LEADER 05590nam 2200793Ia 450 001 9910811064503321 005 20200520144314.0 010 $a9786613618191 010 $a9781280588365 010 $a1280588365 010 $a9781118218440 010 $a1118218442 010 $a9781118218457 010 $a1118218450 010 $a9781118218426 010 $a1118218426 035 $a(CKB)2670000000166850 035 $a(EBL)817908 035 $a(SSID)ssj0000635693 035 $a(PQKBManifestationID)11367411 035 $a(PQKBTitleCode)TC0000635693 035 $a(PQKBWorkID)10653139 035 $a(PQKB)11364458 035 $a(Au-PeEL)EBL817908 035 $a(CaPaEBR)ebr10560585 035 $a(CaONFJC)MIL361819 035 $a(PPN)17061087X 035 $a(FR-PaCSA)88813030 035 $a(MiAaPQ)EBC817908 035 $a(OCoLC)784952441 035 $a(FRCYB88813030)88813030 035 $a(Perlego)2760475 035 $a(EXLCZ)992670000000166850 100 $a20110915d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGalois theory /$fDavid A. Cox 205 $a2nd ed. 210 $aHoboken, NJ $cJohn Wiley & Sons$dc2012 215 $a1 online resource (603 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 08$a9781118072059 311 08$a1118072057 320 $aIncludes bibliographical references and index. 327 $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 327 $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 327 $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 Scho?nemann-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 327 $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 327 $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 327 $aD Stereographic Projection 330 $aPraise for the First Edition "". . .will certainly fascinate anyone interested in abstract algebra: a remarkable book!""-Monatshefte fur Mathematik Galois theory is one of the most established topics in mathematics, with historical roots that led to the development of many central concepts in modern algebra, including groups and fields. Covering classic applications of the theory, such as solvability by radicals, geometric constructions, and finite fields, Galois Theory, Second Edition delves into novel topics like Abel's theory of 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aGalois theory 606 $aEquations, Theory of 615 0$aGalois theory. 615 0$aEquations, Theory of. 676 $a512/.32 700 $aCox$b David A$058032 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910811064503321 996 $aGalois theory$92070501 997 $aUNINA