Extension theory
Author(s)
Bibliographic Information
Extension theory
（History of mathematics, v. 19）
American Mathematical Society, c2000
- Other Title
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Die Ausdehnungslehre
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
Translation of: Die Ausdehnungslehre
Includes bibliographical references and index
Description and Table of Contents
Description
The Ausdehnungslehre of 1862 is Grassmann's most mature presentation of his 'extension theory'. The work was unique in capturing the full sweep of his mathematical achievements. Compared to Grassmann's first book, ""Lineale Ausdehnungslehre"", this book contains an enormous amount of new material, including a detailed development of the inner product and its relation to the concept of angle, the 'theory of functions' from the point of view of extension theory, and Grassmann's contribution to the Pfaff problem.In many ways, this book is the version of Grassmann's system most accessible to contemporary readers. This translation is based on the material in Grassmann's ""Gesammelte Werke"", published by B.G. Teubner (Stuttgart and Leipzig, Germany). It includes nearly all the Editorial Notes from that edition, but the 'improved' proofs are relocated, and Grassmann's original proofs are restored to their proper places. The original Editorial Notes are augmented by Supplementary Notes, elucidating Grassmann's achievement in modern terms. This volume is one of an informal sequence of works within the ""History of Mathematics"" series. Volumes in this subset, 'Sources', are classical mathematical works that served as cornerstones for modern mathematical thought.
Table of Contents
The elementary conjunctions of extensive magnitudes: Addition, subtraction, multiples and fractions of extensive magnitudes The product structure in general Combinatorial product Inner product Applications to geometry The theory of functions: Functions in general Differential calculus Infinite series Integral calculus Index of technical terms Editorial notes Supplementary notes Subject index.
by "Nielsen BookData"
