多様体の基礎 基礎数学
GMD 2563
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- A long-selling text that continues to be published over and over again *First edition 1988, 31st printing as of May 2019 Manifolds are one of the central concepts of modern mathematics. This book maintains the position of describing manifolds in as easy-to-understand a manner as possible for those learning manifolds for the first time, and carefully explains the topics covered, focusing on the basics. Suitable for both those aiming for applications and those aiming for even more advanced theories. 【】 from the Preface of this book Manifolds are one of the central concepts of modern mathematics. The author wrote this book because he wanted to write a textbook that was as easy to understand as possible for manifolds. All the subjects covered are basic. As I tried to give a detailed explanation, this book became surprisingly thick. However, it does not contain as much content as you might imagine from its thickness. As a reader, I had second- and third-year university students in mind. Preliminary knowledge includes the basics of linear algebra (definition of vector spaces and linear mappings, definition of matrices and determinants, simple properties), calculus of multivariables (little by little about partial differentiation and multiple integrals), and elementary knowledge of topological spaces. is sufficient. However, I believe that even readers who are unfamiliar with these concepts can read a large portion of them. 【main table of contents】 Preface Chapter 1 Preparation §1 What is a manifold §2 m-dimensional number space §3 Vector space §4 Continuous mapping and Cr-class mapping §5 Phase space Chapter 2 Cr-class manifolds and Cr-class maps §6 Definition of manifold §7 Cs-class functions and Cs-class maps Chapter 3 Tangent vector space §8 Tangent vector space §9 Differentiation of Cr class maps §10 Local properties of maps §11 Projective space Chapter 4 Inset and Embedding §12 Inset and embedding §13 Embedding theorem §14 Division of 1 §15 Regular and critical points Chapter 5 Vector fields §16 Vector field §17 Integral curve Chapter 6 Differential Form §18 First-order differential form §19 k-order differential form §20 External differentiation and Stokes' theorem Appendix A Relationship between Dpr (M) and Tp (M) Appendix B Proof that the projective plane P² cannot be embedded in R³ Exercise questions answered
| Publisher | University of Tokyo Press |
| Publication date | September 25, 1988 |
| Language | Japanese |
| Print length | 350 pages |
| ISBN-10 | 4130621033 |
| ISBN-13 | 978-4130621038 |
| Item Weight | 500 g |
| Book 5 of 14 | Basic mathematics |
Who Should Buy?
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Math Students
Ideal for undergraduate or graduate students studying mathematics, particularly in areas of geometry and topology.
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Graduate Programs
Beneficial for those enrolled in advanced courses that require a solid understanding of manifolds in mathematics.
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Researchers
Useful for mathematicians and researchers looking for foundational knowledge in manifolds for academic work.
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Casual Readers
Not suitable for general readers without a strong mathematical background or interest in manifolds.
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Beginner level
Not recommended for beginners in mathematics; assumes prior knowledge of advanced mathematical concepts.
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Non-mathematicians
Individuals outside the field of mathematics may find the content too technical or complex without prior knowledge.
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