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Record Nr. |
UNISA996490345103316 |
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Autore |
Edwards Harold M. |
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Titolo |
Essays in constructive mathematics / / Harold M. Edwards |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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Edizione |
[Second edition.] |
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Descrizione fisica |
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1 online resource (325 pages) |
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Disciplina |
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Soggetti |
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Constructive mathematics |
Matemàtica constructiva |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- 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 xⁿ + c₁xⁿ⁻¹ + c₂xⁿ⁻² + · · · + cₙ -- 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 |
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