Cogalois Theory

Author : Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 51,6 Mb
Release : 2008-10-20
Category : Mathematics
ISBN : 9780387875750

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Galois Theory by Steven H. Weintraub Pdf

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 : Emil Artin
Publisher : Unknown
Page : 82 pages
File Size : 41,9 Mb
Release : 1948
Category : Galois theory
ISBN : OCLC:1110469399

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Galois Theory by Emil Artin Pdf

Author : Juliusz Brzeziński
Publisher : Springer
Page : 296 pages
File Size : 52,8 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9783319723266

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Galois Theory Through Exercises by Juliusz Brzeziński Pdf

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 : Jörg Bewersdorff
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 43,8 Mb
Release : 2006
Category : Galois theory
ISBN : 9780821838174

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Galois Theory for Beginners by Jörg Bewersdorff Pdf

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 : Ian Stewart
Publisher : Unknown
Page : 0 pages
File Size : 45,9 Mb
Release : 2021
Category : Galois theory
ISBN : 7560396437

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Galois Theory (Fourth Edition) by Ian Stewart Pdf

Author : John M. Howie
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 40,9 Mb
Release : 2007-10-11
Category : Mathematics
ISBN : 9781852339869

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Fields and Galois Theory by John M. Howie Pdf

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 : David A. Cox
Publisher : John Wiley & Sons
Page : 602 pages
File Size : 40,9 Mb
Release : 2012-03-27
Category : Mathematics
ISBN : 9781118218426

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Galois Theory by David A. Cox Pdf

Praise for the First Edition ". . .will certainly fascinate anyone interested in abstractalgebra: a remarkable book!" —Monatshefte fur Mathematik Galois theory is one of the most established topics inmathematics, with historical roots that led to the development ofmany central concepts in modern algebra, including groups andfields. Covering classic applications of the theory, such assolvability by radicals, geometric constructions, and finitefields, Galois Theory, Second Edition delves into noveltopics like Abel’s theory of Abelian equations, casusirreducibili, and the Galois theory of origami. In addition, this book features detailed treatments of severaltopics 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 primeor prime-squared degree Abel's theorem about geometric constructions on thelemniscates Galois groups of quartic polynomials in allcharacteristics Throughout the book, intriguing Mathematical Notes andHistorical Notes sections clarify the discussed ideas andthe historical context; numerous exercises and examples use Mapleand Mathematica to showcase the computations related to Galoistheory; and extensive references have been added to provide readerswith additional resources for further study. Galois Theory, Second Edition is an excellent book forcourses on abstract algebra at the upper-undergraduate and graduatelevels. The book also serves as an interesting reference for anyonewith a general interest in Galois theory and its contributions tothe field of mathematics.

Author : D. J. H. Garling
Publisher : Cambridge University Press
Page : 180 pages
File Size : 43,7 Mb
Release : 1986
Category : Mathematics
ISBN : 0521312493

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A Course in Galois Theory by D. J. H. Garling Pdf

This textbook, based on lectures given over a period of years at Cambridge, is a detailed and thorough introduction to Galois theory.

Author : Jacques Sauloy
Publisher : American Mathematical Soc.
Page : 275 pages
File Size : 43,5 Mb
Release : 2016-12-07
Category : Galois theory
ISBN : 9781470430955

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Differential Galois Theory through Riemann-Hilbert Correspondence by Jacques Sauloy Pdf

Differential Galois theory is an important, fast developing area which appears more and more in graduate courses since it mixes fundamental objects from many different areas of mathematics in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot Theory, was purely algebraic. This approach has been extensively developed and is well covered in the literature. An alternative approach consists in tagging algebraic objects with transcendental information which enriches the understanding and brings not only new points of view but also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot approach is not easily extended. This book offers a hands-on transcendental approach to differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it provides a smooth, down-to-earth introduction to algebraic geometry, category theory and tannakian duality. Since the book studies only complex analytic linear differential equations, the main prerequisites are complex function theory, linear algebra, and an elementary knowledge of groups and of polynomials in many variables. A large variety of examples, exercises, and theoretical constructions, often via explicit computations, offers first-year graduate students an accessible entry into this exciting area.

Author : Marius van der Put,Michael F. Singer
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642557507

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Galois Theory of Linear Differential Equations by Marius van der Put,Michael F. Singer Pdf

From the reviews: "This is a great book, which will hopefully become a classic in the subject of differential Galois theory. [...] the specialist, as well as the novice, have long been missing an introductory book covering also specific and advanced research topics. This gap is filled by the volume under review, and more than satisfactorily." Mathematical Reviews

Author : Francis Borceux,George Janelidze
Publisher : Cambridge University Press
Page : 360 pages
File Size : 41,9 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521803098

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Galois Theories by Francis Borceux,George Janelidze Pdf

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

Author : Patrick Morandi
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240402

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Field and Galois Theory by Patrick Morandi Pdf

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.

Author : M.M. Postnikov
Publisher : Elsevier
Page : 122 pages
File Size : 43,9 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483156477

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Foundations of Galois Theory by M.M. Postnikov Pdf

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 : John Swallow
Publisher : Cambridge University Press
Page : 224 pages
File Size : 40,7 Mb
Release : 2004-10-11
Category : Computers
ISBN : 0521544998

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Exploratory Galois Theory by John Swallow Pdf

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.

Author : Helmut Koch
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 43,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662049679

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Galois Theory of p-Extensions by Helmut Koch Pdf

Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.