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＜電子ブック＞
Essays in Constructive Mathematics / by Harold M. Edwards

版	1st ed. 2005.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2005
本文言語	英語
大きさ	XX, 211 p : online resource
著者標目	*Edwards, Harold M author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Mathematics LCSH:Algebraic geometry LCSH:Sequences (Mathematics) LCSH:Mathematical logic LCSH:Number theory FREE:Algebra FREE:Mathematics FREE:Algebraic Geometry FREE:Sequences, Series, Summability FREE:Mathematical Logic and Foundations FREE:Number Theory
一般注記	A Fundamental Theorem -- Topics in Algebra -- Some Quadratic Problems -- The Genus of an Algebraic Curve -- Miscellany "... The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. And it proves that the philosophical orientation of an author really can make a big difference. The mathematical content is intensely classical. ... Edwards makes it warmly accessible to any interested reader. And he is breaking fresh ground, in his rigorously constructive or constructivist presentation. So the book will interest anyone trying to learn these major, central topics in classical algebra and algebraic number theory. Also, anyone interested in constructivism, for or against. And even anyone who can be intrigued and drawn in by a masterly exposition of beautiful mathematics." Reuben Hersh 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. Harold M. Edwards is Emeritus Professor of Mathematics at NewYork 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 HTTP:URL=https://doi.org/10.1007/b138656

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