Galois Theory

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John Wiley & Sons, Mar 27, 2012 - Mathematics - 602 pages
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.

 

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Contents

as follows
116
The Galois Group
125
The Galois Correspondence
147
13
164
APPLICATIONS
189
Cyclotomic Extensions
229
Geometric Constructions
255
Finite Fields
291
The Lemniscate
463
A Abstract Algebra
515
B Hints to Selected Exercises
537
Student Projects
551
Index
557
Notation
xxiii
Cubic Equations
1
A Fields of Characteristic 0 Here is an application of Lemmas 5 34 and 5 3
5

FURTHER TOPICS
313
Preface to the First Edition
xvii
Computing Galois Groups
357
Solvable Permutation Groups
413
characteristic p separately Since we encounter fields of characteristic 0 most often
419
Symmetric Polynomials
25
Roots of Polynomials
55
Extension Fields
73
Copyright

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About the author (2012)

DAVID A. COX, PhD, is Professor in the Department of Mathematics at Amherst College. He has published extensively in his areas of research interest, which include algebraic geometry, number theory, and the history of mathematics. Dr. Cox is consulting editor for Wiley's Pure and Applied Mathematics book series and the author of Primes of the Form x2 + ny2 (Wiley).

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