Galois Theory 2e

Praise for the First Edition

". . .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.

Galois theory is the algebraic study of groups that can be associated with polynomial equations, and this book brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.  Whether solutions to an equation can be written down using rational functions and square roots, cube roots, etc. depends on certain group-theoretic properties of this Galois group.  Most other books on Galois theory tend to treat the topic very eloquently, yet they do not include the fascinating context in which it was developed.  An important organizational feature of this book is that many sections include Mathematical and Historical Notes that explain the ideas and their history in more detail.  The Second Edition features new exercises and an updated bibliography.  A new Index of Notation has also been added, which lists the notation used in the book together with the page where the item first appears.  A new discussion on a resolvent for quartic polynomials provides a different method for computing the Galois group of a quartic polynomial over a field of arbitrary characteristics.  Chapter coverage includes: cubic equations; symmetric polynomials; roots of polynomials; extension fields; normal and separable extensions; the Galois group; the Galois correspondence; solvability by radical; cyclotomic extensions; geometric constructions; finite field; computing Galois groups; solvable permutation groups; the Lemniscate; and an introduction to abstract algebra.

Praise for the First Edition . . .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 Abels 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 ·         Galoiss results about irreducible polynomials of prime or         prime-squared degree ·         Abels 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.