| Preface Synopsis 1 A Fundamental Theorem 1.1 General Arithmetic 1.2 A Fundamental Theorem 1.3 Root Fields (Simple Algebraic Extensions) 1.4 Factorization of Polynomials with Integer Coefficients ... 1.5 A Factorization Algorithm 1.6 Validation of the Factorization Algorithm 1.7 About the Factorizati0n Algorithm 1.8 Proof of the Fundamental Theorem 1.9 Minimal Splitting Polynomials 2 Topics in Algebra 2.1 Galois's Fundamental Theorem 2.2 Algebraic Quantities 2.3 Adjunctions and the Factorization of Polynomials 2.4 The Splitting Field of xn+c1xn-1+c2xn-2+...+cn 2.5 A Pundamental Theorem of Divisor Theory 3 Some Quadratic Problems 3.1 The Problem An + B = [] and "Hypernumbers" . 3.2 Modules 3.3 The Class Semigroup. Solution of A[] + B = [] 3.4 Multiplication of Modules and Module Classes 3.5 Is A a Square Mod p? 3.6 Gauss's Composition of Forms 3.7 The Construction of Compositions 4 The Genus of an Algebraic Curve 4.1 Abel's Memoir 4.2 Euler's Addition Formula 4.3 An Algebraic Definition of the Genus 4.4 Newton's Polygon 4.5 Determination of the Genus 4,6 Holomorphic Differentials 4.7 The Riemann-Roch Theorem 4.8 The Cenus Is a Birational Invariant 5 Miscellany 5.1 On the So-Called Fundainental Theorem of Algebra 5.2 Proof by Contradiction and the Sylow Theorems 5.3 Overview of 'Linear Algebra' 5.4 The Spectral Theorem 5.5 Kronecker as One of E. T. Bell's "Men of Mathematics" References Index |
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