Modern Geometry— Methods and Applications: Part II: The Geometry and Topology of Manifolds
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1985
|
| Schriftenreihe: | Graduate Texts in Mathematics
104 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e |
| Beschreibung: | 1 Online-Ressource (XV, 432 p) |
| ISBN: | 9781461211006 9781461270119 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-1100-6 |
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| 500 | |a Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e | ||
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Datensatz im Suchindex
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| author | Dubrovin, Boris Anatol'evič 1950-2019 |
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| bvnumber | BV042419744 |
| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)863771324 (DE-599)BVBBV042419744 |
| dewey-full | 514.34 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.34 |
| dewey-search | 514.34 |
| dewey-sort | 3514.34 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1100-6 |
| format | Electronic eBook |
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| id | DE-604.BV042419744 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461211006 9781461270119 |
| issn | 0072-5285 |
| language | English |
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| spelling | Dubrovin, Boris Anatol'evič 1950-2019 Verfasser (DE-588)115874417X aut Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds by B. A. Dubrovin, S. P. Novikov, A. T. Fomenko New York, NY Springer New York 1985 1 Online-Ressource (XV, 432 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 104 0072-5285 Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik Novikov, S. P. Sonstige oth Fomenko, A. T. Sonstige oth https://doi.org/10.1007/978-1-4612-1100-6 Verlag Volltext |
| spellingShingle | Dubrovin, Boris Anatol'evič 1950-2019 Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik |
| title | Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds |
| title_auth | Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds |
| title_exact_search | Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds |
| title_full | Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds by B. A. Dubrovin, S. P. Novikov, A. T. Fomenko |
| title_fullStr | Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds by B. A. Dubrovin, S. P. Novikov, A. T. Fomenko |
| title_full_unstemmed | Modern Geometry— Methods and Applications Part II: The Geometry and Topology of Manifolds by B. A. Dubrovin, S. P. Novikov, A. T. Fomenko |
| title_short | Modern Geometry— Methods and Applications |
| title_sort | modern geometry methods and applications part ii the geometry and topology of manifolds |
| title_sub | Part II: The Geometry and Topology of Manifolds |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik |
| url | https://doi.org/10.1007/978-1-4612-1100-6 |
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