代数曲线几何初步(经典英文数学教材系列)(Elementary geometry of algebraic curves)
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品牌: 菌吉布森
基本信息·出版社：世界图书出版公司
·页码：250 页
·出版日期：2009年
·ISBN：7506292645/9787506292641
·条形码：9787506292641
·包装版本：1版
·装帧：平装
·开本：24
·正文语种：英语
·丛书名：经典英文数学教材系列
·外文书名：Elementary geometry of algebraic curves
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内容简介General Background I first became involved in the teaching of geometry about twenty years ago，when my department introduced an optional second year course on the geometry of plane curves，partly to redress the imbalance in the teaching of the subject。It Was mildly revolutionary，since it went back to an earlier sct of precepts where the differential and algebraic geometry of cuwes were pursued simultaneously,to their mutua！advantage.
目录
List of Illustrations
List of Tables
Preface
1 Real Algebraic Curves
1.1 Parametrized and Implicit Curves
1.2 Introductory Examples
1.3 Curves in Planar Kinematics
2 General Ground Fields
2.1 Two Motivating Examples
2.2 Groups, Rings and Fields
2.3 General Affine Planes and Curves
2.4 Zero Sets of Algebraic Curves
3 Polynomial Algebra
3.1 Factorization in Domains
3.2 Polynomials in One Variable
3.3 Polynomials in Several Variables
3.4 Homogeneous Polynomials
3.5 Formal Differentiation
4 Atfine Equivalence
4.1 Affine Maps
4.2 Affline Equivalent Curves
4.3 Degree as an Affine Invariant
4.4 Centres as Affine Invariants
5 Affline Conics
5.1 Affline Classification
5.2 The Delta Invariants
5.3 Uniqueness of Equations
6 Singularities of Afline Curves
6.1 Intersection Numbers
6.2 Multiplicity of a Point on a Curve
6.3 Singular Points
7 Tangents to Afline Curves
7.1 Generalities about Tangents
7.2 Tangents at Simple Points
7.3 Tangents at Double Points
7.4 Tangents at Points of Higher Multiplicity
8 Rational Afline Curves
8.1 Rational Curves
8.2 Diophantine Equations
8.3 Conics and Integrals
9 Projective Algebraic Curves
9.1 The Projective Plane
9.2 Projective Lines
9.3 Atfine Planes in the Projective Plane
9.4 Projective Curves
9.5 Affine Views of Projective Curves
10 Singularities of Projective Curves
10.1 Intersection Numbers
10.2 Multiplicity of a Point on a Curve
10.3 Singular Points
10.4 Delta Invariants viewed Projectively
11 Projective Equivalence
11.1 Projective Maps
11.2 Projective Equivalence
11.3 Projective Conics
11.4 Afline and Projective Equivalence
12 Projective Tangents
12.1 Tangents to Projective Curves
12.2 Tangents at Simple Points
12.3 Centres viewed Projectively
12.4 Foci viewed Projectively
12.5 Tangents at Singular Points
12.6 Asymptotes
13 Flexes
13.1 Hessian Curves
13.2 Configurations of Flexes
14 Intersections of Proiective Curves
14．1 The Geometric Idea
14．2 Resultants in One Variable
14．3 Resultants in Severa!Variables
14．4 B6zout’S Theorem
14．5 Thc Multiplicity Inequality
14．6 Invariance of the Intersection Number
15 Proiective Cubics
15．1 Geometric Types 0f Cubics
15．2 Cubics of General Type
15．3 Singular Irreducible Cubics
15．4 Reducible Cubics
16 Linear Systems
16．1 Projective Spaces of Curves
16．2 Pcncils of CuiNes
16．3 Solving Quartic Equations
16．4 Subspaces or Projective Spaces
16．5 Linear Systems of Culwes
16．6 Dual CulNes
17 The Group Structure on a Cubic
17．1 The Nine Associated Points
17．2 The Star Operation
17．3 Cubics as Groups
17．4 Group Computations
17．5 Determination of the Groups
18 Rational Projective Curves
18．1 Thc Projective Concept
18．2 Quartics with Three Double Points
18．3 Thc Deficiency of a CHIve
18．4 Some Rational Curves
18．5 Some Non-Rational Curves
Index
……[看更多目录]
序言For some time I have felt there is a good case fob raising the profile o! undergraduate geometry The case can be argued on academic grounds alone Geometry represents a way of thinking within mathematics，quite distinct from algebra and analysis，and So offers a fresh perspective on the subject It can also be argued on purely practical grounds My experience is that there is a measure of concern in various practical disciplines where geometry plays a substantial role（engineering science for instance） that their students no longer receive a basic geometric training And thirdly，it can be argued on psychological grounds Few would deny that substantial areas of mathematics fail to excite student interest：yet there are many students attracted to geometry by its sheer visual content The decline in undergraduate geometry is a bit of a mystery It probably has something to do with the fashion for formalism which seemed to permeate mathematics some decades ago But things are changing The enormous progress made in studying non.1inear phenomena by geometrical methods has certainly revived interest in geometry And for material reasons， tertiary institutions are ever more conscious of the need to offer their students more attractive courses.
0.1 General Background I first became involved in the teaching of geometry about twenty years ago，when my department introduced an optional second year course on the geometry of plane curves，partly to redress the imbalance in the teaching of the subject。It Was mildly revolutionary，since it went back to an earlier sct of precepts where the differential and algebraic geometry of cuwes were pursued simultaneously,to their mutua！advantage.
In the final year of study students could pursue this kind of geometry
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