Overview

Hermann G. Grasmann (1809-1877) - mathematician, physicist, linguist, educator - was trained in the universalist scientific spirit of nineteenth-century neohumanism. That neohumanism postulated the ideal unity and complementarity of language and mathematics. Grasmann pursued the vision of that ideal unity, and upon it he rested his seminal achievements. While his writings on linguistics and physics enjoyed immediate influence, decades were to pass before mathematicians recognized the full power of his major work, the Lineale Ausdehnungslehre of 1844, to reshape the foundations of modern mathematics. In this volume specialists from several disciplines present a comprehensive analysis of Grasmann's thought, its historical context and emergence, its reception, and its continuing influence on many branches of learning. The book addresses a general public in mathematics, physics, and linguistics, including graduate students in these fields, as well as historians of these disciplines.

Full Product Details

Author:   Gert Schubring
Publisher:   Springer
Imprint:   Springer
Edition:   1996 ed.
Volume:   187
Dimensions:   Width: 15.60cm , Height: 2.30cm , Length: 23.40cm
Weight:   1.640kg
ISBN:  

9780792342618

ISBN 10:   0792342615
Pages:   370
Publication Date:   31 August 1996
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

A survey of Grassmann’s Ausdehnungslehre.- On Grassmann’s life and his work as a mathematics teacher.- Remarks on the fate of Grassmann’s Nachlaß.- The influence of Grassmann’s theory of tides on the Ausdehnungslehre.- The influence of Justus Grassmann’s crystallographic works on Hermann Grassmann.- Geometrical Product — Exponentiation — Evo-lution. Justus Günther Grassmann and dynamist Naturphilosophie.- The cooperation between Hermann and Robert Grassmann on the foundations of mathematics.- The origins of colorimetry: What did Helmholtz and Maxwell learn from Grassmann?.- Hermann Grassmann’s contribution to the construction of a German “Kulturnation” — Scientific school grammar between Latin tradition and French conceptions.- The reception of Grassmann’s mathematical achievements by A. Clebsch and his school.- The reception of Grassmann’s work in Germany during the 1870s.- Reception of Grassmann’s ideas in Bohemia.- The influence of Grassmann on Italian projective n-dimensional geometry.- Hermann Günther Grassmann and the theory of hypercomplex number systems.- Basis and Dimension — from Grassmann to van der Waerden.- Emergence of vector calculus in physics: the early decades.- Where does Grassmann fit in the history of logic?.- The influence of Hermann Günther Grassmann and Robert Grassmann on Ernst Schröder’s Algebra of Logic.- Grassmann progressive and regressive products and CG-Algebras.- Grassmann’s Vision.- Grassmann’s Dialectics and Category Theory.- The completion of Grassmann’s Natur-Wissenschaftliche Methode.- Grassmannian manifolds in geometry.- Regressive products and Bourbaki.- The Grassmann product in physics.- Array-based logic.- An application of Grassmann geometry to a problem in robotics.- Notes oncontributors.- Notes and Credits to the Illustrations.

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