LEADER 01239nam--2200373---450- 001 990003132650203316 005 20080728104034.0 035 $a000313265 035 $aUSA01000313265 035 $a(ALEPH)000313265USA01 035 $a000313265 100 $a20080728d1974----km-y0itay50------ba 101 $aita 102 $aIT 105 $aa---||||001yy 200 1 $a<> bronzo con scena di battaglia da una tomba longobarda$fAlessandra Melucco Vaccaro 210 $aRoma$cAccademia nazionale dei Lincei$d1974 215 $aP. 342-364, [13] c. di tav.$cill.$d27 cm. 225 2 $aAtti della Accademia nazionale dei Lincei$iClasse di scienze morali, storiche e filologiche$iMemorie 300 $aTit. dalla cop. 410 0$12001$aAtti della Accademia nazionale dei Lincei 454 1$12001 461 1$1001-------$12001 606 0 $aNecropoli longobarde$yNocera Umbra 676 $a937.7 700 1$aMELUCCO VACCARO,$bAlessandra$0212132 801 0$aIT$bsalbc$gISBD 912 $a990003132650203316 951 $aFC M 1308$bDLM$cFC M 959 $aBK 969 $aDILAM 979 $aDILAM$b90$c20080728$lUSA01$h1040 996 $aBronzo con scena di battaglia da una tomba longobarda$91016911 997 $aUNISA LEADER 04934nam 22006015 450 001 9910300129503321 005 20200630115116.0 010 $a3-319-94773-7 024 7 $a10.1007/978-3-319-94773-0 035 $a(CKB)4100000005471752 035 $a(DE-He213)978-3-319-94773-0 035 $a(MiAaPQ)EBC6226857 035 $a(PPN)229916767 035 $a(EXLCZ)994100000005471752 100 $a20180807d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA History of Abstract Algebra $eFrom Algebraic Equations to Modern Algebra /$fby Jeremy Gray 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIV, 415 p. 18 illus.) 225 1 $aSpringer Undergraduate Mathematics Series,$x1615-2085 311 $a3-319-94772-9 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- 1 Simple quadratic forms -- 2 Fermat?s Last Theorem -- 3 Lagrange?s theory of quadratic forms -- 4 Gauss?s Disquisitiones Arithmeticae -- 5 Cyclotomy -- 6 Two of Gauss?s proofs of quadratic reciprocity -- 7 Dirichlet?s Lectures -- 8 Is the quintic unsolvable? -- 9 The unsolvability of the quintic -- 10 Galois?s theory -- 11 After Galois ? Introduction -- 12 Revision and first assignment -- 13 Jordan?s Traité -- 14 Jordan and Klein -- 15 What is ?Galois theory?? -- 16 Algebraic number theory: cyclotomy -- 17 Dedekind?s first theory of ideals -- 18 Dedekind?s later theory of ideals -- 19 Quadratic forms and ideals -- 20 Kronecker?s algebraic number theory -- 21 Revision and second assignment -- 22 Algebra at the end of the 19th century -- 23 The concept of an abstract field -- 24 Ideal theory -- 25 Invariant theory -- 26 Hilbert?s Zahlbericht -- 27 The rise of modern algebra ? group theory -- 28 Emmy Noether -- 29 From Weber to van der Waerden -- 30 Revision and final assignment -- A Polynomial equations in the 18th Century -- B Gauss and composition of forms -- C Gauss on quadratic reciprocity -- D From Jordan?s Traité -- E Klein?s Erlanger Programm -- F From Dedekind?s 11th supplement -- G Subgroups of S4 and S5 -- H Curves -- I Resultants -- Bibliography -- Index. 330 $aThis textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss?s theory of numbers and Galois?s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat?s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois?s approach to the solution of equations. The book also describes the relationship between Kummer?s ideal numbers and Dedekind?s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer?s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study. . 410 0$aSpringer Undergraduate Mathematics Series,$x1615-2085 606 $aMathematics 606 $aHistory 606 $aAlgebra 606 $aNumber theory 606 $aHistory of Mathematical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M23009 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aMathematics. 615 0$aHistory. 615 0$aAlgebra. 615 0$aNumber theory. 615 14$aHistory of Mathematical Sciences. 615 24$aAlgebra. 615 24$aNumber Theory. 676 $a512.02 700 $aGray$b Jeremy$4aut$4http://id.loc.gov/vocabulary/relators/aut$053883 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300129503321 996 $aA History of Abstract Algebra$91912862 997 $aUNINA