Classical Invariant Theory (London Mathematical Society Student Texts) Review

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Classical Invariant Theory (London Mathematical Society Student Texts) ReviewExcept for some new terms ( transvectants, Hessians, Syzygies, special Euclidean groups)
and notation ( I haven't figured out exactly what he means by A^(-T) yet, inverse transpose?),
it is a well written book that revives the ancient Hilbert
invariant theory and translates that into
modern terms. I was hooked when I realized the connection to the elliptic invariant.
It has this neat section on Gordon's method of digraphs as algebraic invariants.
I really think some of this could be made where it could be taught to undergraduates without calculus.
For me the treatment of invariants tied a lot of loose ends together.Classical Invariant Theory (London Mathematical Society Student Texts) OverviewThere has been a resurgence of interest in classical invariant theory driven by several factors: new theoretical developments; a revival of computational methods coupled with powerful new computer algebra packages; and a wealth of new applications, ranging from number theory to geometry, physics to computer vision. This book provides readers with a self-contained introduction to the classical theory as well as modern developments and applications.The text concentrates on the study of binary forms (polynomials) in characteristic zero, and uses analytical as well as algebraic tools to study and classify invariants, symmetry, equivalence and canonical forms.A variety of innovations make this text of interest even to veterans of the subject; these include the use of differential operators and the transform approach to the symbolic method, extension of results to arbitrary functions, graphical methods for computing identities and Hilbert bases, complete systems of rationally and functionally independent covariants, introduction of Lie group and Lie algebra methods, as well as a new geometrical theory of moving frames and applications. Aimed at advanced undergraduate and graduate students the book includes many exercises and historical details, complete proofs of the fundamental theorems, and a lively and provocative exposition.

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