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Algebraic Geometry for Scientists and Engineers : Mathematical Surveys and Monographs - S.S. Abhyankar

Algebraic Geometry for Scientists and Engineers

Mathematical Surveys and Monographs

Paperback Published: January 1990
ISBN: 9780821815359
Number Of Pages: 295

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This book, based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, is intended for engineers and scientists (especially computer scientists), as well as graduate students and advanced undergraduates in mathematics. In addition to providing a concrete or algorithmic approach to algebraic geometry, the author also attempts to motivate and explain its link to more modern algebraic geometry based on abstract algebra.The book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities. The emphasis is on presenting heuristic ideas and suggestive arguments rather than formal proofs. Readers will gain new insight into the subject of algebraic geometry in a way that should increase appreciation of modern treatments of the subject, as well as enhance its utility in applications in science and industry.

Rational and polynomial parametrizations
Fractional linear transformations
Cubic curves Cubic surfaces and general hypersurfaces
Outline of the theory of plane curves
Affine plane and projective plane
Sphere with handles
Functions and differentials on a curve
Polynomials and power series
Review of abstract algebra
Some commutative algebra
Hensel's lemma and Newton's theorem
More about Newton's theorem Branches and valuations
Divisors of functions and differentials
Weierstrass preparation theorem
Intersection multiplicity
Resolution of singularities of plane curves
Infinitely near singularities
Parametrizing a quartic with three double points
Characteristic pairs Criterion for one place and Jacobian problem
Inversion formula and Jacobian problem
Surfaces Hypersurfaces Resolution of singularities of algebraic surfaces
Birational and polyrational transformations
Valuations and birational correspondence
Rational cylinders through a variety Resultants
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780821815359
ISBN-10: 0821815350
Series: Mathematical Surveys and Monographs
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 295
Published: January 1990
Publisher: American Mathematical Society
Country of Publication: US
Dimensions (cm): 25.4 x 17.78  x 1.91
Weight (kg): 0.54

Earn 151 Qantas Points
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