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.
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"...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
"...a skillful, readable, coherent presentation, with a contemporary flavor..." The American Mathematical Monthly
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Text: English (translation)
Original Language: German
Original Language: German
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The theory of algebraic invariants, with which we want to concern ourselves here, is a modern discipline. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
full invariant system, isobaric function, irreducible syzygies, full form system, simultaneous invariants, simultaneous covariant, integral algebraic function, integral rational functions, substitution determinant, arbitrarily many variables, biquadratic form, covariant with respect, simultaneous forms, transformed coefficients, transformation determinant, invariant theory, null form, finiteness theorem, independent invariants, general linear transformation, rational representation, invariant field, invariant ring, linear substitution, each invariant Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Every, Theorem Each, Theorem Given New!
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The theory of algebraic invariants, with which we want to concern ourselves here, is a modern discipline. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
full invariant system, isobaric function, irreducible syzygies, full form system, simultaneous invariants, simultaneous covariant, integral algebraic function, integral rational functions, substitution determinant, arbitrarily many variables, biquadratic form, covariant with respect, simultaneous forms, transformed coefficients, transformation determinant, invariant theory, null form, finiteness theorem, independent invariants, general linear transformation, rational representation, invariant field, invariant ring, linear substitution, each invariant Key Phrases - Capitalized Phrases (CAPs): (learn more)
Theorem Every, Theorem Each, Theorem Given New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
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- Gesammelte Abhandlungen. Erster Band: Zahlentheorie (AMS Chelsea Publishing) by David Hilbert in Front Matter (1), and Front Matter (2)
- Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud on page 173
- Algorithms in Invariant Theory (Archives of Virology) by Bernd Sturmfels in Front Matter
- Theory of Linear and Integer Programming by Alexander Schrijver in Front Matter
- The Classical Groups: Their Invariants and Representations by Hermann Weyl in Front Matter
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- Mathematics and the Historian's Craft: The Kenneth O. May Lectures (CMS Books in Mathematics) by Michael Kinyon on page 211, and page 212
- Normal Forms, Bifurcations and Finiteness Problems in Differential Equations (NATO Science Series II: Mathematics, Physics and Chemistry) by Gert Sabidussi in Back Matter
- Classical Invariant Theory (London Mathematical Society Student Texts) by Peter J. Olver in Back Matter
- Normal Forms, Bifurcations and Finiteness Problems in Differential Equations (NATO Science Series II: Mathematics, Physics and Chemistry) by Gert Sabidussi in Back Matter
- Lectures on Invariant Theory (London Mathematical Society Lecture Note Series) by Igor Dolgachev in Back Matter
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