Essays in Constructive Mathematics

Edwards, Harold M.

ISBN 10: 1489990186 / ISBN 13: 9781489990181

Published by Springer 2014-12, 2014

About this Item

Seller Inventory # 6666-IUK-9781489990181

Bibliographic Details

• Title: Essays in Constructive Mathematics
• Publisher: Springer 2014-12
• Publication Date: 2014
• Language: English
• ISBN 10: 1489990186
• ISBN 13: 9781489990181
• Binding: PF
• Condition: New

About this title

Synopsis

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.

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.