Lectures on the Hyperreals: An Introduction to Nonstandard Analysis: 188 (Graduate Texts in Mathematics, 188) - Tapa dura

Goldblatt, R.; Goldblatt, Robert

 
9780387984643: Lectures on the Hyperreals: An Introduction to Nonstandard Analysis: 188 (Graduate Texts in Mathematics, 188)
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ISBN 10: 038798464X ISBN 13: 9780387984643
Editorial: Springer, 1998

Sinopsis

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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Críticas

R. Goldblatt

Lectures on the Hyperreals

An Introduction to Nonstandard Analysis

"Suitable for a graduate course . . . could be covered in an advanced undergraduate course . . . The author’s ideas on how to achieve both intelligibility and rigor . . . will be useful reading for anyone intending to teach nonstandard analysis."―AMERICAN MATHEMATICAL SOCIETY

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
1998
Idioma
Inglés
ISBN 10 
038798464X
ISBN 13 
9780387984643
Encuadernación
Tapa dura
Número de páginas
312
Contacto del fabricante
no disponible
Persona responsable
CMN Printpool Inh. Mathis Neumann
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Friedrich-Karl-Str. 9
Hamburg
Alemania

Otras ediciones populares con el mismo título

9781461268413: Lectures on the Hyperreals: An Introduction to Nonstandard Analysis: 188 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  1461268419 ISBN 13:  9781461268413
Editorial: Springer, 2012
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