Algebraic Equations

Book Details

• Publisher: Dover

• Author: Edgar Dehn

• Language: English

• ISBN: 9780486439006

• Pages: 224

• Cover: Paperback

• Edition: Dover Ed

• Release Date: 21-06-2017

• Dimensions: 8.4 x 5.4 x 0.6 inches

About The Book

Algebraic Equations by Edgar Dehn presents a meticulous and thorough exposition of Galois' theory of algebraic equations, making it an ideal resource for upper-level undergraduate and graduate students. The book presents the theories of both Lagrange and Galois in a logical rather than historical order, offering students a concrete introduction to the abstract principles of Galois theory.

The text is structured to provide a solid foundation in algebraic theory and its application, with a focus on the properties of equations, functions, and groups. A third of the book is dedicated to basic algebraic concepts, such as integral functions, permutations, and the symmetric group, followed by a detailed study of Lagrange’s theory.

The heart of the book is a comprehensive treatment of Galois theory, which includes an exploration of Galoisian functions, the general equation, and reductions of groups, among other topics. The book also offers a clear understanding of natural irrationality and other critical aspects of Galois' work.

Key Topics Covered:

• Integral Functions and Permutations: The book begins with a detailed exploration of these basic algebraic concepts.

• Symmetric Group: A clear explanation of the symmetric group and its functions.

• Lagrange’s Theory: A study of the theory of Lagrange, building a foundation for the Galoisian approach.

• Galois Theory: A thorough exposition of Galois theory, including Galoisian functions, the general equation, and group reductions.

• Special Equations: Application of Galois theory to solve special equations like Abelian, cyclic, metacyclic, and quintic equations.

Features:

• Logical and Complete Exposition: The theories are presented in a logical, well-structured form, making the abstract concepts more accessible.

• Numerical Examples: The book includes many numerical examples, with complete solutions, to help students understand how the theory applies in practice.

• Advanced Topics: A thorough exploration of Galois theory, ideal for students familiar with abstract algebra.

This book is an excellent supplementary text for students studying algebra and Galois theory, offering both theoretical explanations and practical applications of algebraic equations.