Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1992
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra. Until recently, these topics involved a lot of abstract mathematics and were only taught in graduate school. But in the 1960's, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have seen a minor revolution in commutative algebra. The ability to compute efficiently with polynomial equations has made it possible to investigate complicated examples that would be impossible to do by hand, and has changed the practice of much research in algebraic geometry. This has also enhanced the importance of the subject for computer scientists and engineers, who have begun to use these techniques in a whole range of problems. It is our belief that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time, one can do some substantial mathematics, including the Hilbert Basis Theorem, Elimination Theory and the Nullstellensatz. The mathematical prerequisites of the book are modest: the students should have had a course in linear algebra and a course where they learned how to do proofs. Examples of the latter sort of course include discrete math and abstract algebra |
| Beschreibung: | 1 Online-Ressource (XI, 514 p) |
| ISBN: | 9781475721812 9781475721836 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4757-2181-2 |
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Datensatz im Suchindex
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| dewey-ones | 516 - Geometry |
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| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-2181-2 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
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| isbn | 9781475721812 9781475721836 |
| issn | 0172-6056 |
| language | English |
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| series2 | Undergraduate Texts in Mathematics |
| spelling | Cox, David Verfasser aut Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra by David Cox, John Little, Donal O’Shea New York, NY Springer New York 1992 1 Online-Ressource (XI, 514 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra. Until recently, these topics involved a lot of abstract mathematics and were only taught in graduate school. But in the 1960's, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have seen a minor revolution in commutative algebra. The ability to compute efficiently with polynomial equations has made it possible to investigate complicated examples that would be impossible to do by hand, and has changed the practice of much research in algebraic geometry. This has also enhanced the importance of the subject for computer scientists and engineers, who have begun to use these techniques in a whole range of problems. It is our belief that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time, one can do some substantial mathematics, including the Hilbert Basis Theorem, Elimination Theory and the Nullstellensatz. The mathematical prerequisites of the book are modest: the students should have had a course in linear algebra and a course where they learned how to do proofs. Examples of the latter sort of course include discrete math and abstract algebra Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Computeralgebra (DE-588)4010449-7 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s Datenverarbeitung (DE-588)4011152-0 s 1\p DE-604 Algebraische Geometrie (DE-588)4001161-6 s Algorithmische Geometrie (DE-588)4130267-9 s 2\p DE-604 Computeralgebra (DE-588)4010449-7 s 3\p DE-604 4\p DE-604 Little, John Sonstige oth O’Shea, Donal Sonstige oth https://doi.org/10.1007/978-1-4757-2181-2 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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cox, David Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algorithmische Geometrie (DE-588)4130267-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd Kommutative Algebra (DE-588)4164821-3 gnd Computeralgebra (DE-588)4010449-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4130267-9 (DE-588)4011152-0 (DE-588)4164821-3 (DE-588)4010449-7 (DE-588)4001161-6 |
| title | Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra |
| title_auth | Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra |
| title_exact_search | Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra |
| title_full | Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra by David Cox, John Little, Donal O’Shea |
| title_fullStr | Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra by David Cox, John Little, Donal O’Shea |
| title_full_unstemmed | Ideals, Varieties, and Algorithms An Introduction to Computational Algebraic Geometry and Commutative Algebra by David Cox, John Little, Donal O’Shea |
| title_short | Ideals, Varieties, and Algorithms |
| title_sort | ideals varieties and algorithms an introduction to computational algebraic geometry and commutative algebra |
| title_sub | An Introduction to Computational Algebraic Geometry and Commutative Algebra |
| topic | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algorithmische Geometrie (DE-588)4130267-9 gnd Datenverarbeitung (DE-588)4011152-0 gnd Kommutative Algebra (DE-588)4164821-3 gnd Computeralgebra (DE-588)4010449-7 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Mathematics Geometry, algebraic Algebraic Geometry Mathematik Algorithmische Geometrie Datenverarbeitung Kommutative Algebra Computeralgebra Algebraische Geometrie |
| url | https://doi.org/10.1007/978-1-4757-2181-2 |
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