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Extension Theory

Hermann Grassmann
Publisher: 
American Mathematical Society/London Mathematical Society
Publication Date: 
2000
Number of Pages: 
411
Format: 
Paperback
Series: 
History of Mathematics 19
Price: 
83.00
ISBN: 
978-0-8218-2031-5
Category: 
Monograph
[Reviewed by
Fernando Q. Gouvêa
, on
05/17/2000
]

Hermann Grassmann’s Extension Theory (Ausdehnungslehre), first published in 1862, is a legendary book in the history of mathematics. Extending the ideas in his earlier book Linear Extension Theory, Grassmann here introduces a whole “calculus of extensive magnitudes” that is one of the historical roots of modern linear and multilinear algebra. In contrast to Grassmann’s earlier book, this one is more mathematical and less philosophical. It also goes much deeper into the subject, including applications of the ideas to what we would describe as multivariable calculus.

Grassmann’s earlier book and some of his shorter works were translated into English by Lloyd C. Kannenberg a few years ago and published as A New Branch of Mathematics (Open Court, 1995). Here the same translator brings us Grassmann’s more mature book. This new book in the “Sources” subseries is a most welcome addition to the AMS/LMS History of Mathematics series. It is a must-buy for those seriously interested in the history of mathematics.


Fernando Q. Gouvêa is the editor of MAA Reviews.

 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

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