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Grundzüge Der Algebra by Otto Schafmeister, Hartmut Wiebe

Grundzüge Der Algebra

by Otto Schafmeister , Hartmut Wiebe
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Book cover type: Paperback
  • ISBN13: 9783519027546
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 248
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 1978
  • Item Weight: 295 grams
  • BISAC Subject(s): Engineering (General)

Algebra ist neben Analysis und Geometrie eine der tragenden Säulen der Schulmathe- matik und der Mathematik überhaupt. Wir haben in diesem Band versucht, eine Aus- wahl aus der klassischen Algebra und der elementaren Zahlentheorie zu treffen, die als Hintergrundinformation ftir den Mathematiklehrer am Gymnasium sinnvoll erscheint. Bei der ersten Bekanntschaft mit Algebra stehen das Zahlenrechnen und die Suche nach Lösungen ftir einfache Gleichungen im Vordergrund. Wir geben daher nach einer kurzen Darstellung der wichtigsten algebraischen Grundbegriffe einen vollständigen überblick über den Aufbau des Zahlsystems, wobei es uns darauf ankam, die Zahl- bereichserweiterungen als Spezialfall allgemeiner algebraischer Konstruktionen heraus- zuarbeiten. So zeigen wir die Gemeinsamkeiten bei der Konstruktion der ganzen und der rationalen Zahlen auf und gewinnen die reellen Zahlen und die komplexen Zahlen durch die allgemeinen Prozesse der Vervollständigung angeordneter Körper bzw. der Adjunktion von Nullstellen. Bei den Ausftihrungen über Gruppen legen wir besonderes Gewicht auf Beispiele ftir endliche Gruppen: Permutationsgruppen, Gruppen kleiner Ordnung, endliche Bewe- gungsgruppen der Ebene. Einen zentralen Platz nimmt die ausftihrliche Behandlung der Teilbarkeitslehre ein. Neben den Anwendungen bei ganzen Zahlen und Polynomen gehen wir exemplarisch auf die Zahlentheorie des Ringes der ganzen Gau schen Zahlen ein und zeigen, wie sich zahlentheoretische Aussagen über diesen Ring in Aussagen über Quadratsummen natürlicher Zahlen übersetzen lassen.

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