Non-standard Analysis by Abraham Robinson (PDF)

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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.

User’s Reviews

Editorial Reviews: Review “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. About the Author Abraham Robinson (1918-1974) was born in Prussia and taught mathematics at universities in Canada, Israel, and the United States. At the time of his death he was Sterling Professor of Mathematics at Yale University. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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)

⭐Llegó muy antes y estoy satisfecha porque es como lo esperabaexcellent text for an infinitesimal approach

⭐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

⭐by Henle and Kleinberg which is a nice short introduction to the topic. (See also my review about the book in the corresponding page.)

⭐Don’t waste your time

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