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".
發表於2024-10-31
An Introduction to Manifolds 2024 pdf epub mobi 電子書 下載
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...
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...
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。
圖書標籤: 數學 流形 Manifolds 微分幾何 幾何 Mathematics Tu differential_geometry
down to earth的書,需要的基礎很多都會講一遍。
評分三年前的書,二刷復習仍舊親切, 少有的好書. 流形是光滑麯麵的自然推廣,微分形式很好的總結瞭何種流形上的積分是可能的.斯托剋斯定理是經典嚮量分析的一個推廣,在嚮量分析裏麵,無鏇嚮量場是否有一個潛在的特定域取決於域的拓撲屬性(簡單連通), 這問題基本概括瞭De Rham理論
評分用現代的數學術語介紹微分流形,可惜最後的de rham cohomology就看不明白瞭。5/20. 寫書當如Loring Tu!
評分長度適中
評分down to earth的書,需要的基礎很多都會講一遍。
An Introduction to Manifolds 2024 pdf epub mobi 電子書 下載