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Author : D. J. H. Garling
Publisher : Cambridge University Press
Page : 207 pages
File Size : 53,7 Mb
Release : 2021-07-22
Category : MATHEMATICS
ISBN : 9781108838924
This textbook contains a full account of Galois Theory and the algebra that it needs, with exercises, examples and applications.
Author : D. J. H. Garling
Publisher : Cambridge University Press
Page : 180 pages
File Size : 55,7 Mb
Release : 1986
Category : Mathematics
ISBN : 0521312493
This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.
Author : Jörg Bewersdorff
Publisher : American Mathematical Soc.
Page : 217 pages
File Size : 50,8 Mb
Release : 2021-07-15
Category : Education
ISBN : 9781470465001
Galois theory is the culmination of a centuries-long search for a solution to the classical problem of solving algebraic equations by radicals. In this book, Bewersdorff follows the historical development of the theory, emphasizing concrete examples along the way. As a result, many mathematical abstractions are now seen as the natural consequence of particular investigations. Few prerequisites are needed beyond general college mathematics, since the necessary ideas and properties of groups and fields are provided as needed. Results in Galois theory are formulated first in a concrete, elementary way, then in the modern form. Each chapter begins with a simple question that gives the reader an idea of the nature and difficulty of what lies ahead. The applications of the theory to geometric constructions, including the ancient problems of squaring the circle, duplicating the cube, and trisecting the angle, and the construction of regular n n-gons are also presented. This new edition contains an additional chapter as well as twenty facsimiles of milestones of classical algebra. It is suitable for undergraduates and graduate students, as well as teachers and mathematicians seeking a historical and stimulating perspective on the field.
Author : Siegfried Bosch
Publisher : Springer
Page : 352 pages
File Size : 53,8 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783319951775
The material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date.
Author : Joseph Rotman
Publisher : Springer Science & Business Media
Page : 170 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206170
A clear, efficient exposition of this topic with complete proofs and exercises, covering cubic and quartic formulas; fundamental theory of Galois theory; insolvability of the quintic; Galoiss Great Theorem; and computation of Galois groups of cubics and quartics. Suitable for first-year graduate students, either as a text for a course or for study outside the classroom, this new edition has been completely rewritten in an attempt to make proofs clearer by providing more details. It now begins with a short section on symmetry groups of polygons in the plane, for there is an analogy between polygons and their symmetry groups and polynomials and their Galois groups - an analogy which serves to help readers organise the various field theoretic definitions and constructions. The text is rounded off by appendices on group theory, ruler-compass constructions, and the early history of Galois Theory. The exposition has been redesigned so that the discussion of solvability by radicals now appears later and several new theorems not found in the first edition are included.
Author : Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 50,6 Mb
Release : 2008-10-20
Category : Mathematics
ISBN : 9780387875750
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 : David A. Cox
Publisher : John Wiley & Sons
Page : 586 pages
File Size : 45,9 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118031339
An introduction to one of the most celebrated theories of mathematics Galois theory is one of the jewels of mathematics. Its intrinsic beauty, dramatic history, and deep connections to other areas of mathematics give Galois theory an unequaled richness. David Cox’s Galois Theory helps readers understand not only the elegance of the ideas but also where they came from and how they relate to the overall sweep of mathematics. Galois Theory covers classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields. The book also delves into more novel topics, including Abel’s theory of Abelian equations, the problem of expressing real roots by real radicals (the casus irreducibilis), and the Galois theory of origami. Anyone fascinated by abstract algebra will find careful discussions of such topics as: 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 lemniscate With intriguing Mathematical and Historical Notes that clarify the ideas and their history in detail, Galois Theory brings one of the most colorful and influential theories in algebra to life for professional algebraists and students alike.
Author : Grégory Berhuy
Publisher : Cambridge University Press
Page : 328 pages
File Size : 41,9 Mb
Release : 2010-09-09
Category : Mathematics
ISBN : 9781139490887
This is the first detailed elementary introduction to Galois cohomology and its applications. The introductory section is self-contained and provides the basic results of the theory. Assuming only a minimal background in algebra, the main purpose of this book is to prepare graduate students and researchers for more advanced study.
Author : John M. Howie
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 42,8 Mb
Release : 2007-10-11
Category : Mathematics
ISBN : 9781852339869
A modern and student-friendly introduction to this popular subject: it takes a more "natural" approach and develops the theory at a gentle pace with an emphasis on clear explanations Features plenty of worked examples and exercises, complete with full solutions, to encourage independent study Previous books by Howie in the SUMS series have attracted excellent reviews
Author : Simeon Ivanov
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 42,6 Mb
Release : 1992
Category : Mathematics
ISBN : 0821831402
This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.
Author : M.M. Postnikov
Publisher : Elsevier
Page : 123 pages
File Size : 50,9 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483156477
Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.
Author : Mohamed Ayad
Publisher : World Scientific Publishing Company
Page : 452 pages
File Size : 51,8 Mb
Release : 2018-04-26
Category : Mathematics
ISBN : 9789813238329
Author : Emil Artin
Publisher : Courier Corporation
Page : 86 pages
File Size : 43,9 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780486158259
Clearly presented discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well as sections on solvable groups, permutation groups, solution of equations by radicals, and other concepts. 1966 edition.
Author : Falko Lorenz
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 55,6 Mb
Release : 2006-07-02
Category : Mathematics
ISBN : 9780387316086
This translation of the 1987 German edition is an introduction into the classical parts of algebra with a focus on fields and Galois theory. It discusses nonstandard topics, such as the transcendence of pi, and new concepts are defined in the framework of the development of carefully selected problems. It includes an appendix with exercises and notes on the previous parts of the book, and brief historical comments are scattered throughout.
Author : Patrick Morandi
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 45,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240402
In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.