Essays in Constructive Mathematics

2005
ISBN: 978-1-4899-9018-1
Verlag: Springer

Buch, Englisch, 211 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 359 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Edwards, Harold M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

A Fundamental Theorem.- Topics in Algebra.- Some Quadratic Problems.- The Genus of an Algebraic Curve.- Miscellany.

Über Autor(innen)

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.