TY  - GEN
AU  - Abhyankar,Shreeram S
TI  - Algebraic geometry for scientists and engineers
T2  - Mathematical Surveys and Monographs
SN  - 9780821868942
U1  - 516.35 23rd
PY  - 2011///
CY  - Providence
PB  - AMS
KW  - Mathematics
KW  - Algebraic Geometry
KW  - Algebraic Curves
KW  - Algebraic Surfaces
KW  - Rational Parametrization
KW  - Polynomial Parametrization
N1  - Includes bibliography and index; 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
N2  - 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
ER  -