Galois Theory (Fourth Edition)
Author: Ian Stewart
Publisher:
Published: 2021
Total Pages: 0
ISBN-13: 9787560396439
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Galois Theory
Author: Ian Nicholas Stewart
Publisher: CRC Press
Published: 2015-03-06
Total Pages: 338
ISBN-13: 1482245833
DOWNLOAD EBOOKSince 1973, Galois Theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fourth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today's algebra students. New to the Fourth EditionThe replacement of the topological proof of the fundame
Galois Theory
Author: David A. Cox
Publisher: John Wiley & Sons
Published: 2012-03-27
Total Pages: 602
ISBN-13: 1118218426
DOWNLOAD EBOOKPraise 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
Author: Steven H. Weintraub
Publisher: Springer Science & Business Media
Published: 2008-10-20
Total Pages: 220
ISBN-13: 0387875751
DOWNLOAD EBOOKGalois 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.
Galois Theory for Beginners
Author: Jörg Bewersdorff
Publisher: American Mathematical Soc.
Published: 2006
Total Pages: 202
ISBN-13: 0821838172
DOWNLOAD EBOOKGalois 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.
Introduction to the Galois Correspondence
Author: Maureen H. Fenrick
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 253
ISBN-13: 146121792X
DOWNLOAD EBOOKIn this presentation of the Galois correspondence, modern theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were concerned with constructibility problems. For example, they tried to determine if it was possible, using straightedge and compass alone, to perform any of the following tasks? (1) Double an arbitrary cube; in particular, construct a cube with volume twice that of the unit cube. (2) Trisect an arbitrary angle. (3) Square an arbitrary circle; in particular, construct a square with area 1r. (4) Construct a regular polygon with n sides for n > 2. If we define a real number c to be constructible if, and only if, the point (c, 0) can be constructed starting with the points (0,0) and (1,0), then we may show that the set of constructible numbers is a subfield of the field R of real numbers containing the field Q of rational numbers. Such a subfield is called an intermediate field of Rover Q. We may thus gain insight into the constructibility problems by studying intermediate fields of Rover Q. In chapter 4 we will show that (1) through (3) are not possible and we will determine necessary and sufficient conditions that the integer n must satisfy in order that a regular polygon with n sides be constructible.
Fields and Galois Theory
Author: John M. Howie
Publisher: Springer Science & Business Media
Published: 2007-10-11
Total Pages: 230
ISBN-13: 1852339861
DOWNLOAD EBOOKA 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
Topics in Galois Theory
Author: Jean-Pierre Serre
Publisher: CRC Press
Published: 2016-04-19
Total Pages: 120
ISBN-13: 1439865256
DOWNLOAD EBOOKThis 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
A Book of Abstract Algebra
Author: Charles C Pinter
Publisher: Courier Corporation
Published: 2010-01-14
Total Pages: 402
ISBN-13: 0486474178
DOWNLOAD EBOOKAccessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Introduction to Field Theory
Author: Iain T. Adamson
Publisher: Courier Corporation
Published: 2007-01-01
Total Pages: 194
ISBN-13: 0486462668
DOWNLOAD EBOOKAcclaimed by American Mathematical Monthly as "an excellent introduction,"this treatment ranges from basic definitions to important results and applications, introducing both the spirit and techniques of abstract algebra. It develops the elementary properties of rings and fields, explores extension fields and Galois theory, and examines numerous applications. 1982 edition.
