An Introduction to Manifolds 2025 pdf epub mobi 電子書下載

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An Introduction to Manifolds pdf epub mobi 著者簡介

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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 foundation for Springer's GTM 82, "Differential Forms in Algebraic Topology".

An Introduction to Manifolds 2025 pdf epub mobi 電子書下載

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發表於2025-01-22

An Introduction to Manifolds 2025 pdf epub mobi 電子書下載

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學完近世代數，看這本書應該不成問題。比北大陳維桓的書好看的多，由於使用瞭代數學的理論，使得證明過程大為精煉。Boothby的書該講的沒講透，大傢都知道的扯瞭一大堆。總的來說，這本書很和我的胃口，力薦！

評分☆☆☆☆☆

內容比較少，淺顯。不算Appendix的話就300頁左右，比較適閤初學者。想再深入點就沒辦法瞭。作者說是這本書是經典的“Differential forms in algebraic topology”的前傳。但是，正如很多經典電影的前傳一樣，這本書差瞭原書幾個檔次。Bott大師已逝，經典不再重現。

評分☆☆☆☆☆

沒有人評價的一本書，好奇怪。在我看來，這本書是流形理論最佳的入門書。作者是曾經和Raul Bott閤寫Differential Forms in Algebraic Topology的Loring Tu。讀這本書不需要什麼太多的數學基礎，作者從最基礎的東西一步步develop整個流形理論。習題大部分都有答案或者提示，而且...

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出版者:Springer

作者:Loring W. Tu

出品人:

頁數:410

譯者:

出版時間:2010-10-8

價格:USD 59.95

裝幀:Paperback

isbn號碼:9781441973993

叢書系列: