000 04379nam a22004455i 4500
001 978-1-4614-6333-7
003 DE-He213
005 20140220082824.0
007 cr nn 008mamaa
008 130723s2013 xxu| s |||| 0|eng d
020 _a9781461463337
_9978-1-4614-6333-7
024 7 _a10.1007/978-1-4614-6333-7
_2doi
050 4 _aQA21-27
072 7 _aPBX
_2bicssc
072 7 _aMAT015000
_2bisacsh
082 0 4 _a510.9
_223
100 1 _aHawkins, Thomas.
_eauthor.
245 1 4 _aThe Mathematics of Frobenius in Context
_h[electronic resource] :
_bA Journey Through 18th to 20th Century Mathematics /
_cby Thomas Hawkins.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXIII, 699 p. 9 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSources and Studies in the History of Mathematics and Physical Sciences,
_x2196-8810
505 0 _a1. 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.
520 _aFrobenius 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 “in 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 context” 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 18th–20th 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 Frobenius’ 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).
650 0 _aMathematics.
650 0 _aMatrix theory.
650 1 4 _aMathematics.
650 2 4 _aHistory of Mathematical Sciences.
650 2 4 _aLinear and Multilinear Algebras, Matrix Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461463320
830 0 _aSources and Studies in the History of Mathematics and Physical Sciences,
_x2196-8810
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-6333-7
912 _aZDB-2-SMA
999 _c95645
_d95645