Field And Galois Theory

Author : Patrick Morandi
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 49,8 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 : John M. Howie
Publisher : Springer Science & Business Media
Page : 230 pages
File Size : 51,8 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 : Julio R. Bastida
Publisher : Cambridge University Press
Page : 354 pages
File Size : 51,5 Mb
Release : 1984-12-28
Category : Mathematics
ISBN : 0521302420

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Field Extensions and Galois Theory by Julio R. Bastida Pdf

This 1984 book aims to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is regarded amongst the central and most beautiful parts of algebra and its creation marked the culmination of generations of investigation.

Author : Juliusz Brzeziński
Publisher : Springer
Page : 296 pages
File Size : 49,8 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 : Steven H. Weintraub
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 40,6 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 : Jörg Bewersdorff
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 52,8 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 : Steven Roman
Publisher : Springer Science & Business Media
Page : 335 pages
File Size : 48,8 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780387276786

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Field Theory by Steven Roman Pdf

"Springer has just released the second edition of Steven Roman’s Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there....Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all...a well-written expository account of a very exciting area in mathematics." --THE MAA MATHEMATICAL SCIENCES DIGITAL LIBRARY

Author : D. J. H. Garling
Publisher : Cambridge University Press
Page : 180 pages
File Size : 54,6 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 : Emil Artin
Publisher : Unknown
Page : 82 pages
File Size : 50,9 Mb
Release : 1948
Category : Galois theory
ISBN : OCLC:1110469399

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Galois Theory by Emil Artin Pdf

Author : Helmut Koch
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 52,8 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.

Author : David A. Cox
Publisher : John Wiley & Sons
Page : 602 pages
File Size : 43,5 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.

Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 120 pages
File Size : 52,8 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

Author : David Harari
Publisher : Springer Nature
Page : 336 pages
File Size : 51,9 Mb
Release : 2020-06-24
Category : Mathematics
ISBN : 9783030439019

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Galois Cohomology and Class Field Theory by David Harari Pdf

This graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory. Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.

Author : Charles Robert Hadlock
Publisher : Cambridge University Press
Page : 348 pages
File Size : 43,9 Mb
Release : 2000-12-07
Category : Mathematics
ISBN : 088385032X

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Field Theory and Its Classical Problems by Charles Robert Hadlock Pdf

An introduction to the classical notions behind modern Galois theory.

Author : Marius van der Put,Michael F. Singer
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 40,5 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