Galois Theory

". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!"
—Monatshefte fur Mathematik

Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel’s theory of Abelian equations, casus irreducibili, and the Galois theory of origami.

In addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including:

• The contributions of Lagrange, Galois, and Kronecker
• How to compute Galois groups
• Galois's results about irreducible polynomials of prime or prime-squared degree
• Abel's theorem about geometric constructions on the lemniscates
• Galois groups of quartic polynomials in all characteristics

Throughout the book, intriguing Mathematical Notes and Historical Notes sections clarify the discussed ideas and the historical context; numerous exercises and examples use Maple and Mathematica to showcase the computations related to Galois theory; and extensive references have been added to provide readers with additional resources for further study.

Galois Theory, Second Edition is an excellent book for courses on abstract algebra at the upper-undergraduate and graduate levels. The book also serves as an interesting reference for anyone with a general interest in Galois theory and its contributions to the field of mathematics.

Avainsanat: Applied Mathematics, cubic equations, symmetric polynomials, roots of polynomials, extension fields, normal extensions, separable extensions, Galois group, Galois correspondence, solvability by radical, cyclotomic extensions, geometric constructions, finite field, computing Galois groups, solvable permutation groups, the Lemniscate, introduction to abstract algebra