LEADER 05144nam 2200637 450 001 9910462709003321 005 20200520144314.0 010 $a1-118-83752-5 010 $a1-118-55203-2 035 $a(CKB)2670000000430703 035 $a(EBL)1443883 035 $a(OCoLC)847986001 035 $a(SSID)ssj0001002012 035 $a(PQKBManifestationID)11532416 035 $a(PQKBTitleCode)TC0001002012 035 $a(PQKBWorkID)10967740 035 $a(PQKB)10272132 035 $a(MiAaPQ)EBC1443883 035 $a(DLC) 2013023830 035 $a(Au-PeEL)EBL1443883 035 $a(CaPaEBR)ebr10895755 035 $a(CaONFJC)MIL629202 035 $a(EXLCZ)992670000000430703 100 $a20140804h20132013 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroductory modern algebra $ea historical approach /$fSaul Stahl 205 $aSecond edition. 210 1$aHoboken, New Jersey :$cWiley,$d2013. 210 4$dİ2013 215 $a1 online resource (691 p.) 300 $aDescription based upon print version of record. 311 $a0-470-87616-6 320 $aIncludes bibliographical references and index. 327 $aCover; Half Title page; Title page; Copyright page; Preface; Chapter 1: The Early History; 1.1 The Breakthrough; Chapter 2: Complex Numbers; 2.1 Rational Functions of Complex Numbers; 2.2 Complex Roots; 2.3 Solvability by Radicals I; 2.4 Ruler-and-Compass Constructibility of Regular Polygons; 2.5 Orders of Roots of Unity; 2.6 The Existence of Complex Numbers; Chapter 3: Solutions of Equations; 3.1 The Cubic Formula; 3.2 Solvability by Radicals II; 3.3 Other Types of Solutions; Chapter 4: Modular Arithmetic; 4.1 Modular Addition, Subtraction, and Multiplication 327 $a4.2 The Euclidean Algorithm and Modular Inverses4.3 Radicals in Modular Arithmetic; 4.4 The Fundamental Theorem of Arithmetic; Chapter 5: The Binomial Theorem and Modular Powers; 5.1 The Binomial Theorem; 5.2 Fermat's Theorem and Modular Exponents; 5.3 The Multinomial Theorem; 5.4 The Euler ?-Function; Chapter 6: Polynomials Over A Field; 6.1 Fields and Their Polynomials; 6.2 The Factorization of Polynomials; 6.3 The Euclidean Algorithm for Polynomials; 6.4 Elementary Symmetric Polynomials; 6.5 Lagrange's Solution of the Quartic Equation; Chapter 7: Galois Fields 327 $a7.1 Galois's Construction of His Fields7.2 The Galois Polynomial; 7.3 The Primitive Element Theorem; 7.4 On the Variety of Galois Fields; Chapter 8: Permutations; 8.1 Permuting the Variables of a Function I; 8.2 Permutations; 8.3 Permuting the Variables of a Function II; 8.4 The Parity of a Permutation; Chapter 9: Groups; 9.1 Permutation Groups; 9.2 Abstract Groups; 9.3 Isomorphisms of Groups and Orders of Elements; 9.4 Subgroups and Their Orders; 9.5 Cyclic Groups and Subgroups; 9.6 Cayley's Theorem; Chapter 10: Quotient Groups and Their Uses; 10.1 Quotient Groups; 10.2 Group Homomorphisms 327 $a10.3 The Rigorous Construction of Fields10.4 Galois Groups and the Resolvability of Equations; Chapter 11: Topics in Elementary Group Theory; 11.1 The Direct Product of Groups; 11.2 More Classifications; Chapter 12: Number Theory; 12.1 Pythagorean Triples; 12.2 Sums of Two Squares; 12.3 Quadratic Reciprocity; 12.4 The Gaussian Integers; 12.5 Eulerian Integers and Others; 12.6 What Is the Essence of Primality?; Chapter 13: The Arithmetic of Ideals; 13.1 Preliminaries; 13.2 Integers of a Quadratic Field; 13.3 Ideals; 13.4 Cancelation of Ideals; 13.5 Norms of Ideals 327 $a13.6 Prime Ideals and Unique Factorization13.7 Constructing Prime Ideals; Chapter 14: Abstract Rings; 14.1 Rings; 14.2 Ideals; 14.3 Domains; 14.4 Quotients of Rings; A. Excerpts from Al-Khwarizmi's Solution of the Quadratic Equation1; B. Excerpts from Cardano's Ars Magna1; C. Excerpts from Abel's A Demonstration of the Impossibility of the Algebraic Resolution of General Equations Whose Degree Exceeds Four1; D. Excerpts from Galois's On the Theory of Numbers1; E. Excerpts from Cayley's The Theory of Groups1; F. Mathematical Induction; G. Logic, Predicates, Sets, and Functions 327 $aG.1 Truth Tables 330 $aPraise for the First Edition ""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.""-CHOICE Introductory Modern Algebra: A Historical Approach, Second Edition 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 Second Edition 606 $aAlgebra, Abstract 608 $aElectronic books. 615 0$aAlgebra, Abstract. 676 $a512/.02 700 $aStahl$b Saul$0141807 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910462709003321 996 $aIntroductory modern algebra$92039062 997 $aUNINA LEADER 01956oam 2200589M 450 001 9910716192103321 005 20200213070900.1 035 $a(CKB)5470000002518190 035 $a(OCoLC)1065589303 035 $a(OCoLC)995470000002518190 035 $a(EXLCZ)995470000002518190 100 $a20071213d1926 ua 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAndrew Radel Oyster Co. May 21, 1926. -- Committed to the Committee of the Whole House and ordered to be printed 210 1$a[Washington, D.C.] :$c[U.S. Government Printing Office],$d1926. 215 $a1 online resource (11 pages) 225 1 $aHouse report / 69th Congress, 1st session. House ;$vno. 1285 225 1 $a[United States congressional serial set] ;$v[serial no. 8537] 300 $aBatch processed record: Metadata reviewed, not verified. Some fields updated by batch processes. 300 $aFDLP item number not assigned. 606 $aClaims 606 $aMalicious mischief 606 $aVandalism 606 $aDredging 606 $aJurisdiction 606 $aLeases 606 $aLegislative amendments 606 $aOysters 606 $aWildlife conservation 608 $aLegislative materials.$2lcgft 615 0$aClaims. 615 0$aMalicious mischief. 615 0$aVandalism. 615 0$aDredging. 615 0$aJurisdiction. 615 0$aLeases. 615 0$aLegislative amendments. 615 0$aOysters. 615 0$aWildlife conservation. 701 $aUnderhill$b Charles Lee$f1867-1946$pRepublican (MA)$01386821 801 0$bWYU 801 1$bWYU 801 2$bOCLCO 801 2$bOCLCQ 906 $aBOOK 912 $a9910716192103321 996 $aAndrew Radel Oyster Co. May 21, 1926. -- Committed to the Committee of the Whole House and ordered to be printed$93487935 997 $aUNINA