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Field name	Details
Dewey Class	510.9
Title	The Mathematics of Frobenius in Context ([Ebook]) : A Journey Through 18th to 20th Century Mathematics / by Thomas Hawkins.
Author	Hawkins, Thomas. , 1938-
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer
Publication	, 2013.
Physical Details	XIII, 699 pages. 9 illus. : online resource.
Series	Sources and studies in the history of mathematics and physical sciences 2196-8810
ISBN	9781461463337
Summary Note	Frobenius is best known as creator of the theory of group characters and representations, but his name is attached to a multitude of theorems and concepts from a broad spectrum of mathematical disciplines. In this book his mathematics' is presented âin context in two senses. The first provides the reader with the historical background necessary to understand why Frobenius undertook to solve a particular problem and to appreciate the magnitude of his achievement. Part of the context involves Frobenius' training in the Berlin school of mathematics presided over by Weierstrass, Kronecker, and Kummer, from whom he learned disciplinary ideals as well as theorems. Frobenius' mathematics is also presented in contextâ in that the author traces the ways in which his work was subsequently applied, developed, and ultimately incorporated into present-day mathematics. As a consequence of the contextual approach, the reader will encounter a broad swath of diverse and important strands of 18thâ20th century mathematics, ranging from the work of Lagrange and Laplace on stability of linear systems of differential equations to the theory of complex abelian varieties. The book is divided into three parts. Part I provides an overview of Frobeniusâ entire mathematical career and thus serves as an introduction to the main body of the book. Here, within the framework of his educational and professional career, his contributions to mathematics and the attendant backgrounds are briefly sketched and their subsequent impact upon the development of mathematics indicated. Part II presents the development of core aspects of linear algebra up to and including the work of Weierstrass and Kronecker. The chapters of Part III deal in depth with Frobenius' major works and can be read independently of one another. Thomas Hawkins was awarded the MAA Chauvenet Prize for expository writing and was the first recipient of the AMS Whiteman Prize for historical exposition. His last book was Emergence of the Theory of Lie Groups (Springer, 2000).:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4614-6333-7
Links to Related Works	Subject References: Alebras, Linear . Frobenius, Ferdinand Georg . History of Mathematical Sciences . Linear and Multilinear Algebras, Matrix Theory . Mathematics — History — 18th century . Matrix theory . Authors: Hawkins, Thomas. 1938- . Corporate Authors: SpringerLink (Online service) . Series: Sources and studies in the history of mathematics and physical sciences . Classification: 510.9 . 510.9 (DDC 23) .

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The Mathematics of Frobenius in Context: A Journey Through 18th to 20th Century Mathematics

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