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Mathematics Zahlen f¨¹r Einsteiger. Elemente der Algebra und Aufbau der Zahlbereiche
Posted on 2010-04-12
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More J¨¹rg Kramer ¡°Zahlen f¨¹r Einsteiger. Elemente der Algebra und Aufbau der Zahlbereiche" In dem Lehrbuch werden ausgehend von den nat¨¹rlichen Zahlen systematisch die ganzen, rationalen und reellen Zahlen konstruiert. Dazu werden jeweils die aus der Algebra ben?tigten Grundlagen bereitgestellt und unmittelbar angewendet. Besonderes Augenmerk wird den verschiedenen Konstruktionsm?glichkeiten der reellen Zahlen geschenkt. ¨¹berdies finden verschiedene Darstellungsarten reeller Zahlen durch Dezimal- und Kettenbr¨¹che Ber¨¹cksichtigung. Im letzten Teil wird die feinere Struktur reeller Zahlen in Bezug auf Algebraizit?t und Transzendenz untersucht, wobei insbe-sondere Konstruktionen mit Zirkel und Lineal eine wichtige Rolle spielen.Dieses Buch richtet sich an Mathematikstudierende der ersten Semester und vermittelt einen ersten Einstieg in Elemente der Zahlentheorie und Algebra. Ausgehend von den nat¨¹rlichen Zahlen werden systematisch die ganzen, rationalen, reellen, komplexen Zahlen konstruiert. Dazu werden jeweils die aus der Algebra ben?tigten Grundlagen bereitgestellt und unmittelbar angewendet. Z?hlen geh?rt zu einem der Uranliegen der Menschheit und die Entwicklung von Zahl- und Ziffernbegriffen nimmt in jeder Zivilisation ihren speziellen Platz ein. Die systematische Vermittlung des Zahlbegriffs erfolgt in einem wesentlichen Ma?e durch die Schule. Es ist Ziel und Hauptanliegen dieses Buches, Studierenden, und hierbei vor allem Lehramtsstudierenden, eine systematische Einf¨¹hrung in den Aufbau der Zahlbereiche von einem mathematisch-fachwissenschaftlichen Standpunkt aus mit Blick auf fachdidaktische Bez¨¹ge anzubieten. "
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