Essays In Constructive Mathematics (Hardcover)

Preface Synopsis PART 1: A Fundamental Theorem General Arithmetic A Fundamental Theorem Roots Field (Simple Algebraic Extensions) Factorization of Polynomials with Integer Coefficients A Factorization Algorithm Validation of the Factorization Algorithm About the Factorization Algorithm Proof of the Fundamental Theorem Minimal Splitting Polynomials PART 2: Topics in Algebra Galois' Fundamental Theorem Algebraic Quantities Adjunctions and the Factorization of Polynomials Symmetric Polynomials and the Splitting Field of x^n + c_1x^{n-1} + ... + c_n A Fundamental Theorem of Divisor Theory PART 3: Some Quadratic Problems Hypernumbers Modules The Class Semigroup Multiplication of Modules and Module Classes Is A a Square Mod p? Gauss's Composition of Forms The Construction of Compositions PART 4: The Genus of an Algebraic Curve Abel's Memoir Euler's Addition Formula An Algebraic Definition of the Genus Newton's Polygon Determination of the Genus Holomorphic Differentials The Riemann-Roch Theorem The Genus is a Birational Invariant PART 5: Miscellany On the So-Called Fundamental Theorem of Algebra Proof by Contradiction and the Sylow Theorems Overview of 'Linear Algebra' The Spectral Theorem Kronecker as One of E.T. Bell's 'Men of Mathematics' References