LEADER 00825nam0-22003251i-450- 001 990003264610403321 005 20001010 010 $a0-582-30135-1 035 $a000326461 035 $aFED01000326461 035 $a(Aleph)000326461FED01 035 $a000326461 100 $a20000920d1987----km-y0itay50------ba 101 0 $aita 105 $ay-------001yy 200 1 $aINDUSTRIAL GEOGRAPHY 205 $a1 210 $aEngland$cLongman S. and T.$d1987 215 $app.260 610 0 $aManuali di Geografia Industriale 676 $a045.001 700 1$aWatts,$bDoug$f<1941- >$0376424 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990003264610403321 952 $a045.001.WAT$b1130$fDECGE 959 $aDECGE 996 $aIndustrial geography$948532 997 $aUNINA DB $aING01 LEADER 00867nam0-22002891i-450 001 990005551120203316 005 20200326173556.0 035 $a000555112 035 $aUSA01000555112 035 $a(ALEPH)000555112USA01 100 $a20081003d2009----km y1itay5003----ba 101 0 $aeng 102 $aGB 200 1 $aIntelligent data analysis$edeveloping new methodologies through pattern discovery and recovery$fHsiao-Fan Wang [editor] 210 $aInformation Science Reference$dc2009 215 $aXX, 344 p.$cill.$d29 cm 606 0 $aSistemi$2BNCF 676 $a003.52 700 1$aWANG,$bHsiao-Fan$0614520 801 0$aIT$bSOL$c20120104 912 $a990005551120203316 951 $a000 003.52 HSI$b14901 DISES 951 $a000 003.52 HSI$b14902 DISES 959 $aBK 969 $aDISES 996 $aIntelligent data analysis$91131358 997 $aUNISA LEADER 05549nam 2200481 450 001 9910616204903321 005 20230718152815.0 010 $a3-030-98558-X 035 $a(MiAaPQ)EBC7102180 035 $a(Au-PeEL)EBL7102180 035 $a(CKB)24950465700041 035 $a(PPN)264959310 035 $a(EXLCZ)9924950465700041 100 $a20230225d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEssays in constructive mathematics /$fHarold M. Edwards 205 $aSecond edition. 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$dŠ2022 215 $a1 online resource (325 pages) 311 08$aPrint version: Edwards, Harold M. Essays in Constructive Mathematics Cham : Springer International Publishing AG,c2022 9783030985578 320 $aIncludes bibliographical references and index. 327 $aIntro -- To the Reader -- Contents -- Part I The Original Essays -- 1 A Fundamental Theorem -- Essay 1.1 General Arithmetic -- Essay 1.2 A Fundamental Theorem -- Essay 1.3 Root Fields (Simple Algebraic Extensions) -- Essay 1.4 Factorization of Polynomials with Integer Coefficients -- Essay 1.5 A Factorization Algorithm -- Essay 1.6 Validation of the Factorization Algorithm -- Essay 1.7 About the Factorization Algorithm -- Essay 1.8 Proof of the Fundamental Theorem -- Essay 1.9 Minimal Splitting Polynomials -- 2 Topics in Algebra -- Essay 2.1 Galois's Fundamental Theorem -- Essay 2.2 Algebraic Quantities -- Essay 2.3 Adjunctions and the Factorization of Polynomials -- Essay 2.4 The Splitting Field of x? + c?x??š + c?x??˛ + ˇ ˇ ˇ + c? -- Essay 2.5 A Fundamental Theorem of Divisor Theory -- 3 Some Quadratic Problems -- Essay 3.1 The Problem A? + B = ? and "Hypernumbers -- Essay 3.2 Modules -- Essay 3.3 The Class Semigroup. Solution of A? + B = ? -- Essay 3.4 Multiplication of Modules and Module Classes -- Essay 3.5 Is A a Square Mod p? -- Essay 3.6 Gauss's Composition of Forms -- Essay 3.7 The Construction of Compositions -- 4 The Genus of an Algebraic Curve -- Essay 4.1 Abel's Memoir -- Essay 4.2 Euler's Addition Formula -- Essay 4.3 An Algebraic Definition of the Genus -- Essay 4.4 Newton's Polygon -- Essay 4.5 Determination of the Genus -- Essay 4.6 Holomorphic Differentials -- Essay 4.7 The Riemann-Roch Theorem -- Essay 4.8 The Genus Is a Birational Invariant -- 5 Miscellany -- Essay 5.1 On the So-Called Fundamental Theorem of Algebra -- Essay 5.2 Proof by Contradiction and the Sylow Theorems -- Essay 5.3 Overview of ``Linear Algebra'' -- Essay 5.4 The Spectral Theorem -- Essay 5.5 Kronecker as One of E. T. Bell's ``Men of Mathematics'' -- Part II Three Topics in Rational Arithmetic. 327 $a6 Constructive Algebra -- Essay 6.1 Fields -- Essay 6.2 Factorization -- Essay 6.3 Algorithms -- Endnotes to Chapter 6 -- 7 The Algorithmic Foundations of Galois's Theory -- Essay 7.1 What Are the Roots of a Polynomial? -- Essay 7.2 Galois's Overlooked Construction -- Essay 7.3 The Idea of Galois's Construction -- Essay 7.4 Galois's Determination of the Roots of f(x) in Q(V) -- Essay 7.5 The Galois Group and Galois's Proposition 1 -- Essay 7.6 The Foundation -- Essay 7.7 Extension of the Notion of the Galois Group of a Polynomial -- Essay 7.8 The Solution of Cubic Polynomials -- Essay 7.9 Galois's Proposition 2 -- Essay 7.10 Galois's Proposition 3 -- Essay 7.11 Solvability by Radicals -- Essay 7.12 The Simplest Case -- Essay 7.13 Solvability by Radicals Implies Solvability of the Galois Group -- Essay 7.14 Roots of Unity -- Essay 7.15 Solvability of the Galois Group implies Solvability by Radicals -- Essay 7.16 The Explicit Solution of Cubics by Radicals -- 8 A Constructive Definition of Points on an Algebraic Curve -- Essay 8.1 The Points on an Algebraic Curve -- Essay 8.2 Curve Fields That Contain Indeterminates -- Essay 8.3 Points of Curve Fields of the Form A(x) -- Essay 8.4 Expansions at a Point Where x Is a Local Parameter -- Essay 8.5 Augmentation and the Newton Diagram -- Essay 8.6 Stub Solutions and Ambiguities -- Essay 8.7 The Algorithm of Essay 8.6 Must Terminate -- Essay 8.8 Expansion Rules -- Essay 8.9 Points -- Essay 8.10 Points Are Intrinsic to K -- Essay 8.11 Quantities Integral Over x -- Essay 8.12 Points as Divisors -- 9 Abel's Theorem -- Essay 9.1 What Was Abel's Theorem? -- Essay 9.2 Normal Bases -- Essay 9.3 The Field of Constants -- Essay 9.4 Differentials and Holomorphic Differentials -- Essay 9.5 The Construction of Holomorphic Differentials. 327 $aEssay 9.6 Parametric Points Constructed Using a Normal Basis -- Essay 9.7 The Theorem of Abel's Last Paper -- Essay 9.8 A Theorem About Holomorphic Differentials -- Essay 9.9 A Change of Parameters -- Essay 9.10 Abel's Addition Theorems -- Essay 9.11 Addition on an Elliptic Curve -- Endnotes to Chapter 9 -- Postscript -- References -- Index. 606 $aConstructive mathematics 606 $aMatemātica constructiva$2thub 608 $aLlibres electrōnics$2thub 615 0$aConstructive mathematics. 615 7$aMatemātica constructiva 676 $a511.3 700 $aEdwards$b Harold M.$042829 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910616204903321 996 $aEssays in constructive mathematics$93020077 997 $aUNINA