Science/Engineering Essays in Constructive Mathematics (Repost) (0387219781)

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Essays in Constructive Mathematics

By Harold M. Edwards

& 8220;This book aims to promote 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. 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 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.

& 8221;

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	Study Mathematics As A Constructive Activity: Learners Generating Examples (Studies in Mathematical Think pic info:2007-05-23/1_787_origAnne Watson / John H. Mason, Mathematics As A Constructive Activity: Learners Generating Examples (Studies in Mathematical Thinking and Learning Series) Lawrence Erlbaum Associates \| ISBN 0805843442 \| May 24, ...
	Science/Engineering Essays in Constructive Mathematics Harold M. Edwards, "Essays in Constructive Mathematics"Publisher: Springer \| Pages: 211 \| ISBN: 0387219781 \| PDF \| 10.6 MBThis book aims to promote constructive mathematics not by defining it or formalizing it but by practicing it. This mea ...
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	[Hot]Essays in Constructive Mathematics [Hot]Essays in Constructive MathematicsPublisher: Springer \| 2004 \| 211 Pages \| ISBN: 0387219781 \| PDF \| 11.5 MB? This book aims to promote constructive mathematics not by defining it or formalizing it but by practicing it. This means that ...
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	Study Mathematics As A Constructive Activity: Learners Generating Examples (Studies in Mathematical Think pic info:2007-05-23/1_787_origAnne Watson / John H. Mason, Mathematics As A Constructive Activity: Learners Generating Examples (Studies in Mathematical Thinking and Learning Series) Lawrence Erlbaum Associates \| ISBN 0805843442 \| May 24, ...
	Science/Engineering Essays in Constructive Mathematics Harold M. Edwards, "Essays in Constructive Mathematics"Publisher: Springer \| Pages: 211 \| ISBN: 0387219781 \| PDF \| 10.6 MBThis book aims to promote constructive mathematics not by defining it or formalizing it but by practicing it. This mea ...
	Science/Engineering Trends and Applications in Constructive Approximation (International Series of Numerical Mathematics) Trends and Applications in Constructive Approximation (International Series of Numerical Mathematics): Detlef H. Mache, Jazsef Szabados, Marcel G. de Bruin Birkhauser \| ISBN: 3764371242 \| 1899-12-31 \| PDF / djvu (ocr) \| 281 pages \| 4.64 / ...
	[Hot]Essays in Constructive Mathematics [Hot]Essays in Constructive MathematicsPublisher: Springer \| 2004 \| 211 Pages \| ISBN: 0387219781 \| PDF \| 11.5 MB? This book aims to promote constructive mathematics not by defining it or formalizing it but by practicing it. This means that ...
	Mathematics Constructive Real Numbers and Constructive Function Spaces 325 pages \| American Mathematical Society (1968) \| ISBN: 0821832662 \| PDF \| 17.9 MB This book is devoted to certain problems of constructive mathematical analysis. The basic sections are devoted to the foundations of the theory of constru ...
	Nonfiction Constructive Real Numbers and Constructive Function Spaces This book is devoted to certain problems of constructive mathematical analysis. The basic sections are devoted to the foundations of the theory of constructive function spaces. Information from the theory of constructive real numbers needed ...

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