Title
An Introduction to Manifolds (Universitext),Used
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Manifolds, the higherdimensional 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 pointset 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 onesemester graduate or advanced undergraduate course, as well as by students engaged in selfstudy. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's GTM 82, 'Differential Forms in Algebraic Topology'.
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- Q: What is the main focus of 'An Introduction to Manifolds'? A: The book focuses on the theory of manifolds, which are higher-dimensional analogs of smooth curves and surfaces, combining algebra, topology, and analysis.
- Q: Who is the author of this book? A: The author of 'An Introduction to Manifolds' is Loring W. Tu.
- Q: What topics are covered in this book? A: The book covers essential topics in manifold theory, including topological invariants like de Rham cohomology, point-set topology, real analysis, and linear algebra.
- Q: What is the intended audience for this book? A: This book is suitable for graduate students, advanced undergraduates, and anyone engaged in self-study of geometry and topology.
- Q: How many pages does 'An Introduction to Manifolds' have? A: The book has a total of 428 pages.
- Q: What is the binding type of this book? A: The book is available in paperback binding.
- Q: When was 'An Introduction to Manifolds' published? A: The book was published on October 6, 2010.
- Q: Is there any supplemental material included in this book? A: Yes, the book includes appendices reviewing point-set topology, real analysis, and linear algebra, as well as hints and solutions for many exercises.
- Q: What prerequisites are needed to understand the material in this book? A: Only minimal undergraduate prerequisites are required to understand the material presented in 'An Introduction to Manifolds'.
- Q: What edition is 'An Introduction to Manifolds'? A: This book is the 2nd edition, published in 2011.