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Geometric trilogy:英文:Ⅱ:An algebraic approach to geometry 版權信息
- ISBN：9787519220754
- 條形碼：9787519220754 ; 978-7-5192-2075-4
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>>
Geometric trilogy:英文:Ⅱ:An algebraic approach to geometry 內容簡介
復投影平面中代數曲線的研究是幾何應用如密碼技術研究的重要內容，也是線性幾何研究向代數幾何研究的自然過渡。本書論述的就是幾何空間中的各種不同代數方法，給出了解析幾何、仿射幾何、歐幾里得幾何和投影幾何研究的具體內容，并詳盡地描述了各類幾何空間和代數曲線的性質。本書適合從事數學史、幾何學、代數及其相關領域研究生和科研人員閱讀和參考。 第2卷目次：解析幾何起源；仿射幾何；再論實仿射空間；歐幾里得幾何；厄米空間；投射幾何；代數曲線。附錄：域上的多項式；多變量中的多項式；齊次多項式；結式；對稱多項式；復數；二次型；對偶空間。
Geometric trilogy:英文:Ⅱ:An algebraic approach to geometry 目錄
1 The Birth of Analytic Geometry
1．1 Fermat's Analytic Geometry
1．2 Descartes' Analytic Geometry
1．3 More on Cartesian Systems of Coordinates
1．4 Non-Cartesian Systems of Coordinates
1．5 Computing Distances and Angles
1．6 Planes and Lines in Solid Geometry
1．7 The Cross Product
1．8 Forgetting the Origin
1．9 The Tangent to a Curve
1．10 The Conics
1．11 The Ellipse
1．12 The Hyperbola
1．13 The Parabola
1．14 The Quadrics
1．15 The Ruled Quadrics
1．16 Problems
1．17 Exercises
2 Affine Geometry
2．1 Affine Spaces over a Field
2．2 Examples of Affine Spaces
2．3 Affine Subspaces
2．4 Parallel Subspaces
2．5 Generated Subspaces
2．6 Supplementary Subspaces
2．7 Lines and Planes
2．8 Bary centers
2．9 Bary centric Coordinates
2．10 Triangles
2．11 Parallelograms
2，12 Affine Transformations
2．13 Affine Isomorphism
2．14 Translations
2．15 Projections
2．16 Symmetries
2．17 Homotheties and Affinities
2．18 The Intercept Thales Theorem
2．19 Affine Coordinates
2．20 Change of Coordinates
2．21 The Equations of a Subspace
2．22 The Matrix of an Affine Transformation
2．23 The Quadrics
2．24 The Reduced Equation of a Quadric
2．25 The Symmetries ofa Quadric
2．26 The Equation of a Non-degenerate Quadric
2．27 Problems
2．28 Exercises
……
3 More on Real Affine Spaces
4 Euclidean Geometry
5 Hermitian Spaces
6 Projective Geometry
7 Algebraic Curves
Appendix
References and Furtber Reading
Index
1．1 Fermat's Analytic Geometry
1．2 Descartes' Analytic Geometry
1．3 More on Cartesian Systems of Coordinates
1．4 Non-Cartesian Systems of Coordinates
1．5 Computing Distances and Angles
1．6 Planes and Lines in Solid Geometry
1．7 The Cross Product
1．8 Forgetting the Origin
1．9 The Tangent to a Curve
1．10 The Conics
1．11 The Ellipse
1．12 The Hyperbola
1．13 The Parabola
1．14 The Quadrics
1．15 The Ruled Quadrics
1．16 Problems
1．17 Exercises
2 Affine Geometry
2．1 Affine Spaces over a Field
2．2 Examples of Affine Spaces
2．3 Affine Subspaces
2．4 Parallel Subspaces
2．5 Generated Subspaces
2．6 Supplementary Subspaces
2．7 Lines and Planes
2．8 Bary centers
2．9 Bary centric Coordinates
2．10 Triangles
2．11 Parallelograms
2，12 Affine Transformations
2．13 Affine Isomorphism
2．14 Translations
2．15 Projections
2．16 Symmetries
2．17 Homotheties and Affinities
2．18 The Intercept Thales Theorem
2．19 Affine Coordinates
2．20 Change of Coordinates
2．21 The Equations of a Subspace
2．22 The Matrix of an Affine Transformation
2．23 The Quadrics
2．24 The Reduced Equation of a Quadric
2．25 The Symmetries ofa Quadric
2．26 The Equation of a Non-degenerate Quadric
2．27 Problems
2．28 Exercises
……
3 More on Real Affine Spaces
4 Euclidean Geometry
5 Hermitian Spaces
6 Projective Geometry
7 Algebraic Curves
Appendix
References and Furtber Reading
Index
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Geometric trilogy:英文:Ⅱ:An algebraic approach to geometry 作者簡介
Francis Borceux，比利時魯汶大學（Universite catholique de Louvain）教授，魯汶大學是比利時久負盛名的學府，歐洲十大名校之一。
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