Applied Nonstandard Analysis (Dover Books on Mathematics) by Martin Davis (PDF)

Description

Geared toward upper-level undergraduates and graduate students, this text explores the applications of nonstandard analysis without assuming any knowledge of mathematical logic. It develops the key techniques of nonstandard analysis at the outset from a single, powerful construction; then, beginning with a nonstandard construction of the real number system, it leads students through a nonstandard treatment of the basic topics of elementary real analysis, topological spaces, and Hilbert space.Important topics include nonstandard treatments of equicontinuity, nonmeasurable sets, and the existence of Haar measure. The focus on compact operators on a Hilbert space includes the Bernstein-Robinson theorem on invariant subspaces, which was first proved with nonstandard methods. Ever mindful of the needs of readers with little background in these subjects, the text offers a straightforward treatment that provides a strong foundation for advanced studies of analysis

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Has plenty on how to use the transfer principle along with concurrent relations and their applications. Covers all the basics of calculus within the nonstandard framework and parts of functional analysis.

⭐Nonstandard analysis is one of those ideas that came too late, (Abraham Robinson, 1970s.) Since the ‘standard analysis’ of e – d-proofs took root some decades back and does, less clearly, what nonstandard analysis does – provide an easily accessible foundation for calculus. The whole first-year -calculus industry with its textbooks of astronomical expense and planetary mass, precludes ‘nonstandard’ views of getting the attention they deserve.Martin Davis’ book is clear and well-writen,and pitched at a post-calculus

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