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Theory of Algebraic Invariants : Cambridge Mathematical Library - David Hilbert

Theory of Algebraic Invariants

Cambridge Mathematical Library

By: David Hilbert, Bernd Sturmfels (Editor, Introduction by), Reinhard C. Laubenbacher (Translator)


Published: 25th April 1994
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In the summer of 1897, David Hilbert (1862-1943) gave an introductory course in Invariant Theory at the University of Gottingen. This book is an English translation of the handwritten notes taken from this course by Hilbert's student Sophus Marxen. At that time his research in the subject had been completed, and his famous finiteness theorem had been proved and published in two papers that changed the course of invariant theory dramatically and that laid the foundation for modern commutative algebra. Thus, these lectures take into account both the old approach of his predecessors and his new ideas. This bridge from nineteenth to twentieth century mathematics makes these lecture notes a special and fascinating account of invariant theory. Hilbert's course was given at a level accessible to graduate students in mathematics, requiring only a familiarity with linear algebra and the basics of ring and group theory. The text will be useful as a self-contained introduction to invariant theory. But it will also be invaluable as a historical source for anyone interested in the foundations of twentieth-century mathematics.

"...Highly recommended for college libraries, undergraduate through faculty..." D.V. Feldman, Choice "...a skillful, readable, coherent presentation, with a contemporary flavor..." The American Mathematical Monthly

The Elements of Invariant Theory
The forms
The linear transformation
The concept of an invariant
Properties of invariants and covariants
The operation symbols D and D
The smallest system of conditions for the determination of the invariants and covariants
The number of invariants of degree g
The invariants and covariants of degree two and three
Simultaneous invariants and covariants
Covariants of covariants
The invariants and covariants as functions of the roots
The invariants and covariants as functions of the one-sided derivatives
The symbolic representation of invariants and covariants
The Theory of Invariant Fields
Proof of the finitenesss of the full invariant system via representation by root differences
A generalizable proof for the finiteness of the full invariant system
The system of invariants I; I1, I2, ..., Ik
The vanishing of the invariants
The ternary nullform
The finiteness of the number of irreducible syzygies and of the syzygy chain
The inflection point problem for plane curves of order three
The generalization of invariant theory
Observations about new types of coordinates
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521449038
ISBN-10: 0521449030
Series: Cambridge Mathematical Library
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 208
Published: 25th April 1994
Country of Publication: GB
Dimensions (cm): 23.5 x 15.88  x 1.27
Weight (kg): 0.3