The Theory of Equations, Vol. 2: Introduction to the Theory of Binary Algebraic Forms (Classic Reprint)

Mastery of determinants, elimination, and the theory of invariants unfolds in this advanced volume.

Dive into a rigorous treatment of how linear systems give rise to determinants, and explore diverse elimination methods that reveal the roots of equations. The work blends classical techniques with modern approaches to binary forms and their covariants and invariants, offering a deep mathematical framework for solving complex problems.

This edition surveys a broad spectrum of topics, from the fundamentals of determinant notation to the intricate structure of semivariants, semicovariants, and covariants. It also delves into transformations, substitutions, and the Galois perspective, connecting symbolic computation with the algebraic solution of equations.

• Clear definitions and examples of determinants and their properties.
• Elimination methods, including symmetric and dialytic approaches, and discriminants.
• Development of symmetric functions, semivariants, and semicovariants.
• Covariants and invariants of quadratic, cubic, quartic, and combined forms.

Ideal for readers of advanced algebra who want a comprehensive, methodical treatment of the theory behind equations and their transformations. This edition is suited for serious study by students and professionals seeking a solid, reference-grade foundation in the subject.