Elementary geometry of algebraic curves : an undergraduate introduction
著者
書誌事項
Elementary geometry of algebraic curves : an undergraduate introduction
Cambridge University Press, 1998
- : hardback
- : pbk
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注記
Includes index
内容説明・目次
内容説明
This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book contains several hundred worked examples and exercises, making it suitable for adoption as a course text. From the lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, whilst the ideas of linear systems are used to discuss the classical group structure on the cubic.
目次
- List of illustrations
- List of tables
- Preface
- 1. Real algebraic curves
- 2. General ground fields
- 3. Polynomial algebra
- 4. Affine equivalence
- 5. Affine conics
- 6. Singularities of affine curves
- 7. Tangents to affine curves
- 8. Rational affine curves
- 9. Projective algebraic curves
- 10. Singularities of projective curves
- 11. Projective equivalence
- 12. Projective tangents
- 13. Flexes
- 14. Intersections of projective curves
- 15. Projective cubics
- 16. Linear systems
- 17. The group structure on a cubic
- 18. Rational projective curves
- Index.
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