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Beschreibung
Currently, nonstandard analysis is barely considered in university teaching. The author argues that nonstandard analysis is valuable not only for teaching, but also for understanding standard analysis and mathematics itself. An axiomatic approach wich pays attention to different language levels (for example, in the distinction between sums of ones and the natural numbers of the theory) leads… naturally to a nonstandard theory. For motivation historical ideas of Leibniz can be taken up. The book contains an elaborated concept that follows this approach and is suitable, for example, as a basis for a lecture-supplementary course.
The monograph part presents all major approaches to nonstandard analysis and discusses logical, model-theoretic, and set-theoretic investigations to reveal possible mathematical reasons that may lead to reservations about nonstandard analysis. Also various foundational positions as well as ontological, epistemological, and application-related issues are addressed. It turns out that the one-sided preference for standard analysis is justified neither from a didactic, mathematical nor philosophical point of view.
Thus, the book is especially valuable for students and instructors of analysis who are also interested in the foundations of their subject. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
16.12.2024
Sprache
Englisch
EAN
9783111428871
Herausgeber
De Gruyter
Serien- oder Bandtitel
De Gruyter STEM
Sonderedition
Nein
Autor
Karl Kuhlemann
Seitenanzahl
216
Auflage
1
Einbandart
Broschiert
Hersteller: Walter de Gruyter GmbH, Genthiner Straße 13, Berlin, Deutschland, 10785, productsafety@degruyterbrill.com, Walter de Gruyter GmbH, Genthiner Straße 13, DE-10785 Berlin
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