Non-standard Analysis Revised ed. Edition

by Abraham Robinson (Author)

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ISBN-13: 978-0691044903

ISBN-10: 0691044902

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Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body.

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Editorial Reviews

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"Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and application of non-standard analysis which grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus." ― L'Enseignement Mathématique

From the Back Cover

This book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus.

Publisher : Princeton University Press; Revised ed. edition (January 8, 1996)
Language: : English
Paperback : 308 pages
ISBN-10 : 0691044902
ISBN-13 : 978-0691044903
Item Weight : 15 ounces
Dimensions : 6 x 0.73 x 9.25 inches

Best Sellers Rank: #1,469,125 in Books (See Top 100 in Books)
- #1,007 in Mathematical Analysis (Books)
- #1,069 in Calculus (Books)

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Amazon Customer

Not modern langauge

Reviewed in the United States on September 19, 2020

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I am someone with a knowledge of measure theory and understand analysis at a lower graduate level, so I am not totally unfamiliar with math.

However, the first chapter is near impossible to read. I have no idea what he is talking about. He talks about lower level predicate languages or something without giving any examples. I think he is simply saying there exists symbols and relationships and structure you can build from these symbols, but without ANY examples and with extremely verbose, unclear langauge, I really can't be sure I understand anything.

I would probably try to find something more modern. I haven't given up on it yet, but I am tempted.

tl;dr the structure and pedagogy is exceptionally poor - the worst of ANY math book I own (I own many)

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ana herrera

Eficiencia y calidad

Reviewed in the United States on January 13, 2020

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Llegó muy antes y estoy satisfecha porque es como lo esperaba

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Amazon Customer

Five Stars

Reviewed in the United States on August 20, 2017

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excellent text for an infinitesimal approach

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ScienceThinker

The classic text for non-standard analysis

Reviewed in the United States on June 8, 2012

This book is a reprint of Robinson's book originally published in 1965 and revised in 1974. It was written to explain the topic of non-standard analysis that he developed a few years earlier before the publication of the book. Many books have been written on non-standard analysis since then but this book remains a must-read classic for any serious mathematician. It is well written but it is neither a book for superficial reading, nor a book for the light-hearted.

If you are someone without serious ambitions to become an expert on non-standard analysis or someone who wants an introductory book before reading advanced books on the topic, then this is not the book for you. Instead read the book Infinitesimal Calculus (Dover Books on Mathematics) by Henle and Kleinberg which is a nice short introduction to the topic. (See also my review about the book in the corresponding page.)

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