Die Ausdehnungslehre
Vollständig und in strenger Form bearbeitet

The 1862 extended version of a revolutionary 1844 work in German by the mathematician Hermann Grassmann (1809–77).

Hermann Grassmann (Author)

9781108065610, Cambridge University Press

Paperback / softback, published 16 October 2013

406 pages
21.6 x 14 x 2.3 cm, 0.51 kg

In 1844, the Prussian schoolmaster Hermann Grassmann (1809–77) published Die Lineale Ausdehnungslehre (also reissued in the Cambridge Library Collection). This revolutionary work anticipated the modern theory of vector spaces and exterior algebras. It was little understood at the time and the few sympathetic mathematicians, rather than trying harder to comprehend it, urged Grassmann to write an extended version of his theories. The present work is that version, first published in 1862. However, this also proved too far ahead of its time and Grassmann turned to historical linguistics, in which field his contributions are still remembered. His mathematical work eventually found champions such as Hankel, Peano, Whitehead and Élie Cartan, and it is now recognised for the brilliant achievement that it was in the history of mathematics.

I. Die einfachen Verknüpfungen extensiver Grössen: 1. Addition, Subtraktion, Vielfachung und Theilung extensiver Grössen
2. Die Produktbildung im Allgemeinen
3. Kombinatorisches Produkt
4. Inneres Produkt
5. Anwendung auf die Geometrie
II. Funktionslehre: 1. Funktionen im Allgemeinen
2. Differenzialrechnung
3. Unendliche Reihen
4. Integralrechnung.

Subject Areas: History of mathematics [PBX]