{"product_id":"introduction-to-abstract-algebra-4e-set-isbn-9781118296035","title":"Introduction to Abstract Algebra, 4e Set","description":"\u003cp\u003e\u003cb\u003ePraise for the Third Edition\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . .\"—Zentralblatt MATH\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eThe Fourth Edition of \u003ci\u003eIntroduction to Abstract Algebra\u003c\/i\u003e continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately begin to perform computations using abstract concepts that are developed in greater detail later in the text.\u003c\/p\u003e \u003cp\u003eThe Fourth Edition features important concepts as well as specialized topics, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe treatment of nilpotent groups, including the Frattini and Fitting subgroups\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eSymmetric polynomials\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of the fundamental theorem of algebra using symmetric polynomials\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of Wedderburn's theorem on finite division rings\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eThe proof of the Wedderburn-Artin theorem\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout the book, worked examples and real-world problems illustrate concepts and their applications, facilitating a complete understanding for readers regardless of their background in mathematics. A wealth of computational and theoretical exercises, ranging from basic to complex, allows readers to test their comprehension of the material. In addition, detailed historical notes and biographies of mathematicians provide context for and illuminate the discussion of key topics. A solutions manual is also available for readers who would like access to partial solutions to the book's exercises.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eIntroduction to Abstract Algebra, Fourth Edition\u003c\/i\u003e is an excellent book for courses on the topic at the upper-undergraduate and beginning-graduate levels. The book also serves as a valuable reference and self-study tool for practitioners in the fields of engineering, computer science, and applied mathematics.\u003c\/p\u003e Preface ix \u003cp\u003eAcknowledgment xv\u003c\/p\u003e \u003cp\u003eNotations Used in the Text xvii\u003c\/p\u003e \u003cp\u003eA Sketch of the History of Algebra to 1929 xxi\u003c\/p\u003e \u003cp\u003ePreliminaries 1\u003c\/p\u003e \u003cp\u003eProofs 1\u003c\/p\u003e \u003cp\u003eSets 5\u003c\/p\u003e \u003cp\u003eMappings 9\u003c\/p\u003e \u003cp\u003eEquivalences 17\u003c\/p\u003e \u003cp\u003eIntegers and Permutations 22\u003c\/p\u003e \u003cp\u003eInduction 22\u003c\/p\u003e \u003cp\u003eDivisors and Prime Factorization 30\u003c\/p\u003e \u003cp\u003eIntegers Modulo n 41\u003c\/p\u003e \u003cp\u003ePermutations 51\u003c\/p\u003e \u003cp\u003eAn Application to Cryptography 63\u003c\/p\u003e \u003cp\u003eGroups 66\u003c\/p\u003e \u003cp\u003eBinary Operations 66\u003c\/p\u003e \u003cp\u003eGroups 73\u003c\/p\u003e \u003cp\u003eSubgroups 82\u003c\/p\u003e \u003cp\u003eCyclic Groups and the Order of an Element 87\u003c\/p\u003e \u003cp\u003eHomomorphisms and Isomorphisms 95\u003c\/p\u003e \u003cp\u003eCosets and Lagrange's Theorem 105\u003c\/p\u003e \u003cp\u003eGroups of Motions and Symmetries 114\u003c\/p\u003e \u003cp\u003eNormal Subgroups 119\u003c\/p\u003e \u003cp\u003eFactor Groups 127\u003c\/p\u003e \u003cp\u003eThe Isomorphism Theorem 133\u003c\/p\u003e \u003cp\u003eAn Application to Binary Linear Codes 140\u003c\/p\u003e \u003cp\u003eRings 155\u003c\/p\u003e \u003cp\u003eExamples and Basic Properties 155\u003c\/p\u003e \u003cp\u003eIntegral Domains and Fields 166\u003c\/p\u003e \u003cp\u003eIdeals and Factor Rings 174\u003c\/p\u003e \u003cp\u003eHomomorphisms 183\u003c\/p\u003e \u003cp\u003eOrdered Integral Domains 193\u003c\/p\u003e \u003cp\u003ePolynomials 196\u003c\/p\u003e \u003cp\u003ePolynomials 196\u003c\/p\u003e \u003cp\u003eFactorization of Polynomials over a Field 209\u003c\/p\u003e \u003cp\u003eFactor Rings of Polynomials over a Field 222\u003c\/p\u003e \u003cp\u003ePartial Fractions 231\u003c\/p\u003e \u003cp\u003eSymmetric Polynomials 233\u003c\/p\u003e \u003cp\u003eFormal Construction of Polynomials 243\u003c\/p\u003e \u003cp\u003eFactorization in Integral Domains 246\u003c\/p\u003e \u003cp\u003eIrreducibles and Unique Factorization 247\u003c\/p\u003e \u003cp\u003ePrincipal Ideal Domains 259\u003c\/p\u003e \u003cp\u003eFields 268\u003c\/p\u003e \u003cp\u003eVector Spaces 269\u003c\/p\u003e \u003cp\u003eAlgebraic Extensions 277\u003c\/p\u003e \u003cp\u003eSplitting Fields 285\u003c\/p\u003e \u003cp\u003eFinite Fields 293\u003c\/p\u003e \u003cp\u003eGeometric Constructions 299\u003c\/p\u003e \u003cp\u003eThe Fundamental Theorem of Algebra 304\u003c\/p\u003e \u003cp\u003eAn Application to Cyclic and BCH Codes 305\u003c\/p\u003e \u003cp\u003eModules over Principal Ideal Domains 318\u003c\/p\u003e \u003cp\u003eModules 318\u003c\/p\u003e \u003cp\u003eModules over a PID 327\u003c\/p\u003e \u003cp\u003ep-Groups and the Sylow Theorems 341\u003c\/p\u003e \u003cp\u003eFactors and Products 341\u003c\/p\u003e \u003cp\u003eCauchy's Theorem 349\u003c\/p\u003e \u003cp\u003eGroup Actions 356\u003c\/p\u003e \u003cp\u003eThe Sylow Theorems 364\u003c\/p\u003e \u003cp\u003eSemidirect Products  371\u003c\/p\u003e \u003cp\u003eAn Application to Combinatorics 375\u003c\/p\u003e \u003cp\u003eSeries of Subgroups 381\u003c\/p\u003e \u003cp\u003eThe Jordan-Holder Theorem 382\u003c\/p\u003e \u003cp\u003eSolvable Groups 387\u003c\/p\u003e \u003cp\u003eNilpotent Groups 394\u003c\/p\u003e \u003cp\u003eGalois Theory 401\u003c\/p\u003e \u003cp\u003eGalois Groups and Separability 402\u003c\/p\u003e \u003cp\u003eThe Main Theorem of Galois Theory 410\u003c\/p\u003e \u003cp\u003eInsolvability of Polynomials 423\u003c\/p\u003e \u003cp\u003eCyclotomic Polynomials and Wedderburn's Theorem 430\u003c\/p\u003e \u003cp\u003eFiniteness Conditions for Rings and Modules 435\u003c\/p\u003e \u003cp\u003eWedderburn's Theorem 435\u003c\/p\u003e \u003cp\u003eThe Wedderburn-Artin Theorem 444\u003c\/p\u003e \u003cp\u003eAppendices\u003c\/p\u003e \u003cp\u003eComplex Numbers 455\u003c\/p\u003e \u003cp\u003eMatrix Arithmetic 462\u003c\/p\u003e \u003cp\u003eZorn's Lemma 467\u003c\/p\u003e \u003cp\u003eProof of the Recursion Theorem 471\u003c\/p\u003e \u003cp\u003eBibliography 473\u003c\/p\u003e \u003cp\u003eSelected Answers 475\u003c\/p\u003e \u003cp\u003eIndex 499\u003c\/p\u003e  \u003cp\u003e“This could also be an excellent adjunct to more theoretically oriented textbooks used in more intensive courses.”  (\u003ci\u003eComputing Reviews\u003c\/i\u003e, 5 November 2012)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003eW. KEITH NICHOLSON, PhD,\u003c\/b\u003e is Professor in the Department of Mathematics and Statistics at the University of Calgary, Canada. He has published extensively in his areas of research interest, which include clean rings, morphic rings and modules, and quasi-morphic rings. Dr. Nicholson is the coauthor of \u003ci\u003eModern Algebra with Applications\u003c\/i\u003e, Second Edition, also published by Wiley.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989455257829,"sku":"NP9781118296035","price":142.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118296035.jpg?v=1761784167","url":"https:\/\/k12savings.com\/products\/introduction-to-abstract-algebra-4e-set-isbn-9781118296035","provider":"K12savings","version":"1.0","type":"link"}