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Lectures on the Hyperreals - An Introduction to Nonstandard Analysis (Paperback, Softcover reprint of the original 1st ed. 1998)
Loot Price: R1,834
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Lectures on the Hyperreals - An Introduction to Nonstandard Analysis (Paperback, Softcover reprint of the original 1st ed. 1998)
Series: Graduate Texts in Mathematics, 188
Expected to ship within 10 - 15 working days
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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.
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