Title
An Introduction To Manifolds (Universitext)
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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: How many pages does this book have? A: This book has four hundred twenty-eight pages. It provides a comprehensive introduction to manifolds and their applications.
- Q: What is the binding type of 'An Introduction to Manifolds'? A: The binding type is paperback. This makes it lightweight and easy to handle for readers.
- Q: What are the dimensions of this book? A: The dimensions are six point one inches in length, one point zero two inches in width, and nine point two five inches in height. This size is typical for academic textbooks.
- Q: What is the target audience for this book? A: This book is suitable for graduate students and advanced undergraduates. It can also benefit those engaged in self-study.
- Q: What prerequisites are needed to understand this book? A: Minimal undergraduate prerequisites are required. It is designed to help readers quickly grasp essential concepts in differential geometry.
- Q: How does one use this book for self-study? A: Readers can follow the structured chapters and exercises to master the content at their own pace. Hints and solutions are provided to enhance understanding.
- Q: Is this book suitable for beginners in mathematics? A: Yes, it is suitable for beginners with minimal background in mathematics. The book includes an appendix on point-set topology to aid comprehension.
- Q: Can this book be used as a course textbook? A: Yes, it can be used as a text for a one-semester graduate or advanced undergraduate course. It is structured to facilitate classroom learning.
- Q: How should I care for this paperback book? A: To care for the book, keep it in a dry place to avoid moisture damage. Avoid bending the spine to maintain its condition.
- Q: What is the best way to store this book? A: Store this book upright on a bookshelf. Ensure it is not exposed to direct sunlight to prevent fading.
- Q: Is there a warranty or return policy for this book? A: Typically, books have a return policy depending on the retailer. Check with the specific store for details on returns and warranties.
- Q: What if my book arrives damaged? A: If your book arrives damaged, contact the retailer for a replacement or refund. Keep the original packaging for the return process.
- Q: Are there any exercises included in this book? A: Yes, the book includes exercises and problems to reinforce learning. Hints and solutions are provided for many of these exercises.
- Q: How does this book compare to other texts in differential geometry? A: This book is streamlined and focuses on essential topics, making it accessible compared to more comprehensive texts. It serves as a foundation for further study.
- Q: Does this book cover advanced topics in geometry? A: Yes, it covers advanced topics like de Rham cohomology, which is fundamental for further studies in geometry and topology.