The Algebra of Invariants by John Grace and Alfred Young
The Algebra of Invariants - Table of Contents
- Part I: Invariants & Fundamental Theorems
- 1. Introduction
- 2. The Fundamental Theorem of Invariant Theory
- 3. Transvectants (Part 1)
- 4. Transvectants (Part 2)
- 5. Elementary Complete Systems
- 6. Gordan's Theorem
- 7. The Quintic
- 8. Simultaneous Systems
- 9. Hilbert's Theorem
- 10. Geometry of Invariants
- Part II: Advanced Forms & Appendices
- 11. Apolarity and Rational Curves
- 12. Ternary Forms (Part 1)
- 13. Ternary Forms (Part 2)
- 14. Apolarity
- 15. Types of Covariants
- 16. General Theorems on Quantics
- A-I. The Symbolical Notation
- A-II. Wronski's Theorem
- A-III. Jordan's Lemma
- A-IV. Types of Covariants
What You Will Learn in The Algebra of Invariants
Daniel Rogalski's "An Introduction to Noncommutative Projective Geometry" is a foundational text providing a comprehensive introduction to the field. It introduces key topics such as Artin–Schelter regular algebras, which serve as noncommutative analogues of polynomial rings, and the construction of noncommutative projective schemes associated with graded algebras, essential for understanding the geometry of noncommutative spaces. This volume serves as an excellent resource for those interested in the intersection of algebra and geometry, offering clear explanations and a structured approach to this complex subject.
Alongside this, "The Algebra of Invariants" stands as a monumental abstract algebra theory and applications volume, particularly in the study of invariant theory, which examines polynomial functions that remain unchanged under linear transformations. This work introduced the historic contributions of German mathematicians Alfred Clebsch and Paul Gordan to the British mathematical community, significantly influencing the development of the field. The book covers various advanced topics, including the fundamental theorem of invariant theory, transvectants, Gordan’s theorem, and Hilbert’s theorem, making it an indispensable invariant theory study guide and a highly valuable free abstract algebra textbook for beginners and advanced researchers alike.
Book Details & Specifications
Title:
The Algebra of Invariants by John Grace and Alfred Young
Publisher:
Cambridge University Press
Year:
1903
Pages:
404
Type:
PDF
Language:
English
ISBN-10 #:
1108013090
ISBN-13 #:
License:
Public Domain Work
Amazon:
Amazon
About the Author: John Hilton Grace
The author John Hilton Grace
(1873 – 1958) was a British mathematician, made a Fellow of Peterhouse in 1897 and a Lecturer of Mathematics. Known for his 1902 paper on the zeros of a polynomial, he collaborated with Alfred Young on their definitive abstract algebra theory and applications work. Elected a Fellow of the Royal Society in 1908, his research remains an essential invariant theory study guide reference worldwide.
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