Algebra II
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Das vorliegende, nunmehr zum neunten Male herausgebrachte Werk von B. L. VAN DER W AERDEN nimmt unter den mathematischen Lehrbiichem eine auBergewohnliche Stellung ein. Selten nur hat in der Vergangenheit ein Lehrbuch eine iihnlich groBe Wirkung auf das mathematische Leben ausgeiibt wie dieses. Seit seinem ersten Erscheinen im Sommer 1930, also vor nunmehr 63 Jahren, haben Generationen von Mathematikem nach ihm die Algebra gelemt, zumindest im deutschsprachigen Bereich. Fiir zahllose Studenten bedeutete es Eintritt und Aufnahme in die hOhere Mathematik, fur viele war es die erste Stufe zu wissenschaftlicher Arbeit und mathematischer Forscherlaufbahn. Worin liegt das Geheimnis eines solch langlebigen Erfolges? Auf diese Frage hatte mancher Autor gem eine Antwort. Der eine versucht eine Verbesserung durch eine breitere Grundlegung, der andere durch verein- fachteArgumentation, ein dritter durch groBere Vollstandigkeit, ein vierter durch Verwirklichung aller dieser Moglichkeiten - vergebens, einen "van der Waerden" hat es bis heute nicht wieder gegeben. Zieht man einmal andere beriihmte Lehrbiicher der Vergangenheit zur Betrachtung heran, wie etwa die EULERsche und die WEBERsche "Algebra", den HILBERTschen "Zahlbericht", den "Roten Mumford", die SERREsche "Cohomologie galoisienne" (welche letztere ein Lehrbuch gar nicht hat sein sollen, urn dann doch ein so groBartiges zu werden), so erkennt man, daB es nicht die systematische Vollstandigkeit und die fraglose Vollkommenheit ist, die den Erfolg hervorbringt.
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