{"product_id":"galois-theory-2e-9781118072059","title":"Galois Theory 2e","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/b\u003e  \u003cp\u003e\u003cb\u003e. . .will certainly fascinate anyone interested in abstract algebra:\u003c\/b\u003e \u003cb\u003ea remarkable book!\u003cbr\u003e \u003c\/b\u003e\u003ci\u003e\u003cb\u003eMonatshefte fur Mathematik\u003c\/b\u003e\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eGalois 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, \u003ci\u003eGalois Theory, Second Edition\u003c\/i\u003e delves into novel topics like Abel's theory of Abelian equations, casus irreducibili, and the Galois theory of origami.\u003c\/p\u003e \u003cp\u003eIn addition, this book features detailed treatments of several topics not covered in standard texts on Galois theory, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe contributions of Lagrange, Galois, and Kronecker\u003c\/li\u003e \u003cli\u003eHow to compute Galois groups\u003c\/li\u003e \u003cli\u003eGalois''s results about irreducible polynomials of prime orprime-squared degre\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e“There is barely a better introduction to the subject, in all its theoretical and practical aspects, than the book under review.”  (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 1 December 2012)\u003cbr\u003e\u003cbr\u003e\"the great merit of this book (one of many expositions of the subject) is that everything is taken at a slow pace, with many examples to illustrate every idea. You get the (probably true) impression that the author loves this material, has taught it to undergraduates at Amherst College many times, has learned by experience the ideas which students find difficult, and has then taken great trouble to dissect these ideas and to pick out exactly the right examples and exercises to make them part of the reader’s mental equipment.\" (The Mathematical Gazette 2016)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e\n\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface to the First Edition xvii\u003c\/p\u003e \u003cp\u003ePreface to the Second Edition xxi\u003c\/p\u003e \u003cp\u003eNotation xxiii\u003c\/p\u003e \u003cp\u003e1 Basic Notation xxiii\u003c\/p\u003e \u003cp\u003e2 Chapter-by-Chapter Notation xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART I POLYNOMIALS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Cubic Equations 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Cardan's Formulas 4\u003c\/p\u003e \u003cp\u003e1.2 Permutations of the Roots 10\u003c\/p\u003e \u003cp\u003e1.3 Cubic Equations over the Real Numbers 15\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Symmetric Polynomials 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Polynomials of Several Variables 25\u003c\/p\u003e \u003cp\u003e2.2 Symmetric Polynomials 30\u003c\/p\u003e \u003cp\u003e2.3 Computing with Symmetric Polynomials (Optional) 42\u003c\/p\u003e \u003cp\u003e2.4 The Discriminant 46\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Roots of Polynomials 55\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Existence of Roots 55\u003c\/p\u003e \u003cp\u003e3.2 The Fundamental Theorem of Algebra 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART II FIELDS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Extension Fields 73\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Elements of Extension Fields 73\u003c\/p\u003e \u003cp\u003e4.2 Irreducible Polynomials 81\u003c\/p\u003e \u003cp\u003e4.3 The Degree of an Extension 89\u003c\/p\u003e \u003cp\u003e4.4 Algebraic Extensions 95\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Normal and Separable Extensions 101\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Splitting Fields 101\u003c\/p\u003e \u003cp\u003e5.2 Normal Extensions 107\u003c\/p\u003e \u003cp\u003e5.3 Separable Extensions 109\u003c\/p\u003e \u003cp\u003e5.4 Theorem of the Primitive Element 119\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 The Galois Group 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Definition of the Galois Group 125\u003c\/p\u003e \u003cp\u003e6.2 Galois Groups of Splitting Fields 130\u003c\/p\u003e \u003cp\u003e6.3 Permutations of the Roots 132\u003c\/p\u003e \u003cp\u003e6.4 Examples of Galois Groups 136\u003c\/p\u003e \u003cp\u003e6.5 Abelian Equations (Optional) 143\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 The Galois Correspondence 147\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Galois Extensions 147\u003c\/p\u003e \u003cp\u003e7.2 Normal Subgroups and Normal Extensions 154\u003c\/p\u003e \u003cp\u003e7.3 The Fundamental Theorem of Galois Theory 161\u003c\/p\u003e \u003cp\u003e7.4 First Applications 167\u003c\/p\u003e \u003cp\u003e7.5 Automorphisms and Geometry (Optional) 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART III APPLICATIONS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Solvability by Radicals 191\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Solvable Groups 191\u003c\/p\u003e \u003cp\u003e8.2 Radical and Solvable Extensions 196\u003c\/p\u003e \u003cp\u003e8.3 Solvable Extensions and Solvable Groups 201\u003c\/p\u003e \u003cp\u003e8.4 Simple Groups 210\u003c\/p\u003e \u003cp\u003e8.5 Solving Polynomials by Radicals 215\u003c\/p\u003e \u003cp\u003e8.6 The Casus Irreducbilis (Optional) 220\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Cyclotomic Extensions 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Cyclotomic Polynomials 229\u003c\/p\u003e \u003cp\u003e9.2 Gauss and Roots of Unity (Optional) 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Geometric Constructions 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Constructible Numbers 255\u003c\/p\u003e \u003cp\u003e10.2 Regular Polygons and Roots of Unity 270\u003c\/p\u003e \u003cp\u003e10.3 Origami (Optional) 274\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Finite Fields 291\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Structure of Finite Fields 291\u003c\/p\u003e \u003cp\u003e11.2 Irreducible Polynomials over Finite Fields (Optional) 301\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePART IV FURTHER TOPICS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Lagrange, Galois, and Kronecker 315\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Lagrange 315\u003c\/p\u003e \u003cp\u003e12.2 Galois 334\u003c\/p\u003e \u003cp\u003e12.3 Kronecker 347\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Computing Galois Groups 357\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Quartic Polynomials 357\u003c\/p\u003e \u003cp\u003e13.2 Quintic Polynomials 368\u003c\/p\u003e \u003cp\u003e13.3 Resolvents 386\u003c\/p\u003e \u003cp\u003e13.4 Other Methods 400\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Solvable Permutation Groups 413\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Polynomials of Prime Degree 413\u003c\/p\u003e \u003cp\u003e14.2 Imprimitive Polynomials of Prime-Squared Degree 419\u003c\/p\u003e \u003cp\u003e14.3 Primitive Permutation Groups 429\u003c\/p\u003e \u003cp\u003e14.4 Primitive Polynomials of Prime-Squared Degree 444\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 The Lemniscate 463\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Division Points and Arc Length 464\u003c\/p\u003e \u003cp\u003e15.2 The Lemniscatic Function 470\u003c\/p\u003e \u003cp\u003e15.3 The Complex Lemniscatic Function 482\u003c\/p\u003e \u003cp\u003e15.4 Complex Multiplication 489\u003c\/p\u003e \u003cp\u003e15.5 Abel's Theorem 504\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Abstract Algebra 515\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Basic Algebra 515\u003c\/p\u003e \u003cp\u003eA.2 Complex Numbers 524\u003c\/p\u003e \u003cp\u003eA.3 Polynomials with Rational Coefficients 528\u003c\/p\u003e \u003cp\u003eA.4 Group Actions 530\u003c\/p\u003e \u003cp\u003eA.5 More Algebra 532\u003c\/p\u003e \u003cp\u003eIndex 557\u003c\/p\u003e\n\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48866364653911,"sku":"9781118072059","price":59.36,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118072059.jpg?v=1722278297","url":"https:\/\/bookcurl.com\/products\/galois-theory-2e-9781118072059","provider":"Book Curl","version":"1.0","type":"link"}