Introduction to Smooth Manifolds:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
2003
|
| Schriftenreihe: | Graduate Texts in Mathematics
218 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under standing "space" in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma trices, as easily as we think about the familiar 2-dimensional sphere in ]R3 |
| Beschreibung: | 1 Online-Ressource (XVII, 631 p) |
| ISBN: | 9780387217529 9780387954486 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-0-387-21752-9 |
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| 500 | |a Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under standing "space" in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma trices, as easily as we think about the familiar 2-dimensional sphere in ]R3 | ||
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| discipline | Mathematik |
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| spelling | Lee, John M. Verfasser aut Introduction to Smooth Manifolds by John M. Lee New York, NY Springer New York 2003 1 Online-Ressource (XVII, 631 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 218 0072-5285 Manifolds are everywhere. These generalizations of curves and surfaces to arbitrarily many dimensions provide the mathematical context for under standing "space" in all of its manifestations. Today, the tools of manifold theory are indispensable in most major subfields of pure mathematics, and outside of pure mathematics they are becoming increasingly important to scientists in such diverse fields as genetics, robotics, econometrics, com puter graphics, biomedical imaging, and, of course, the undisputed leader among consumers (and inspirers) of mathematics-theoretical physics. No longer a specialized subject that is studied only by differential geometers, manifold theory is now one of the basic skills that all mathematics students should acquire as early as possible. Over the past few centuries, mathematicians have developed a wondrous collection of conceptual machines designed to enable us to peer ever more deeply into the invisible world of geometry in higher dimensions. Once their operation is mastered, these powerful machines enable us to think geometrically about the 6-dimensional zero set of a polynomial in four complex variables, or the lO-dimensional manifold of 5 x 5 orthogonal ma trices, as easily as we think about the familiar 2-dimensional sphere in ]R3 Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd rswk-swf Glatte Fläche (DE-588)4157467-9 gnd rswk-swf Glatte Kurve (DE-588)4157470-9 gnd rswk-swf Glatte Mannigfaltigkeit (DE-588)4157471-0 s Glatte Kurve (DE-588)4157470-9 s Glatte Fläche (DE-588)4157467-9 s 1\p DE-604 https://doi.org/10.1007/978-0-387-21752-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lee, John M. Introduction to Smooth Manifolds Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Glatte Fläche (DE-588)4157467-9 gnd Glatte Kurve (DE-588)4157470-9 gnd |
| subject_GND | (DE-588)4157471-0 (DE-588)4157467-9 (DE-588)4157470-9 |
| title | Introduction to Smooth Manifolds |
| title_auth | Introduction to Smooth Manifolds |
| title_exact_search | Introduction to Smooth Manifolds |
| title_full | Introduction to Smooth Manifolds by John M. Lee |
| title_fullStr | Introduction to Smooth Manifolds by John M. Lee |
| title_full_unstemmed | Introduction to Smooth Manifolds by John M. Lee |
| title_short | Introduction to Smooth Manifolds |
| title_sort | introduction to smooth manifolds |
| topic | Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik Glatte Mannigfaltigkeit (DE-588)4157471-0 gnd Glatte Fläche (DE-588)4157467-9 gnd Glatte Kurve (DE-588)4157470-9 gnd |
| topic_facet | Mathematics Global differential geometry Cell aggregation / Mathematics Manifolds and Cell Complexes (incl. Diff.Topology) Differential Geometry Mathematik Glatte Mannigfaltigkeit Glatte Fläche Glatte Kurve |
| url | https://doi.org/10.1007/978-0-387-21752-9 |
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