Non-standard Analysis
by Abraham Robinson
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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 show more 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. show lessTags
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From the horse's mouth -- the discoverer of nonstandard analysis himself (1918-1974) wrote this rigorous exposition, noted for its difficult logic-theoretic starting point. Pretty impenetrable, but I came to understand some of the basics of the subject a little better by reading the article on it in the 1972 Jun issue of Scientific American (That, however, was a bit *too* nontechnical.)
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 show more problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. show less
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Abraham Robinson is best known among mathematicians for his revolutionary discovery and development of nonstandard analysis, a rigorous theory of infinitesimals that Robinson used to unite mathematical logic with the larger body of modern mathematics. Born in Waldenburg, Lower Silesia, in 1918, Robinson spent much of his childhood in Breslau. In show more 1933, he emigrated from Nazi Germany to Palestine, where he studied mathematics at the Hebrew University with Abraham Fraenkel. Robinson studied briefly at the Sorbonne, barely escaping to England when the Germans invaded France in June 1940. During World War II, he worked at the Royal Aircraft Establishment in Farnborough, analyzing the design of supersonic airfoils. Beginning with his Ph.D. on model theory at the University of London in 1949, Robinson began to eclipse his wartime aeronautical research. Robinson first taught at the Cranfield College of Aeronautics and, beginning in 1951, in the Mathematics Department at the University of Toronto. In 1957, he returned to pure mathematics as Fraenkel's successor at Hebrew University and was appointed a professor of mathematics and philosophy at the University of California, Los Angeles, in 1962. Robinson finally moved to a position at Yale University in 1967, where he continued his research on model theory and nonstandard analysis until his untimely death in 1974. (Bowker Author Biography) show less
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- English
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- Paper, Ebook
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