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  • © 2013

The Mathematics of Frobenius in Context

A Journey Through 18th to 20th Century Mathematics

Authors:

  • Written by an expert in the field with forty years of research on the subject
  • Presented in three parts for optimal accessibility
  • Contains a detailed table of contents to guide readers to the works of greatest interest to them

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xiii
  2. Overview of Frobenius’ Career and Mathematics

    1. Front Matter

      Pages 1-1
  3. Overview of Frobenius’ Career and Mathematics

    1. A Berlin Education

      • Thomas Hawkins
      Pages 3-31
    2. Berlin Professor: 1892–1917

      • Thomas Hawkins
      Pages 53-70
  4. Berlin-Style Linear Algebra

    1. Front Matter

      Pages 71-71
    2. The Paradigm: Weierstrass’ Memoir of 1858

      • Thomas Hawkins
      Pages 73-113
  5. The Mathematics of Frobenius

    1. Front Matter

      Pages 153-153
    2. The Problem of Pfaff

      • Thomas Hawkins
      Pages 155-204
    3. Arithmetic Investigations: Linear Algebra

      • Thomas Hawkins
      Pages 247-281
    4. Arithmetic Investigations: Groups

      • Thomas Hawkins
      Pages 283-343
    5. The Group Determinant Problem

      • Thomas Hawkins
      Pages 433-460
    6. Alternative Routes to Representation Theory

      • Thomas Hawkins
      Pages 495-514
    7. Characters and Representations After 1897

      • Thomas Hawkins
      Pages 515-565
    8. Loose Ends

      • Thomas Hawkins
      Pages 567-606

About this book

Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices.

Reviews

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)

Authors and Affiliations

  • Dept. Mathematics & Statistics, Boston University, Boston, USA

    Thomas Hawkins

About the author

Thomas Hawkins won the 2001 Whiteman Prize, an AMS prize that honors notable exposition in the history of mathematics. The citation for the prize calls Hawkins "an outstanding historian of mathematics whose current research and numerous publications display the highest standards of mathematical and historical sophistication."  The citation also mentions a number of Hawkins’ works, including his book, The Emergence of the Theory of Lie Groups: An Essay in the History of Mathematics 1869-1926.  "Hawkins’ work has truly transformed our understanding of how modern mathematics has evolved," the citation concludes.

Bibliographic Information

Buy it now

Buying options

eBook USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access