Conics and Cubics: A Concrete Introduction to Algebraic Curves
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1998
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Conics and Cubics is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas: homogenous coordinates and intersection multiplicities. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout's Theorem on the number of intersections of two curves. The book is a text for a one-semester course on algebraic curves for junior-senior mathematics majors. The only prerequisite is first-year calculus. The new edition introduces the deeper study of curves through parametrization by power series. Two uses of parametrizations are presented: counting multiple intersections of curves and proving the duality of curves and their envelopes. About the first edition: "The book...belongs in the admirable tradition of laying the foundations of a difficult and potentially abstract subject by means of concrete and accessible examples." - Peter Giblin, MathSciNet |
| Beschreibung: | 1 Online-Ressource (X, 292 p) |
| ISBN: | 9781475729757 9781475729771 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4757-2975-7 |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2975-7 |
| format | Electronic eBook |
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| isbn | 9781475729757 9781475729771 |
| issn | 0172-6056 |
| language | English |
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| spelling | Bix, Robert Verfasser aut Conics and Cubics A Concrete Introduction to Algebraic Curves by Robert Bix New York, NY Springer New York 1998 1 Online-Ressource (X, 292 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 Conics and Cubics is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas: homogenous coordinates and intersection multiplicities. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout's Theorem on the number of intersections of two curves. The book is a text for a one-semester course on algebraic curves for junior-senior mathematics majors. The only prerequisite is first-year calculus. The new edition introduces the deeper study of curves through parametrization by power series. Two uses of parametrizations are presented: counting multiple intersections of curves and proving the duality of curves and their envelopes. About the first edition: "The book...belongs in the admirable tradition of laying the foundations of a difficult and potentially abstract subject by means of concrete and accessible examples." - Peter Giblin, MathSciNet Mathematics Geometry, algebraic Numerical analysis Geometry Algebraic Geometry Numerical Analysis Mathematik Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Algebraische Kurve (DE-588)4001165-3 s 2\p DE-604 https://doi.org/10.1007/978-1-4757-2975-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bix, Robert Conics and Cubics A Concrete Introduction to Algebraic Curves Mathematics Geometry, algebraic Numerical analysis Geometry Algebraic Geometry Numerical Analysis Mathematik Algebraische Kurve (DE-588)4001165-3 gnd |
| subject_GND | (DE-588)4001165-3 (DE-588)4123623-3 |
| title | Conics and Cubics A Concrete Introduction to Algebraic Curves |
| title_auth | Conics and Cubics A Concrete Introduction to Algebraic Curves |
| title_exact_search | Conics and Cubics A Concrete Introduction to Algebraic Curves |
| title_full | Conics and Cubics A Concrete Introduction to Algebraic Curves by Robert Bix |
| title_fullStr | Conics and Cubics A Concrete Introduction to Algebraic Curves by Robert Bix |
| title_full_unstemmed | Conics and Cubics A Concrete Introduction to Algebraic Curves by Robert Bix |
| title_short | Conics and Cubics |
| title_sort | conics and cubics a concrete introduction to algebraic curves |
| title_sub | A Concrete Introduction to Algebraic Curves |
| topic | Mathematics Geometry, algebraic Numerical analysis Geometry Algebraic Geometry Numerical Analysis Mathematik Algebraische Kurve (DE-588)4001165-3 gnd |
| topic_facet | Mathematics Geometry, algebraic Numerical analysis Geometry Algebraic Geometry Numerical Analysis Mathematik Algebraische Kurve Lehrbuch |
| url | https://doi.org/10.1007/978-1-4757-2975-7 |
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