Author : Francis Borceux
Publisher : Cambridge University Press
Page : 360 pages
File Size : 24,77 MB
Release : 2001-02-22
Category : Mathematics
ISBN : 9780521803090
Develops Galois theory in a more general context, emphasizing category theory.
Author : Régine Douady
Publisher : Springer Nature
Page : 462 pages
File Size : 35,33 MB
Release : 2020-07-13
Category : 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.
Author : Tamás Szamuely
Publisher : Cambridge University Press
Page : 281 pages
File Size : 46,70 MB
Release : 2009-07-16
Category : Mathematics
ISBN : 0521888506
Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.
Author : Steven Weintraub
Publisher : Springer
Page : 212 pages
File Size : 40,27 MB
Release : 2008-12-05
Category : 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.
Author : Jörg Bewersdorff
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 37,78 MB
Release : 2006
Category : 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.
Author : Juliusz Brzeziński
Publisher : Springer
Page : 296 pages
File Size : 28,37 MB
Release : 2018-03-21
Category : 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.
Author : Edgar Dehn
Publisher : Courier Corporation
Page : 225 pages
File Size : 47,82 MB
Release : 2012-09-05
Category : 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.
Author : Emil Artin
Publisher : American Mathematical Soc.
Page : 137 pages
File Size : 38,12 MB
Release : 2007
Category : 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.
Author : Askold Khovanskii
Publisher : Springer
Page : 317 pages
File Size : 46,28 MB
Release : 2014-10-10
Category : 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.
Author : Joseph Rotman
Publisher : Springer Science & Business Media
Page : 115 pages
File Size : 47,19 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468403672
This text offers a clear, efficient exposition of Galois Theory with exercises and complete proofs. Topics include: Cardano's formulas; the Fundamental Theorem; Galois' Great Theorem (solvability for radicals of a polynomial is equivalent to solvability of its Galois Group); and computation of Galois group of cubics and quartics. There are appendices on group theory and on ruler-compass constructions. Developed on the basis of a second-semester graduate algebra course, following a course on group theory, this book will provide a concise introduction to Galois Theory suitable for graduate students, either as a text for a course or for study outside the classroom.
