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001 ocn784952441
003 OCoLC
005 20171115082607.0
006 m o d
007 cr cnu---unuuu
008 120409s2012 njua ob 001 0 eng d
010 _a 2011039044
020 _a9781118218457
_q(electronic bk.)
020 _a1118218450
_q(electronic bk.)
020 _a9781118218426
_q(electronic bk.)
020 _a1118218426
_q(electronic bk.)
020 _z9781118072059
_q(cloth)
020 _z1118072057
_q(cloth)
024 8 _a9786613618191
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035 _a(OCoLC)784952441
_z(OCoLC)784883586
_z(OCoLC)794619794
_z(OCoLC)961599377
_z(OCoLC)962604337
037 _a361819
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040 _aN$T
_beng
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049 _aMAIN
050 4 _aQA214
_b.C69 2012eb
072 7 _aMAT
_x002040
_2bisacsh
082 0 4 _a512/.32
_223
100 1 _aCox, David A.
245 1 0 _aGalois theory /
_cDavid A. Cox.
_h[electronic resource]
250 _a2nd ed.
260 _aHoboken, NJ :
_bJohn Wiley & Sons,
_c©2012.
300 _a1 online resource (xxviii, 570 pages) :
_billustrations.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _adata file
_2rda
380 _aBibliography
490 1 _aPure and aplied mathematics
504 _aIncludes bibliographical references and index.
505 0 _aGalois Theory; CONTENTS; Preface to the First Edition; Preface to the Second Edition; Notation; 1 Basic Notation; 2 Chapter-by-Chapter Notation; PART I POLYNOMIALS; 1 Cubic Equations; 1.1 Cardan's Formulas; Historical Notes; 1.2 Permutations of the Roots; A Permutations; B The Discriminant; C Symmetric Polynomials; Mathematical Notes; Historical Notes; 1.3 Cubic Equations over the Real Numbers; A The Number of Real Roots; B Trigonometric Solution of the Cubic; Historical Notes; References; 2 Symmetric Polynomials; 2.1 Polynomials of Several Variables; A The Polynomial Ring in n Variables.
505 8 _aB The Elementary Symmetric PolynomialsMathematical Notes; 2.2 Symmetric Polynomials; A The Fundamental Theorem; B The Roots of a Polynomial; C Uniqueness; Mathematical Notes; Historical Notes; 2.3 Computing with Symmetric Polynomials (Optional); A Using Mathematica; B Using Maple; 2.4 The Discriminant; Mathematical Notes; Historical Notes; References; 3 Roots of Polynomials; 3.1 The Existence of Roots; Mathematical Notes; Historical Notes; 3.2 The Fundamental Theorem of Algebra; Mathematical Notes; Historical Notes; References; PART II FIELDS; 4 Extension Fields.
505 8 _a4.1 Elements of Extension FieldsA Minimal Polynomials; B Adjoining Elements; Mathematical Notes; Historical Notes; 4.2 Irreducible Polynomials; A Using Maple and Mathematica; B Algorithms for Factoring; C The Schönemann-Eisenstein Criterion; D Prime Radicals; Historical Notes; 4.3 The Degree of an Extension; A Finite Extensions; B The Tower Theorem; Mathematical Notes; Historical Notes; 4.4 Algebraic Extensions; Mathematical Notes; References; 5 Normal and Separable Extensions; 5.1 Splitting Fields; A Definition and Examples; B Uniqueness; 5.2 Normal Extensions; Historical Notes.
505 8 _a5.3 Separable ExtensionsA Fields of Characteristic 0; B Fields of Characteristic p; C Computations; Mathematical Notes; 5.4 Theorem of the Primitive Element; Mathematical Notes; Historical Notes; References; 6 The Galois Group; 6.1 Definition of the Galois Group; Historical Notes; 6.2 Galois Groups of Splitting Fields; 6.3 Permutations of the Roots; Mathematical Notes; Historical Notes; 6.4 Examples of Galois Groups; A The pth Roots of 2; B The Universal Extension; C A Polynomial of Degree 5; Mathematical Notes; Historical Notes; 6.5 Abelian Equations (Optional); Historical Notes; References.
505 8 _a7 The Galois Correspondence7.1 Galois Extensions; A Splitting Fields of Separable Polynomials; B Finite Separable Extensions; C Galois Closures; Historical Notes; 7.2 Normal Subgroups and Normal Extensions; A Conjugate Fields; B Normal Subgroups; Mathematical Notes; Historical Notes; 7.3 The Fundamental Theorem of Galois Theory; 7.4 First Applications; A The Discriminant; B The Universal Extension; C The Inverse Galois Problem; Historical Notes; 7.5 Automorphisms and Geometry (Optional); A Groups of Automorphisms; B Function Fields in One Variable; C Linear Fractional Transformations.
520 _aPraise for the First Edition". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!" & mdash;Monatshefte fur MathematikGalois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel & rsquo;s theory of Abelian equations, casus irreducibili, and the Galois.
588 0 _aPrint version record.
650 0 _aGalois theory.
650 4 _aGalois theory.
650 4 _aMathematics.
650 7 _aMATHEMATICS
_xAlgebra
_xIntermediate.
_2bisacsh
650 7 _aGalois theory.
_2fast
_0(OCoLC)fst00937326
655 4 _aElectronic books.
776 0 8 _iPrint version:
_aCox, David A.
_tGalois theory.
_b2nd ed.
_dHoboken, N.J. : John Wiley & Sons, ©2012
_z9781118072059
_w(DLC) 2011039044
_w(OCoLC)755640849
830 0 _aPure and applied mathematics (John Wiley & Sons : Unnumbered)
856 4 0 _uhttp://onlinelibrary.wiley.com/book/10.1002/9781118218457
_zWiley Online Library
942 _2ddc
_cBK
999 _c205801
_d205801