{"product_id":"introductory-modern-algebra-9780470876169","title":"Introductory Modern Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cb\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/b\u003e  \u003cp\u003eStahl offers the solvability of equations from the historical point of view...one of the best books available to support a one-semester introduction to abstract algebra.\u003cbr\u003e \u003ci\u003eCHOICE\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroductory Modern Algebra: A Historical Approach, Second Edition\u003c\/i\u003e presents the evolution of algebra and provides readers with the opportunity to view modern algebra as a consistent movement from concrete problems to abstract principles. With a few pertinent excerpts from the writings of some of the greatest mathematicians, the \u003ci\u003eSecond Edition\u003c\/i\u003e uniquely facilitates the understanding of pivotal algebraic ideas.\u003c\/p\u003e \u003cp\u003eThe author provides a clear, precise, and accessible introduction to modern algebra and also helps to develop a more immediate and well-grounded understanding of how equations lead to permutation groups and what those groups can inform us about such diverse items as multivariate functions and the 15-puzzle. Featuring new \u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e“An in-depth explanation of the principles and practices of modern algebra in terms of the historical development from the Renaissance solution of the cubic equation to Dedekind's ideals.”  (\u003ci\u003eExpofairs.com\u003c\/i\u003e, 12 November 2015)\u003c\/p\u003e \u003cp\u003e“This book is an excellent book for an upper-level, undergraduate, one or two semester course, in modern algebra, for a typical University student population that is not especially strong in proofs.”  (\u003ci\u003eMAA Reviews\u003c\/i\u003e, 13 January 2014)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003ePreface ix\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 The Early History 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Breakthrough 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Complex Numbers 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Rational Functions of Complex Numbers 9\u003c\/p\u003e \u003cp\u003e2.2 Complex Roots 17\u003c\/p\u003e \u003cp\u003e2.3 Solvability by Radicals I 23\u003c\/p\u003e \u003cp\u003e2.4 Ruler and Compass Constructibility 26\u003c\/p\u003e \u003cp\u003e2.5 Orders of Roots of Unity 36\u003c\/p\u003e \u003cp\u003e2.6 The Existence of Complex Numbers* 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Solutions of Equations 45\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 The Cubic Formula 45\u003c\/p\u003e \u003cp\u003e3.2 Solvability by Radicals II 49\u003c\/p\u003e \u003cp\u003e3.3 Other Types of Solutions* 50\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Modular Arithmetic 57\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Modular Addition, Subtraction, and Multiplication 57\u003c\/p\u003e \u003cp\u003e4.2 The Euclidean Algorithm and Modular Inverses 62\u003c\/p\u003e \u003cp\u003e4.3 Radicals in Modular Arithmetic* 69\u003c\/p\u003e \u003cp\u003e4.4 The Fundamental Theorem of Arithmetic* 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 The Binomial Theorem and Modular Powers 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The Binomial Theorem 75\u003c\/p\u003e \u003cp\u003e5.2 Fermat's Theorem and Modular Exponents 85\u003c\/p\u003e \u003cp\u003e5.3 The Multinomial Theorem* 90\u003c\/p\u003e \u003cp\u003e5.4 The Euler \u003cb\u003eφ\u003c\/b\u003e-Function* 92\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Polynomials Over a Field 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Fields and Their Polynomials 99\u003c\/p\u003e \u003cp\u003e6.2 The Factorization of Polynomials 107\u003c\/p\u003e \u003cp\u003e6.3 The Euclidean Algorithm for Polynomials 113\u003c\/p\u003e \u003cp\u003e6.4 Elementary Symmetric Polynomials* 119\u003c\/p\u003e \u003cp\u003e6.5 Lagrange's Solution of the Quartic Equation* 125\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Galois Fields 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Galois's Construction of His Fields 131\u003c\/p\u003e \u003cp\u003e7.2 The Galois Polynomial 139\u003c\/p\u003e \u003cp\u003e7.3 The Primitive Element Theorem 144\u003c\/p\u003e \u003cp\u003e7.4 On the Variety of Galois Fields* 147\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Permutations 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Permuting the Variables of a Function I 155\u003c\/p\u003e \u003cp\u003e8.2 Permutations 158\u003c\/p\u003e \u003cp\u003e8.3 Permuting the Variables of a Function II 166\u003c\/p\u003e \u003cp\u003e8.4 The Parity of a Permutation 169\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Groups 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Permutation Groups 183\u003c\/p\u003e \u003cp\u003e9.2 Abstract Groups 192\u003c\/p\u003e \u003cp\u003e9.3 Isomorphisms of Groups and Orders of Elements 199\u003c\/p\u003e \u003cp\u003e9.4 Subgroups and Their Orders 206\u003c\/p\u003e \u003cp\u003e9.5 Cyclic Groups and Subgroups 215\u003c\/p\u003e \u003cp\u003e9.6 Cayley's Theorem 218\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Quotient Groups and their Uses 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Quotient Groups 225\u003c\/p\u003e \u003cp\u003e10.2 Group Homomorphisms 234\u003c\/p\u003e \u003cp\u003e10.3 The Rigorous Construction of Fields 240\u003c\/p\u003e \u003cp\u003e10.4 Galois Groups and Resolvability of Equations 253\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Topics in Elementary Group Theory 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 The Direct Product of Groups 261\u003c\/p\u003e \u003cp\u003e11.2 More Classifications 265\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Number Theory 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Pythagorean triples 273\u003c\/p\u003e \u003cp\u003e12.2 Sums of two squares 278\u003c\/p\u003e \u003cp\u003e12.3 Quadratic Reciprocity 285\u003c\/p\u003e \u003cp\u003e12.4 The Gaussian Integers 293\u003c\/p\u003e \u003cp\u003e12.5 Eulerian integers and others 304\u003c\/p\u003e \u003cp\u003e12.6 What is the essence of primality? 310\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 The Arithmetic of Ideals 317\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Preliminaries 317\u003c\/p\u003e \u003cp\u003e13.2 Integers of a Quadratic Field 319\u003c\/p\u003e \u003cp\u003e13.3 Ideals 322\u003c\/p\u003e \u003cp\u003e13.4 Cancelation of Ideals 337\u003c\/p\u003e \u003cp\u003e13.5 Norms of Ideals 341\u003c\/p\u003e \u003cp\u003e13.6 Prime Ideals and Unique Factorization 343\u003c\/p\u003e \u003cp\u003e13.7 Constructing Prime Ideals 347\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Abstract Rings 355\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Rings 355\u003c\/p\u003e \u003cp\u003e14.2 Ideals 358\u003c\/p\u003e \u003cp\u003e14.3 Domains 361\u003c\/p\u003e \u003cp\u003e14.4 Quotients of Rings 367\u003c\/p\u003e \u003cp\u003eA Excerpts: Al-Khwarizmi 377\u003c\/p\u003e \u003cp\u003eB Excerpts: Cardano 383\u003c\/p\u003e \u003cp\u003eC Excerpts: Abel 389\u003c\/p\u003e \u003cp\u003eD Excerpts: Galois 395\u003c\/p\u003e \u003cp\u003eE Excerpts: Cayley 401\u003c\/p\u003e \u003cp\u003eF Mathematical Induction 405\u003c\/p\u003e \u003cp\u003eG Logic, Predicates, Sets and Functions 413\u003c\/p\u003e \u003cp\u003eG.1 Truth Tables 413\u003c\/p\u003e \u003cp\u003eG.2 Modeling Implication 415\u003c\/p\u003e \u003cp\u003eG.3 Predicates and their Negation 418\u003c\/p\u003e \u003cp\u003eG.4 Two Applications 419\u003c\/p\u003e \u003cp\u003eG.5 Sets 421\u003c\/p\u003e \u003cp\u003eG.6 Functions 422\u003c\/p\u003e \u003cp\u003eBiographies 427\u003c\/p\u003e \u003cp\u003eBibliography 431\u003c\/p\u003e \u003cp\u003eSolutions to Selected Exercises 433\u003c\/p\u003e \u003cp\u003eIndex 440\u003c\/p\u003e \u003cp\u003eNotation 444\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":48864640794967,"sku":"9780470876169","price":89.96,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470876169.jpg?v=1722272853","url":"https:\/\/bookcurl.com\/products\/introductory-modern-algebra-9780470876169","provider":"Book Curl","version":"1.0","type":"link"}