This book is a facsimile reprint and may contain imperfections such as marks, notations, marginalia and flawed pages. This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work. Product details Format Hardback | 70 pages Dimensions
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.
Product details
- Paperback | 293 pages
- 155 x 235 x 16.51mm | 480g
- 03 Oct 2012
- Springer-Verlag New York Inc.
- New York, NY, United States
- English
- Softcover reprint of the original 1st ed. 1998
- XIV, 293 p.
- 1461268419
- 9781461268413
- 3,144,173
Download Lectures on the Hyperreals : An Introduction to Nonstandard Analysis (9781461268413).pdf, available at prealblog.org for free.
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