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課程大綱及進度表

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課程大綱及進度表

開課系所 應數所碩一二

開課學年 99

開課學期 1

課程名稱(中文) 微分幾何導論

課程名稱（英文） Introduction to Differential Geometry

課程碼 L154800

分班碼

先修科目或先備能力 Calculus, Linear Algebra

學分數 3

開課教師 江孟蓉

e-mail

[email protected]

電話 65126

Office Hours By Appointment

課程概述 This is the introductory course on differential geometry. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the

calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincare-Hopf theorem relating the Euler number of a manifold and the index of a vector field.

教學目標 Introduction to differential geometry for graduate students in mathematics

授課課程大綱明細 1. Differential Manifolds and Differentiable Maps 2. The Derivatives of

Differentiable Maps 3. Fibre Bundles

4. Differential Forms and

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Integration

5. The Exterior Derivative 6. De Rham Cohomology

7. Degrees, Indices and Related Topics

8. Lie Groups

參考書目 An Introduction to Differential Manifolds by Dennis

Barden and Charles B. Thomas, Imperial College Press (2003)

課程要求 Good understanding of the basic definitions, examples, and theorems

評量方式 Attendance 30%,

Class participation 30%, Weekly quiz 30%, Final Exam 10%

課程網址 助教資訊 備註

參考文獻

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