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Essays in Constructive Mathematics
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Essays in Constructive Mathematics Hardcover - 2004

by Harold M. Edwards


From the publisher

This book promotes constructive mathematics not by defining it or formalizing it but by practicing it. This means that its definitions and proofs use finite algorithms, not algorithms' that require surveying an infinite number of possibilities to determine whether a given condition is met. 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. For Abel's theorem the main algorithm 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.

First line

Kronecker quoted this saying of Pascal in the first of a series of lectures he gave on the concept of number.

Details

  • Title Essays in Constructive Mathematics
  • Author Harold M. Edwards
  • Binding Hardcover
  • Edition U. S. EDITION
  • Pages 211
  • Volumes 1
  • Language ENG
  • Publisher Springer, NY
  • Date November 30, 2004
  • Illustrated Yes
  • ISBN 9780387219783 / 0387219781
  • Weight 24.69 lbs (11.20 kg)
  • Dimensions 9.25 x 6.1 x 0.56 in (23.50 x 15.49 x 1.42 cm)
  • Library of Congress subjects Constructive mathematics
  • Library of Congress Catalog Number 2004049156
  • Dewey Decimal Code 511.3

About the author

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. In 1980 he was awarded the Steele Prize for mathematical exposition for the Riemann and Fermat books.

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