Algebraic Invariants by Leonard E. Dickson
Algebraic Invariants - Table of Contents
- Part I: Illustrations & Applications
- 1–3. Plane Analytics & Projective Transformations
- 4–8. Examples and Definitions of Invariants & Covariants
- 9–11. Canonical Binary Cubics & Intermediate Forms
- 12–14. Plane Coordinates, Hessian & Cubic Curves
- Part II: Non-symbolic Invariant Theory
- 15–17. Homogeneity and Weight of Invariants
- 18–20. Binary Transformations & Annihilators
- 21–23. Homogeneity, Weight & Annihilators of Covariants
- 24–27. Seminvariants & Hermite's Reciprocity Law
- 28–33. Fundamental Systems & Canonical Binary Quartics
- 34–38. Invariants in Terms of Roots & Differential Operators
- Part III: Symbolic Notation
- 39–45. Aronhold-Clebsch Notation & Symbolic Types
- 46–51. Finiteness Problem, Hilbert's Theorem & Syzygies
- 52–54. Transvectants and Apolar Binary Forms
- 55–57. Rational Plane Cubics & Space Quartic Curves
- 58–63. Transvectant Theorems, Induction & Higher Forms
- 64–68. Symbolic Hermite Law, Ternary & Quaternary Forms
What You Will Learn in Algebraic Invariants
Algebraic Invariants by Leonard Eugene Dickson is an authoritative, classic mathematical monograph published by John Wiley & Sons that provides a comprehensive, mathematically rigorous foundation in classical invariant theory, differential operators, and symbolic polynomial methods. This foundational volume guides readers through projective transformations, homogeneous coordinates, geometric interpretations of invariants and covariants, canonical forms of binary cubics and quartics, properties of the Hessian, inflection points of plane cubic curves, differential annihilator operators, seminvariants, Hermite's law of reciprocity, Aronhold-Clebsch symbolic notation, Hilbert's basis theorem, finiteness of fundamental systems and syzygies, transvectants, apolarity, and ternary or quaternary form concomitants with exceptional clarity and logical precision.
Designed for graduate mathematics students, research algebraists, algebraic geometers, theoretical physicists, and history of mathematics scholars, this classic work bridges concrete geometric transformations directly with abstract polynomial representation theory. Dickson details step-by-step algebraic derivations, weight and homogeneity calculations, differential operator applications, symbolic convolution techniques, and explicit fundamental covariant system constructions. Whether you are investigating classical algebraic geometry, studying differential invariants, or exploring the historical foundations of modern commutative algebra, this book offers an indispensable roadmap.
Recognized globally as a definitive masterwork of 20th-century classical exposition, it stands as one of the best foundational references for mastering classical invariant theory and symbolic computation. By connecting geometric transformation groups directly to symbolic calculus and Hilbert's finite basis theorems, it serves as an essential tool for learning algebraic invariant theory with confidence.
Book Details & Specifications
Title:
Algebraic Invariants by Leonard E. Dickson
Publisher:
J. Wiley & Sons
Year:
1914
Pages:
122
Type:
PDF
Language:
English
ISBN-10 #:
1603861750
ISBN-13 #:
License:
Public Domain Work
Amazon:
Amazon
About the Author: Leonard Eugene Dickson
The author Leonard Eugene Dickson
(1874–1954) was a preeminent American mathematician and Professor of Mathematics at the University of Chicago, widely celebrated as one of the most prolific and influential algebraists in history. He was the first recipient of a doctorate in mathematics at the University of Chicago and served as president of the American Mathematical Society (AMS).
Through Algebraic Invariants, Dickson delivers a masterfully structured, clear presentation of projective invariant theory and symbolic polynomial methods. His rigorous proof pathways, historic context, and accessible symbolic algorithms make this volume a classic reference for classical invariants, covariants, and binary forms valued by mathematicians worldwide.
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