleichende und interkulturelle Sprachwissenschaft