Topics In Galois Theory

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Topics in Galois Theory

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 120 pages
File Size : 50,8 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439865255

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Topics in Galois Theory by Jean-Pierre Serre Pdf

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt constructi

Topics in Galois Fields

Author : Dirk Hachenberger,Dieter Jungnickel
Publisher : Springer Nature
Page : 785 pages
File Size : 49,8 Mb
Release : 2020-09-29
Category : Mathematics
ISBN : 9783030608064

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Topics in Galois Fields by Dirk Hachenberger,Dieter Jungnickel Pdf

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.

Galois Theory

Author : Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 47,8 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.

Topics in Field Theory

Author : G. Karpilovsky
Publisher : Elsevier
Page : 545 pages
File Size : 50,5 Mb
Release : 1989-02-01
Category : Mathematics
ISBN : 0080872662

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Topics in Field Theory by G. Karpilovsky Pdf

This monograph gives a systematic account of certain important topics pertaining to field theory, including the central ideas, basic results and fundamental methods. Avoiding excessive technical detail, the book is intended for the student who has completed the equivalent of a standard first-year graduate algebra course. Thus it is assumed that the reader is familiar with basic ring-theoretic and group-theoretic concepts. A chapter on algebraic preliminaries is included, as well as a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.

Galois Cohomology

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 215 pages
File Size : 55,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642591419

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Galois Cohomology by Jean-Pierre Serre Pdf

This is an updated English translation of Cohomologie Galoisienne, published more than thirty years ago as one of the very first versions of Lecture Notes in Mathematics. It includes a reproduction of an influential paper by R. Steinberg, together with some new material and an expanded bibliography.

Galois Theory

Author : David A. Cox
Publisher : John Wiley & Sons
Page : 602 pages
File Size : 54,5 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.

Galois Theory Through Exercises

Author : Juliusz Brzeziński
Publisher : Springer
Page : 296 pages
File Size : 45,9 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.

Topics in Galois Theory

Author : Gail GALLITANO,Shiv GUPTA
Publisher : Unknown
Page : 334 pages
File Size : 55,5 Mb
Release : 2019-02-08
Category : Electronic
ISBN : 1524960241

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Topics in Galois Theory by Gail GALLITANO,Shiv GUPTA Pdf

Galois Theory and Advanced Linear Algebra

Author : Rajnikant Sinha
Publisher : Springer Nature
Page : 351 pages
File Size : 53,5 Mb
Release : 2019-12-28
Category : Mathematics
ISBN : 9789811398490

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Galois Theory and Advanced Linear Algebra by Rajnikant Sinha Pdf

This book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.

Algebra

Author : Siegfried Bosch
Publisher : Springer
Page : 352 pages
File Size : 50,9 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783319951775

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Algebra by Siegfried Bosch Pdf

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.

Field and Galois Theory

Author : Patrick Morandi
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 47,5 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.

Fields and Galois Theory

Author : John M. Howie
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 51,7 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

Galois Theory of p-Extensions

Author : Helmut Koch
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 46,6 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.

Topological Galois Theory

Author : Askold Khovanskii
Publisher : Springer
Page : 307 pages
File Size : 48,8 Mb
Release : 2014-10-10
Category : Mathematics
ISBN : 9783642388712

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Topological Galois Theory by Askold Khovanskii Pdf

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.

Galois Theory of Linear Differential Equations

Author : Marius van der Put,Michael F. Singer
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 50,6 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