The Mathematics of Frobenius in Context
A Journey Through 18th to 20th Century Mathematics
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This book on focuses on the work of Ferdinand Frobenius in linear algebra, its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. Also covers the Berlin school of mathematics and the guiding force of Weierstrass.
Frobenius made many important contributions to mathematics in thelatter part of the 19th century. Hawkins here focuses on his work inlinear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discussesthe Berlin school of mathematics and the guiding force of Weierstrassin that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laidthe groundwork for Frobenius's work in linear algebra. The bookconcludes with a discussion of Frobenius's contribution to the theoryof stochastic matrices.
Inhaltsverzeichnis
1. A Berlin Education. - 2. Professor at the Zurich Polytechnic. - 3. Berlin Professor. - 4. The Paradigm. - 5. Further Development of the Paradigm. - 6. The Problem of Pfaff. - 7. The Cayley-Hermite Problem and Matrix Algebra. - 8. Arithmetical Investigations: Linear Algebra. - 9. Arithmetical Investigations: Groups. - 10. Abelian Functions. - 11. Frobenius' Generalized Theory of Theta Functions. - 12. The Group Determinant Problem. - 13. Group Characters and Representations. - 14. Alternate Routes to Representation Theory. - 15. Characters and Representations after 1897. - 16. Loose Ends. - 17. Nonnegative Matrices. - 18. The Mathematics of Frobenius in Retrospect. - References. - Index.
Produktdetails
Erscheinungsdatum
06. August 2015
Sprache
englisch
Auflage
Softcover reprint of the original 1st edition 2013
Seitenanzahl
716
Reihe
Sources and Studies in the History of Mathematics and Physical Sciences
Autor/Autorin
Thomas Hawkins
Verlag/Hersteller
Produktart
kartoniert
Abbildungen
XIII, 699 p.
Gewicht
1066 g
Größe (L/B/H)
235/155/39 mm
Sonstiges
Previously published in hardcover
ISBN
9781489987006
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From the book reviews:
I highly recommend Hawkins book. It is very mathematical all the way through. Hawkins work is extraordinarily useful. It allows the mathematical community, even the great majority of us who do not read German well, to understand the work of the very important mathematician Frobenius. The great length of the book is essential to the book s success. (David P. Roberts, MAA Reviews, October, 2014)
The author has succeeded admirably in describing the mathematical work of Frobenius. this book is an excellent contribution to the mathematical literature it is, or should be, a role model for historical writing, and for bringing the mathematics of the recent past back to life. (Franz Lemmermeyer, zbMATH, Vol. 1281, 2014)
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