{"product_id":"modern-algebra-isbn-9780470384435","title":"Modern Algebra","description":"The new sixth edition of \u003ci\u003eModern Algebra\u003c\/i\u003e has two main goals: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. The first six chapters present the core of the subject; the remainder are designed to be as flexible as possible. The text covers groups before rings, which is a matter of personal preference for instructors.  \u003ci\u003eModern Algebra, 6e\u003c\/i\u003e is appropriate for any one-semester junior\/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures, or Groups, Rings and Fields.  The course is mostly comprised of mathematics majors, but engineering and computer science majors may also take it as well. \u003cp\u003eIntroduction 1\u003c\/p\u003e \u003cp\u003e\u003cb\u003eI. Mappings and Operations 9\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1 Mappings 9\u003c\/p\u003e \u003cp\u003e2 Composition. Invertible Mappings 15\u003c\/p\u003e \u003cp\u003e3 Operations 19\u003c\/p\u003e \u003cp\u003e4 Composition as an Operation 25\u003c\/p\u003e \u003cp\u003e\u003cb\u003eII. Introduction to Groups 30\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5 Definition and Examples 30\u003c\/p\u003e \u003cp\u003e6 Permutations 34\u003c\/p\u003e \u003cp\u003e7 Subgroups 41\u003c\/p\u003e \u003cp\u003e8 Groups and Symmetry 47\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIII. Equivalence. Congruence. Divisibility 52\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9 Equivalence Relations 52\u003c\/p\u003e \u003cp\u003e10 Congruence. The Division Algorithm 57\u003c\/p\u003e \u003cp\u003e11 Integers Modulo \u003ci\u003en \u003c\/i\u003e61\u003c\/p\u003e \u003cp\u003e12 Greatest Common Divisors. The Euclidean Algorithm 65\u003c\/p\u003e \u003cp\u003e13 Factorization. Euler’s Phi-Function 70\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIV. Groups 75\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14 Elementary Properties 75\u003c\/p\u003e \u003cp\u003e15 Generators. Direct Products 81\u003c\/p\u003e \u003cp\u003e16 Cosets 85\u003c\/p\u003e \u003cp\u003e17 Lagrange’s Theorem. Cyclic Groups 88\u003c\/p\u003e \u003cp\u003e18 Isomorphism 93\u003c\/p\u003e \u003cp\u003e19 More on Isomorphism 98\u003c\/p\u003e \u003cp\u003e20 Cayley’s Theorem 102\u003c\/p\u003e \u003cp\u003eAppendix: RSA Algorithm 105\u003c\/p\u003e \u003cp\u003e\u003cb\u003eV. Group Homomorphisms 106\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21 Homomorphisms of Groups. Kernels 106\u003c\/p\u003e \u003cp\u003e22 Quotient Groups 110\u003c\/p\u003e \u003cp\u003e23 The Fundamental Homomorphism Theorem 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVI. Introduction to Rings 120\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24 Definition and Examples 120\u003c\/p\u003e \u003cp\u003e25 Integral Domains. Subrings 125\u003c\/p\u003e \u003cp\u003e26 Fields 128\u003c\/p\u003e \u003cp\u003e27 Isomorphism. Characteristic 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVII. The Familiar Number Systems 137\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e28 Ordered Integral Domains 137\u003c\/p\u003e \u003cp\u003e29 The Integers 140\u003c\/p\u003e \u003cp\u003e30 Field of Quotients. The Field of Rational Numbers 142\u003c\/p\u003e \u003cp\u003e31 Ordered Fields. The Field of Real Numbers 146\u003c\/p\u003e \u003cp\u003e32 The Field of Complex Numbers 149\u003c\/p\u003e \u003cp\u003e33 Complex Roots of Unity 154\u003c\/p\u003e \u003cp\u003e\u003cb\u003eVIII. Polynomials 160\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e34 Definition and Elementary Properties 160\u003c\/p\u003e \u003cp\u003eAppendix to Section 34 162\u003c\/p\u003e \u003cp\u003e35 The Division Algorithm 165\u003c\/p\u003e \u003cp\u003e36 Factorization of Polynomials 169\u003c\/p\u003e \u003cp\u003e37 Unique Factorization Domains 173\u003c\/p\u003e \u003cp\u003e\u003cb\u003eIX. Quotient Rings 178\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e38 Homomorphisms of Rings. Ideals 178\u003c\/p\u003e \u003cp\u003e39 Quotient Rings 182\u003c\/p\u003e \u003cp\u003e40 Quotient Rings of \u003ci\u003eF\u003c\/i\u003e[\u003ci\u003eX\u003c\/i\u003e] 184\u003c\/p\u003e \u003cp\u003e41 Factorization and Ideals 187\u003c\/p\u003e \u003cp\u003e\u003cb\u003eX. Galois Theory: Overview 193\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e42 Simple Extensions. Degree 194\u003c\/p\u003e \u003cp\u003e43 Roots of Polynomials 198\u003c\/p\u003e \u003cp\u003e44 Fundamental Theorem: Introduction 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003eXI. Galois Theory 207\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e45 Algebraic Extensions 207\u003c\/p\u003e \u003cp\u003e46 Splitting Fields. Galois Groups 210\u003c\/p\u003e \u003cp\u003e47 Separability and Normality 214\u003c\/p\u003e \u003cp\u003e48 Fundamental Theorem of Galois Theory 218\u003c\/p\u003e \u003cp\u003e49 Solvability by Radicals 219\u003c\/p\u003e \u003cp\u003e50 Finite Fields 223\u003c\/p\u003e \u003cp\u003e\u003cb\u003eXII. Geometric Constructions 229\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e51 Three Famous Problems 229\u003c\/p\u003e \u003cp\u003e52 Constructible Numbers 233\u003c\/p\u003e \u003cp\u003e53 Impossible Constructions 234\u003c\/p\u003e \u003cp\u003e\u003cb\u003eXIII. Solvable and Alternating Groups 237\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e54 Isomorphism Theorems and Solvable Groups 237\u003c\/p\u003e \u003cp\u003e55 Alternating Groups 240\u003c\/p\u003e \u003cp\u003e\u003cb\u003eXIV. Applications of Permutation Groups 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e56 Groups Acting on Sets 243\u003c\/p\u003e \u003cp\u003e57 Burnside’s Counting Theorem 247\u003c\/p\u003e \u003cp\u003e58 Sylow’s Theorem 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003eXV. Symmetry 256\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e59 Finite Symmetry Groups 256\u003c\/p\u003e \u003cp\u003e60 Infinite Two-Dimensional Symmetry Groups 263\u003c\/p\u003e \u003cp\u003e61 On Crystallographic Groups 267\u003c\/p\u003e \u003cp\u003e62 The Euclidean Group 274\u003c\/p\u003e \u003cp\u003e\u003cb\u003eXVI. Lattices and Boolean Algebras 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e63 Partially Ordered Sets 279\u003c\/p\u003e \u003cp\u003e64 Lattices 283\u003c\/p\u003e \u003cp\u003e65 Boolean Algebras 287\u003c\/p\u003e \u003cp\u003e66 Finite Boolean Algebras 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA. Sets 296\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB. Proofs 299\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC. Mathematical Induction 304\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eD. Linear Algebra 307\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eE. Solutions to Selected Problems 312\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003ePhoto Credit List 326\u003c\/p\u003e \u003cp\u003eIndex of Notation 327\u003c\/p\u003e \u003cp\u003eIndex 330\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003eDr. John R. Durbin\u003c\/strong\u003e is a professor of Mathematics at The University of Texas Austin. A native Kansan, he received B.A. and M.A. degrees from the University of Wichita (now Wichita State University), and a Ph.D. from the University of Kansas. He came to UT immediately thereafter.\u003cbr\u003eProfessor Durbin has been active in faculty governance at the University for many years. He served as chair of the Faculty Senate, 1982-84 and 1991-92, and as Secretary of the General Faculty, 1975-76 and 1998-2003.\u003cbr\u003eIn September of 2003 he received the University \u0026amp; Civitatis Award,in recognition of dedicated and meritorious service to the University above and beyond the regular expectations of teaching, research, and writing.\u003cbr\u003eHe has received a Teaching Excellence Award from the College of Natural Sciences and an Outstanding Teaching Award from the Department of Mathematics.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989639381221,"sku":"NP9780470384435","price":194.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470384435.jpg?v=1761784915","url":"https:\/\/k12savings.com\/products\/modern-algebra-isbn-9780470384435","provider":"K12savings","version":"1.0","type":"link"}