Type of Credit: Elective
Credit(s)
Number of Students
In this course, we will introduce some basics in topology, topological manifold, and differentiable manifold.
能力項目說明
本課程之目標在建立學生在微分流形的基礎，以作為未來在相關領域之應用。
| 教學週次Course Week | 彈性補充教學週次Flexible Supplemental Instruction Week | 彈性補充教學類別Flexible Supplemental Instruction Type |
|---|---|---|
| 週次Week | 課程主題Course Theme | 課程內容與指定閱讀Content and Reading Assignment | 教學活動與作業Activity and Homework | 學習投入時數Estimated time devoted to coursework per week | |
|---|---|---|---|---|---|
| 課堂講授Lecture Hours | 課程前後Preparation Time | ||||
|
1 |
Topology | Topological spaces and Continuous maps;Quotient spaces |
習題討論 |
3.0 |
6.0 |
|
2 |
Topology | Topological spaces and Continuous maps;Quotient spaces |
習題討論 |
3.0 |
6.0 |
|
3 |
Topology | Topological spaces and Continuous maps;Quotient spaces |
習題討論 |
3.0 |
6.0 |
|
4 |
Topology | product spaces;topological groups |
習題討論 |
3.0 |
6.0 |
|
5 |
Topology | product spaces;topological groups |
習題討論 |
3.0 |
6.0 |
|
6 |
Topology | product spaces;topological groups |
習題討論 |
3.0 |
6.0 |
|
7 |
Topology | compactness and connectedness |
習題討論 |
3.0 |
6.0 |
|
8 |
Topology | compactness and connectedness |
習題討論 |
3.0 |
6.0 |
|
9 |
Topology | compactness and connectedness |
Midterm |
0.0 |
0.0 |
|
10 |
differential manifold | differentiable structure;smooth mapping on manifold |
習題討論 |
3.0 |
6.0 |
|
11 |
differential manifold | differentiable structure;smooth mapping on manifold |
習題討論 |
3.0 |
6.0 |
|
12 |
differential manifold | differentiable structure;smooth mapping on manifold |
習題討論 |
3.0 |
6.0 |
|
13 |
differential manifold | Tangent vectors and vector fields; Derivative of smooth mappings |
習題討論 |
3.0 |
6.0 |
|
14 |
differential manifold | Tangent vectors and vector fields; Derivative of smooth mappings |
習題討論 |
3.0 |
6.0 |
|
15 |
differential manifold | Tangent vectors and vector fields; Derivative of smooth mappings |
習題討論 |
3.0 |
6.0 |
|
16 |
differential manifold | Exterior Algebra and differential form on Euclidean spaces |
習題討論 |
3.0 |
6.0 |
|
17 |
differential manifold | Exterior Algebra and differential form on Euclidean spaces |
習題討論 |
3.0 |
6.0 |
|
18 |
differential manifold | Exterior Algebra and differential form on Euclidean spaces |
Final |
0.0 |
0.0 |
本課程無涉及 AI 使用。
期末 100%
1. An introduction to differential manifolds and Riemannian Geometry, 2nd ed., W.M. Boothby
2. Intoduction to smooth manifolds, 2nd ed., J.M.Lee
3. An introduction to manifolds, 2nd ed., L..W.Tu
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