The Mathematics of Frobenius in Context

A Journey Through 18th to 20th Century Mathematics

Authors:

ISBN: 978-1-4614-6332-0 (Print) 978-1-4614-6333-7 (Online)

Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiii

  2. Overview of Frobenius’ Career and Mathematics

    1. Front Matter

      Pages 1-1

    2. No Access

      Chapter

      Pages 3-31

      A Berlin Education

    3. No Access

      Chapter

      Pages 33-51

      Professor at the Zurich Polytechnic: 1874–1892

    4. No Access

      Chapter

      Pages 53-70

      Berlin Professor: 1892–1917

  3. Berlin-Style Linear Algebra

    1. Front Matter

      Pages 71-71

    2. No Access

      Chapter

      Pages 73-113

      The Paradigm: Weierstrass’ Memoir of 1858

    3. No Access

      Chapter

      Pages 115-152

      Further Development of the Paradigm: 1858–1874

  4. The Mathematics of Frobenius

    1. Front Matter

      Pages 153-153

    2. No Access

      Chapter

      Pages 155-204

      The Problem of Pfaff

    3. No Access

      Chapter

      Pages 205-246

      The Cayley–Hermite Problem and Matrix Algebra

    4. No Access

      Chapter

      Pages 247-281

      Arithmetic Investigations: Linear Algebra

    5. No Access

      Chapter

      Pages 283-343

      Arithmetic Investigations: Groups

    6. No Access

      Chapter

      Pages 345-385

      Abelian Functions: Problems of Hermite and Kronecker

    7. No Access

      Chapter

      Pages 387-431

      Frobenius’ Generalized Theory of Theta Functions

    8. No Access

      Chapter

      Pages 433-460

      The Group Determinant Problem

    9. No Access

      Chapter

      Pages 461-493

      Group Characters and Representations 1896–1897

    10. No Access

      Chapter

      Pages 495-514

      Alternative Routes to Representation Theory

    11. No Access

      Chapter

      Pages 515-565

      Characters and Representations After 1897

    12. No Access

      Chapter

      Pages 567-606

      Loose Ends

    13. No Access

      Chapter

      Pages 607-649

      Nonnegative Matrices

    14. No Access

      Chapter

      Pages 651-657

      The Mathematics of Frobenius in Retrospect

  5. Back Matter

    Pages 659-699