Galois TheoryPraise for the First Edition ". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" 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:
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 |