Product Description
Sophus Lie (1842-1899) was without doubt one of Norway's greatest scientific talents. The terms Lie groups and Lie algebra are today part of the standard mathematical vocabulary. In his comprehensive biography, Arild Stubhaug lets us come close to both the person Sophus Lie and his time. We follow him through childhood at the vicarage in Nodfjordeid, his growing up in Moss, school and studying in Christiania, traveling in Europe and his contacts with the leading mathematicians of his time. The academic and scientific career brought Lie from Christiania to Leipzig as professor, before the attempt to call him back to Norway, when she stood on the threshold to national sovereignty, was successful. ... Read more

Customer Reviews (1)

Mathematical Reviews' reference
Stubhaug/Daly contribution is welcome indeed. Here is information for finding the other book that Mathematical Reviews review of Stubhaug/Daly calls a "definitive history of the mathematical theory" and like Stubhaug/Daly "(a blessing to) the study of the history of Lie groups":

Thomas Hawkins, "Emergence of The Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926", ISBN 0-387-98963-3, Springer, 2000.

Hawkins' history has sections on the contributions of Sophus Lie, Wilhelm Killing, Elie Cartan, and Hermann Weyl. ... Read more

Customer Reviews (2)

This great book must be reprinted!
Unfortunately Birkhauser let it go out of print and there's currently only one used copy for sale for an exorbitant price. I could write a lengthy review to encourage you to buy a copy if it was available at a fair price.

Briefly, I. M. Yaglom has written a very accessible history of 19th century mathematics, with emphasis on interesting biographies of the leading protagonists and on the subjects most closely related to the work of Klein and Lie, whose own work is not discussed in detail until late in the book, despite the book's title.

A great history of geometry and groups in the 19th century
Starting with Galois and his contribution to the evolving subject of group theory Yaglom gives a beautiful account of the lives and works of the major players in the development of the subject in the nineteenth century:Jordan, who was a teacher of Lie and Klein in Paris and their adventures during the Franco-Prussian War. Monge and Poncelet developing projective geometry as well asBolyai, Gauss and Lobachevsky and their discovery of hyperbolic geometry. Riemann's contributions and the development of modern linear Algebra by Grassmann, Cayley and Hamilton are described in detail. The last two chapters are devoted to Lie's development of Lie Algebras and his construction of the geometry from a continuous group and Klein's Erlanger Programm unifying the different approaches to geometry by emphasizing automorphism groups. These last pages are definitely the climax of the book.

All of this only occupies the first half of the book, the second half consists of extensive notes to the former, intended to help the reader deepen her understanding of the subject in a second reading.

I think this book is very readable and should be accessible to any interested reader who has a slight understanding of the terms used so far in this review. In particular I enjoyed the details of the lives of the mathematicians involved and how the whole story seemed to culminate in the works of Lie and Klein. ... Read more

Product Description
An expository work by the originator of the theory of continuous groups. This is a textbook on continuous groups with applications to various topics in geometry and algebra. Whereas Lie's Transformationsgruppen is strictly analytic, this work makes free use of geometrical ideas both in the illustrative examples and in the proofs, so that the underlying geometrical motivations are made clear. The text is in German. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description
Sophus Lie had a tremendous impact in several areas of mathematics. His work centered on understanding continuous transformation groups and showing how these groups supply an organizing principle for different areas of mathematics. One of those areas is differential equations, and this book is his magnum opus on the subject. One of Lie's major interests was to develop a theory for differential equations in analogy to Galois theory for polynomial equations. He showed how one could naturally associate a continuous group to a differential equation, so that the solvability of the group (in the sense of algebra) is related to the solvability of the differential equation (in the sense of ``quadrature'', meaning integration and algebraic manipulations). The book also discusses Lie's remarkable classification of all three-dimensional groups and their possible actions on the plane. The exposition in the book is elementary and contains numerous examples. This is a textbook on the integration of ordinary and partial differential equations in which the Lie theory for solving such equations is expounded. The text is in German. ... Read more

Product Description
The Geometry of Contact Transformation, Sophus Lie's final work. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This Book Is In French. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
Sophus Lie had a tremendous impact in several areas of mathematics. His work centered on understanding continuous transformation groups and showing how these groups supply an organizing principle for different areas of mathematics, including geometry, mechanics, and partial differential equations. This is his main treatise on the theory of transformation groups. The Bible of transformation groups; a work of vast range and great originality. It is written with especial simplicity of language. There are frequent resumes throughout the work and an abundance of illustrations. The text is in German. ... Read more

Product Description
This Book Is In German. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
The Geometry of Contact Transformation, Sophus Lie's final work. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more