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 ...
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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.
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Add this copy of Nonstandard Analysis: In Higher Education, Logic and to cart. $74.99, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2024 by De Gruyter.
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Fine. Contains: Tables, black & white, Illustrations, black & white, Illustrations, color. De Gruyter STEM . 8 b/w and 1 col. ill., 20 b/w tbl. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Nonstandard Analysis: In Higher Education, Logic and to cart. $84.52, new condition, Sold by GreatBookPrices rated 4.0 out of 5 stars, ships from Columbia, MD, UNITED STATES, published 2024 by De Gruyter.
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New. Contains: Tables, black & white, Illustrations, black & white, Illustrations, color. De Gruyter STEM . 8 b/w and 1 col. ill., 20 b/w tbl. Intended for professional and scholarly audience. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
Add this copy of Nonstandard Analysis: in Higher Education, Logic and to cart. $84.53, new condition, Sold by Just one more Chapter, ships from Miramar, FL, UNITED STATES, published 2024 by De Gruyter.
