Lectures on the Hyperreals - An Introduction to Nonstandard Analysis (Hardcover, 1998 ed.)

An introduction to nonstandard analysis based on a course given by the author. It is suitable for beginning graduates or upper undergraduates, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions. It is a source of new ideas, objects and proofs, and a wealth of powerful new principles of reasoning. The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective. It then sets out the theory of enlargements of fragments of the mathematical universe, providing a foundation for the full-scale development of the nonstandard methodology. The final chapters apply this to a number of topics, including Loeb measure theory and its relation to Lebesgue measure on the real line. Highlights include an early introduction of the ideas of internal, external and hyperfinite sets, and a more axiomatic set-theoretic approach to enlargements than is usual.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Graduate Texts in Mathematics, 188
Release date:	October 1998
First published:	1998
Authors:	Robert Goldblatt
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	293
Edition:	1998 ed.
ISBN-13:	978-0-387-98464-3
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Real analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
LSN:	0-387-98464-X
Barcode:	9780387984643

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