| 期刊全称 | An Introduction to Manifolds | | 影响因子2023 | Loring W. Tu | | 视频video | | | 发行地址 | Assumes only one semester of algebra and two semesters of undergraduate analysis, so is accessible to undergraduates and graduate students.Modesty of scope allows the most essential topics to emerge c | | 学科分类 | Universitext | | 图书封面 |  | | 影响因子 | .Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory...In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The requisite point-set topology is included in an appendix of twenty pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems...This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, Introduction to Manifolds is also an excellent found | | Pindex | Textbook 2008Latest edition |
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发表于 2025-3-21 19:15:35
