Abraham Robinson

Broschiertes Buch

Non-standard Analysis

Beschreibung

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.

Autor

Abraham Robinson (born Robinsohn; October 6, 1918 ) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics. He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wäbrzych, in Poland. In 1933, he emigrated to the British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynamics and becoming an expert on the airfoils used in the wings of fighter planes. After the war, Robinson worked in London, Toronto, and Jerusalem, but ended up at University of California, Los Angeles in 1962. He became known for his approach of using the methods of mathematical logic to attack problems in analysis and abstract algebra. He "introduced many of the fundamental notions of model theory". Using these methods, he found a way of using formal logic to show that there are self-consistent nonstandard models of the real number system that include infinite and infinitesimal numbers. Others, such as Wilhelmus Luxemburg, showed that the same results could be achieved using ultrafilters, which made Robinson's work more accessible to mathematicians who lacked training in formal logic. Robinson's book Non-standard Analysis was published in 1966. Robinson was strongly interested in the history and philosophy of mathematics, and often remarked that he wanted to get inside the head of Leibniz, the first mathematician to attempt to articulate clearly the concept of infinitesimal numbers. Abraham Robinson was Professor of Mathematics and Philosophy at the University of California at Los Angeles. He received his M.Sc. Degree from Hebrew University of Jerusalem and his Ph. D. and M.Sc. Degrees at University of London. Dr. Robinson taught at University of Toronto , the Hebrew University of Jerusalem and was a visiting Professor of Mathematics at Princeton University. He had been affiliated with the University of California at Los Angeles since 1962. Dr. Robinson was the author or co-author of five books and over sixty papers in pure and applied mathematics and mathematical logic. While at UCLA his colleagues remember him as working hard to accommodate PhD students of all levels of ability by finding them projects of the appropriate difficulty. He was courted by Yale, and after some initial reluctance, he moved there in 1967. In the Spring of 1973 he was a member of the Institute for Advanced Study. He died on April 11, 1974.

Produktdetails

• Verlag: Princeton University Press
• Seitenzahl: 314
• Erscheinungstermin: 28. Januar 1996
• Englisch
• Abmessung: 234mm x 156mm x 18mm
• Gewicht: 480g
• ISBN-13: 9780691044903
• ISBN-10: 0691044902
• Artikelnr.: 21953617

Rezensionen

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.