{"product_id":"a-classical-introduction-to-galois-theory-9781118091395","title":"A Classical Introduction to Galois Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eWith a focus on one central theme (the Impossibility Theorem) throughout, this highly accessible introduction to Galois theory presents a classical treatment of the topic and poses questions related to the solvability of polynomial equations by radicals. Modern points of view are also discussed in contrast to the historical development and context.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Classical Formulas 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Quadratic Polynomials 3\u003c\/p\u003e \u003cp\u003e1.2 Cubic Polynomials 5\u003c\/p\u003e \u003cp\u003e1.3 Quartic Polynomials 11\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Polynomials and Field Theory 15\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Divisibility 16\u003c\/p\u003e \u003cp\u003e2.2 Algebraic Extensions 24\u003c\/p\u003e \u003cp\u003e2.3 Degree of Extensions 25\u003c\/p\u003e \u003cp\u003e2.4 Derivatives 29\u003c\/p\u003e \u003cp\u003e2.5 Primitive Element Theorem 30\u003c\/p\u003e \u003cp\u003e2.6 Isomorphism Extension Theorem and Splitting Fields 35\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Fundamental Theorem on Symmetric Polynomials and Discriminants 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Fundamental Theorem on Symmetric Polynomials 41\u003c\/p\u003e \u003cp\u003e3.2 Fundamental Theorem on Symmetric Rational Functions 48\u003c\/p\u003e \u003cp\u003e3.3 Some Identities Based on Elementary Symmetric Polynomials 50\u003c\/p\u003e \u003cp\u003e3.4 Discriminants 53\u003c\/p\u003e \u003cp\u003e3.5 Discriminants and Subfields of the Real Numbers 60\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Irreducibility and Factorization 65\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Irreducibility Over the Rational Numbers 65\u003c\/p\u003e \u003cp\u003e4.2 Irreducibility and Splitting Fields 69\u003c\/p\u003e \u003cp\u003e4.3 Factorization and Adjunction 72\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Roots of Unity and Cyclotomic Polynomials 80\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Roots of Unity 80\u003c\/p\u003e \u003cp\u003e5.2 Cyclotomic Polynomials 82\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Radical Extensions and Solvability by Radicals 89\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Basic Results on Radical Extensions 89\u003c\/p\u003e \u003cp\u003e6.2 Gauss’s Theorem on Cyclotomic Polynomials 93\u003c\/p\u003e \u003cp\u003e6.3 Abel’s Theorem on Radical Extensions 104\u003c\/p\u003e \u003cp\u003e6.4 Polynomials of Prime Degree 109\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 General Polynomials and the Beginnings of Galois Theory 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 General Polynomials 117\u003c\/p\u003e \u003cp\u003e7.2 The Beginnings of Galois Theory 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Classical Galois Theory According to Galois 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Modern Galois Theory 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Galois Theory and Finite Extensions 152\u003c\/p\u003e \u003cp\u003e9.2 Galois Theory and Splitting Fields 156\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Cyclic Extensions and Cyclotomic Fields 171\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Cyclic Extensions 171\u003c\/p\u003e \u003cp\u003e10.2 Cyclotomic Fields 179\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Galois’s Criterion for Solvability of Polynomials by Radicals 185\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Polynomials of Prime degree 192\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Periods of Roots of Unity 200\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Denesting Radicals 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Classical Formulas Revisited 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 General Quadratic Polynomial 231\u003c\/p\u003e \u003cp\u003e15.2 General Cubic Polynomial 233\u003c\/p\u003e \u003cp\u003e15.3 General Quartic Polynomial 236\u003c\/p\u003e \u003cp\u003eAppendix A Cosets and Group Actions 245\u003c\/p\u003e \u003cp\u003eAppendix B Cyclic Groups 249\u003c\/p\u003e \u003cp\u003eAppendix C Solvable Groups 254\u003c\/p\u003e \u003cp\u003eAppendix D Permutation Groups 261\u003c\/p\u003e \u003cp\u003eAppendix E Finite fields and Number Theory 270\u003c\/p\u003e \u003cp\u003eAppendix F Further Reading 274\u003c\/p\u003e \u003cp\u003eReferences 277\u003c\/p\u003e \u003cp\u003eIndex 281\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406828478807,"sku":"9781118091395","price":62.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118091395.jpg?v=1730497254","url":"https:\/\/bookcurl.com\/products\/a-classical-introduction-to-galois-theory-9781118091395","provider":"Book Curl","version":"1.0","type":"link"}