Galois Theories

Galois Theories
Author: Francis Borceux
Publisher: Cambridge University Press
Total Pages: 360
Release: 2001-02-22
Genre: Mathematics
ISBN: 9780521803090

Develops Galois theory in a more general context, emphasizing category theory.

Algebra and Galois Theories

Algebra and Galois Theories
Author: Régine Douady
Publisher: Springer Nature
Total Pages: 462
Release: 2020-07-13
Genre: Mathematics
ISBN: 3030327965

Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.

Galois Groups and Fundamental Groups

Galois Groups and Fundamental Groups
Author: Tamás Szamuely
Publisher: Cambridge University Press
Total Pages: 281
Release: 2009-07-16
Genre: Mathematics
ISBN: 0521888506

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

Galois Theory

Galois Theory
Author: Steven Weintraub
Publisher: Springer
Total Pages: 212
Release: 2008-12-05
Genre: Mathematics
ISBN: 9780387875743

Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.

Galois Theory for Beginners

Galois Theory for Beginners
Author: Jörg Bewersdorff
Publisher: American Mathematical Soc.
Total Pages: 202
Release: 2006
Genre: Mathematics
ISBN: 0821838172

Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. This book follows the historical development of the theory, emphasizing concrete examples along the way. It is suitable for undergraduates and beginning graduate students.

Galois Theory Through Exercises

Galois Theory Through Exercises
Author: Juliusz Brzeziński
Publisher: Springer
Total Pages: 296
Release: 2018-03-21
Genre: Mathematics
ISBN: 331972326X

This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises). In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading. A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.

Algebraic Equations

Algebraic Equations
Author: Edgar Dehn
Publisher: Courier Corporation
Total Pages: 225
Release: 2012-09-05
Genre: Mathematics
ISBN: 0486155102

Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.

Topological Galois Theory

Topological Galois Theory
Author: Askold Khovanskii
Publisher: Springer
Total Pages: 317
Release: 2014-10-10
Genre: Mathematics
ISBN: 364238871X

This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in explicit form. In particular, it offers a complete exposition of the relatively new area of topological Galois theory, initiated by the author. Applications of Galois theory to solvability of algebraic equations by radicals, basics of Picard–Vessiot theory, and Liouville's results on the class of functions representable by quadratures are also discussed. A unique feature of this book is that recent results are presented in the same elementary manner as classical Galois theory, which will make the book useful and interesting to readers with varied backgrounds in mathematics, from undergraduate students to researchers. In this English-language edition, extra material has been added (Appendices A–D), the last two of which were written jointly with Yura Burda.

Algebra with Galois Theory

Algebra with Galois Theory
Author: Emil Artin
Publisher: American Mathematical Soc.
Total Pages: 137
Release: 2007
Genre: Mathematics
ISBN: 0821841297

'Algebra with Galois Theory' is based on lectures by Emil Artin. The book is an ideal textbook for instructors and a supplementary or primary textbook for students.