Funktionen- Und Relationenalgebren: Ein Kapitel Der Diskreten Mathematik
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Wie so viele Wissenszweige befindet sich auch die Mathematik im Umbruch. Neue Fragestellungen und neue Methoden tauchen dort auf, wo man sie vor einigen Jahrzehnten gar nicht erwartet hatte. Die Stellung der Mathematik in der Gesell- schaft, ihre Beziehungen zu anderen Wissenschaften, zur Technik und zur Wirt- schaft bekommen Ziige, die vielen Mathematikern der alteren Generation fremd erscheinen. Seit drei Jahrhunderten ist das Kernstiick der Mathematik die Analysis - die "hohere Mathematik", die Mathematik des Kontinuierlichen und die Mathema- tische Physik. In den Augen vieler Wissenschaftler war diese Disziplin die einzige, die anwendungsfahig ist: "Angewandte Mathematik" beinhaltet traditionsgemaB die gewohnlichen und partiellen Differentialgleichungen nebst den numerischen Methoden zu deren Losung. Alles andere war "reine, unangewandte" Mathematik, die - nach H. POINCARE (1854-1912) - "del' Ehre des menschlichen Geistes dient". Dazu gehorten dann die Algebra, Logik, Mengenlehre und fast die gesamte Geometrie. Nun sind einige Resultate dieser Disziplinen tatsachlich notwendig fiir den Aufbau del' angewandten Analysis, und es war wohl diese Eigenschaft, die yom Standpunkt del' Anwendungen die Existenz del' reinen Mathematik notwendig und berechtigt erscheinen lieB.
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