Teilbarkeit und Primzahlen. Einführung und Überblick
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Studienarbeit aus dem Jahr 2021 im Fachbereich Mathematik - Zahlentheorie, Note: 1,3, Universität Erfurt, Veranstaltung: Teilbarkeit, Primzahlen und Zahlenkongruenzen, Sprache: Deutsch, Abstract: Diese Hausarbeit gibt einen Überblick und eine Einführung in die Elementare Zahlentheorie. Dabei wird nach der Einleitung mit einem Zitat von Heinrich Winter, der Komplex der Teilbarkeit behandelt. In diesem wird zuerst der Ausgangspunkt der Teilbarkeit der natürlichen Zahlen beleuchtet, an den sich die Teilbarkeitsregeln anschlie en. Anschlie end liegt der thematische Schwerpunkt auf dem Teilen mit Rest der den euklidischen Algorithmus, den grö ten gemeinsamen Teiler und das kleinste gemeinsame Vielfache impliziert. Im dritten Teil der Arbeit wird sich den Primzahlen gewidmet. Ausgehend von der Definition einer Primzahl, erfolgt die Begründung warum die Zahl 1 nicht als Primzahl anerkannt wird und werden kann. Im Anschluss geht es um die Primfaktorzerlegung und die Verwendung zur Berechnung von dem grö ten gemeinsamen Vielfachen (ggT) und kleinsten gemeinsamen Vielfachen (kgV). Ebenso wird das Primzahlsieb des Eratosthenes und seine Anwendung erläutert. Der vierte Punkt widmet sich der Bedeutung für eine mathematische Allgemeinbildung der seinen Schwerpunkt auf den Klassenstufen 5 und 6 legt. Nach der Bestimmung der Ausgangslage zu Beginn der Klasse 5 wird eine exemplarische Unterrichtsstunde mit didaktischen Aspekten behandelt, an den sich der Punkt Synergieeffekte und Weiterentwicklung von Kompetenzen anschlie t. Eine Zusammenfassung der wichtigsten Punkte schlie t die Arbeit ab.
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