rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    non sort: The
    title: Mathematics of Frobenius in Context
    sub title: A Journey Through 18th to 20th Century Mathematics
  name:
    name part: Hawkins, Thomas.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 699 p. online resource.
  abstract: 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 “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 T…
  table of contents: 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.
  note: by Thomas Hawkins.
  subject:
    topic: Mathematics
  subject:
    topic: Matrix theory
  subject:
    topic: Algebra
  subject:
    topic: History
  subject:
    topic: Mathematics
  subject:
    topic: History of Mathematical Sciences
  subject:
    topic: Linear and Multilinear Algebras, Matrix Theory
  classification: QA21-27
  classification: 510.9
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Sources and Studies in the History of Mathematics and Physical Sciences
  identifier: 9781461463337
  identifier: http://dx.doi.org/10.1007/978-1-4614-6333-7
  record info:
    record creation date: 130723
    record change date: 20151218111759.0
    record identifier: 978-1-4614-6333-7