課程說明(Course Desc<x>ription)：
<br>本課程是微分幾何入門。內容包括光滑流形及其拓撲和分析的基本知識。
<br>為更專業的幾何研究和其它相關領域課程基礎。
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<br>This is an introductory course on differential geometry.  It deals with some basic 
<br>aspects of geometry, topology and analysis  of smooth manifolds. Specific topics 
<br>include smooth manifolds, tangent bundles, differential forms, Stokes’ theorem and 
<br>de Rham cohomology.
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<br>Reference books: 
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<br>1) Introduction to Smooth Manifolds (2nd edition), by John M. Lee, GTM (textbook); 
<br>2) Foundations of Differentiable Manifolds and Lie Groups, by Frank Warner, GTM; 
<br>3) An Introduction to Manifolds, by L. Tu, UTX;  
<br>4) A Comprehensive Introduction to Differential Geometry (Volume I), by Michael 
<br>Spivak.
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<br>Tentative schedule: 
<br>1. Smooth manifold and maps. 
<br>2. Tangent space and vector bundle.
<br>3. Immersion and em<x>bedding.  
<br>4. Vector field and Lie derivative.  
<br>5. Integration on manifolds, Stokes' Theorem.  
<br>6. De Rham cohomology, Poincare Lemma.  
<br>7. Sard's Theorem, degree of a map.  
<br>8. Lie groups, group action on manifolds.  
<br>9. Triangulations, Euler characteristics, Mayer-Vietoris sequence (time pertmits).   
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<br>Evaluation: Homework 25%, first exam 35% and second exam  40%.
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<br>Please check your email account frequently so you do not miss responding to any 
<br>time-sensitive requests from an instructor or other part of NTHU.
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