{"product_id":"introductory-modern-algebra-isbn-9780470876169","title":"Introductory Modern Algebra","description":"\u003cb\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/b\u003e  \u003cp\u003e\"Stahl 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 sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the \u003ci\u003eSecond Edition\u003c\/i\u003e also includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eAn 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\u003c\/li\u003e \u003cli\u003eHistorical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminology\u003c\/li\u003e \u003cli\u003eA new appendix on logic and proofs, sets, functions, and equivalence relations\u003c\/li\u003e \u003cli\u003eOver 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summaries\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroductory Modern Algebra: A Historical Approach, Second Edition\u003c\/i\u003e is an excellent textbook for upper-undergraduate courses in modern and abstract algebra.\u003c\/p\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 \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 \u003cp\u003e\u003cb\u003eSAUL STAHL, PhD, \u003c\/b\u003eis Professor in the Department of Mathematics at the University of Kansas. In addition to authoring six previous books and more than thirty papers in the field of geometry, Dr. Stahl has twice been the recipient of the Carl B. Allendoerfer Award from the Mathematical Association of America.\u003c\/p\u003e   \u003cp\u003ePraise for the \u003ci\u003eFirst Edition\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\"Stahl 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.\"— \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 sections on topics such as group homomorphisms, the RSA algorithm, complex conjugation, the factorization of real polynomials, and the fundamental theorem of algebra, the \u003ci\u003eSecond Edition\u003c\/i\u003e also includes:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eAn 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\u003c\/li\u003e \u003cli\u003eHistorical discussions integrated with the development of modern and abstract algebra in addition to many new explicit statements of theorems, definitions, and terminology\u003c\/li\u003e \u003cli\u003eA new appendix on logic and proofs, sets, functions, and equivalence relations\u003c\/li\u003e \u003cli\u003eOver 1,000 new examples and multi-level exercises at the end of each section and chapter as well as updated chapter summaries\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eIntroductory Modern Algebra: A Historical Approach, Second Edition\u003c\/i\u003e is an excellent textbook for upper-undergraduate courses in modern and abstract algebra.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989470200037,"sku":"NP9780470876169","price":100.5,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470876169.jpg?v=1761784230","url":"https:\/\/k12savings.com\/products\/introductory-modern-algebra-isbn-9780470876169","provider":"K12savings","version":"1.0","type":"link"}