Essays in Constructive Mathematics

Harold M. Edwards

211 pages, parution le 11/02/2005

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Résumé

This book aims to promote constructive mathematics not by defining it or formalizing it but by practicing it, by basing all definitions and proofs on finite algorithms.

The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices.

L'auteur - Harold M. Edwards

Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemann's Zeta Function (1974, 2001), Fermat's Last Theorem (1977), Galois Theory (1984), Divisor Theory (1990) and Linear Algebra (1995). Readers of his Advanced Calculus will know that his preference for constructive mathematics is not new.

Sommaire

Preface
Synopsis
A Fundamental Theorem
Topics in Algebra
Some Quadratic Problems
The Genus of an Algebraic Curve
Miscellany
References

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Harold M. Edwards
Parution	11/02/2005
Nb. de pages	211
Format	16 x 24
Couverture	Relié
Poids	513g
Intérieur	Noir et Blanc
EAN13	9780387219783
ISBN13	978-0-387-21978-3