Introduction to the Theory of Algebraic Equations (Classic Reprint) - Hardcover

Leonard Eugene Dickson

9780331669213: Introduction to the Theory of Algebraic Equations (Classic Reprint)

Hardcover

ISBN 10: 0331669218 ISBN 13: 9780331669213

Publisher: Forgotten Books, 2022

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Unravel the roots of algebra with Galois theory and the power of symmetry.

This rigorous text explains how complex equations can be approached by studying groups of permutations and rational functions of roots, revealing the structure behind their solvability.

In clear, methodical steps, the book traces how the solution of a given equation can be reduced to a chain of simpler equations, and how the groups that arise govern what is possible to compute. It also introduces the idea that certain groups must appear, regardless of the auxiliary methods used, shaping what techniques will work in solving the equation.

The material blends foundational theory with practical results, including discussions of symmetric functions, resolvents, and the relationship between coefficients and roots. It situates these ideas within the broader development of Galois theory and its applications to equations of different degrees.

Learn how to connect equations to group theory and use that link to understand solvability by radicals
Explore the role of Galois resolvents, symmetric functions, and elementary relations among roots
See how the structure of groups dictates the limits of algebraic methods
Encounter historical context showing the evolution of key theorems and proofs

Ideal for readers of advanced algebra and the history of mathematical ideas, this edition offers a rigorous, rewarding journey into the theory behind solving polynomial equations.

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