An Introduction to the Algebra of Quantics by Edwin B. Elliott
An Introduction to the Algebra of Quantics - Table of Contents
- 1. Principles and Direct Methods
- 2. Essential Qualities of Invariants
- 3. Essential Qualities of Covariants
- 4. Cogredient and Contragredient Quantities
- 5. Binary Quantics: Functions of Differences
- 6. Annihilators and Seminvariants
- 7. Operators O and O, and Reciprocity
- 8. Generating Functions for Invariants
- 9. Hilbert's Proofs of Gordan's Theorem
- 10. Protomorphs and Fundamental Forms
- 11. Binary Quantics of Infinite Order
- 12. Canonical Forms of Binary Quantics
- 13. Binary Quintic and Sextic Systems
- 14. Systems of Several Binary Quantics
- 15. Restricted Substitutions & Geometry
- 16. Ternary Quantics: Quadratic & Cubic
What You Will Learn in An Introduction to the Algebra of Quantics
An Introduction to the Algebra of Quantics by Edwin Bailey Elliott is an authoritative, classic mathematical monograph published by the Clarendon Press (Oxford) that delivers a rigorous, foundational exposition of classical invariant theory and homogeneous algebraic forms. This comprehensive volume guides readers through direct methods of invariant formation, essential qualities of invariants and covariants, cogredient and contragredient variable transformations, binary quantics, differential operator annihilators (Omega and Omicron), seminvariant constructions, Hermite's law of reciprocity, generating function applications, Hilbert's finiteness proofs of Gordan's theorem, protomorphs, infinite order binary quantics, canonical forms, binary quintic and sextic concomitant systems, systems of multiple binary forms, Cartesian geometric applications under restricted substitutions, and ternary quadratic and cubic forms with exceptional structural clarity and logical precision.
Designed for graduate mathematics majors, research algebraists, algebraic geometers, theoretical physicists, and historians of mathematics, this foundational text bridges explicit algebraic operator mechanics directly with abstract representation theory. Elliott details step-by-step operator derivations, seminvariant table constructions, Hilbert basis methods, generating function series expansions, and explicit canonical representations. Whether you are investigating classical invariant theory, studying geometric transformation groups, or reviewing foundational proofs in modern polynomial algebra, this book offers an indispensable roadmap.
Recognized globally as a definitive masterwork of 19th-century British algebraic exposition, it stands as one of the best foundational references for mastering quantics, binary forms, and invariant operators. By connecting differential operator mechanics directly to Hilbert's finiteness proofs and ternary quantics, it serves as an essential tool for learning classical quantics and invariant theory with confidence.
Book Details & Specifications
Title:
An Introduction to the Algebra of Quantics by Edwin B. Elliott
Publisher:
The Clarendon Press
Year:
1913
Pages:
444
Type:
PDF
Language:
English
ISBN-10 #:
B005GE94HU
ISBN-13 #:
N\A
License:
Public Domain Work
Amazon:
Amazon
About the Author: Edwin Bailey Elliott
The author Edwin Bailey Elliott
(1851 -1937) was an eminent British mathematician, Waynflete Professor of Pure Mathematics at Oxford University, and Fellow of the Royal Society, widely celebrated for his groundbreaking contributions to the theory of quantics, binary forms, and differential operators.
Through An Introduction to the Algebra of Quantics, Elliott delivers a masterfully structured, systematically ordered presentation of classical invariant theory. His rigorous operator derivations, comprehensive topical coverage, and clear geometric applications make this volume a classic reference for quantics, seminvariants, and algebraic forms valued by mathematicians worldwide.
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