THE MATHEMATICS OF FROBENIUS IN CONTEXT. A JOURNEY THROUGH 18TH TO 20TH CENTURY MATHEMATICS

1. A Berlin Education
2. Professor at the Zurich Polytechnic: 1874–1892
3. Berlin Professor: 1892–1917
4. The Paradigm: Weierstrass’ Memoir of 1858
5. Further Development of the Paradigm: 1858–1874
6. The Problem of Pfaff
7. The Cayley–Hermite Problem and Matrix Algebra
8. Arithmetic Investigations: Linear Algebra
9. Arithmetic Investigations: Groups
10. Abelian Functions: Problems of Hermite and Kronecker
11. Frobenius’ Generalized Theory of Theta Functions
12. The Group Determinant Problem
13. Group Characters and Representations 1896–1897
14. Alternative Routes to Representation Theory
15. Characters and Representations After 1897
16. Loose Ends
17. Nonnegative Matrices
18. The Mathematics of Frobenius in Retrospect

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.

Features
• 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

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.