The Algebra of Invariants

This 1903 book, which became a standard work, made recent German research on invariant theory available to British mathematicians.

John Hilton Grace (Author), Alfred Young (Author)

9781108013093, Cambridge University Press

Paperback / softback, published 31 October 2010

398 pages
21.6 x 14 x 2.2 cm, 0.5 kg

Invariant theory is a subject within abstract algebra that studies polynomial functions which do not change under transformations from a linear group. John Hilton Grace (1873–1958) was a research mathematician specialising in algebra and geometry. He was elected a Fellow of the Royal Society in 1908. His co-author Dr Alfred Young (1873–1940) was also a research mathematician before being ordained in 1908; in 1934 he too was elected a Fellow of the Royal Society. Abstract algebra was one of the new fields of study within mathematics which developed out of geometry during the nineteenth century. It became a major area of research in the late nineteenth and early twentieth centuries. First published in 1903, this book introduced the work on invariant theory of the German mathematicians Alfred Clebsch and Paul Gordan into British mathematics. It was considered the standard work on the subject.

Preface
1. Introduction
2. The fundamental theorem
3. Transvectants
4. Transvectants (continued)
5. Elementary complete systems
6. Gordan's theorem
7. The quintic
8. Simultaneous systems
9. Hilbert's theorem
10. Geometry
11. Apolarity and rational curves
12. Ternary forms
13. Ternary forms (continued)
14. Apolarity (continued)
15. Types of covariants
16. General theorems on quantics
Appendices
Index.

Subject Areas: Algebra [PBF]