Book Essays in Constructive Mathematics [Repost] free online

Harold M. Edwards Essays in Constructive Mathematics

Publisher: Sringer | 2004-11-30 | ISBN: 0387219781 | PDF | 230 pages | 11.56 MB

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 mathematicsamong them Galois theory of algebraic equations, Gausss theory of binary quadratic forms and Abels theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructivelyalthough the constructive treatments shed a surprising amount of light on thembut 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 Newtons 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.

Harold M. Edwards is Emeritus Professor of Mathematics at New York University. His previous books are Advanced Calculus (1969, 1980, 1993), Riemanns Zeta Function (1974, 2001), Fermats 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.

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