基本素養 Basic Literacy

核心能力 Competence

掌握連續與逼進的能力
Ability to handle continuity phenomena and approximations.
處理數字及符號運算的能力
Ability to operate with symbols and digits.
透視形像與空間的能力
Ability to visualize space, shape, and images.
利用計算機處理數學的能力
Ability of using computer to do mathematics.
應用隨機理論的能力
Ability to apply stochastic mathematics.
處理大量數據的能力
Ability to handle large amount of data.
處理離散型數學的能力
Ability to do mathematics relating to discrete models.
獨立研究的能力
Ability to do independent studies of mathematics.
使用計算機的能力
Abilities to use computer as a tool.

課程概述 Course Description

這門課的目的是研究曲線和曲面的幾何性質。我們將討論曲線的曲率和撓率、Frenet–Serret 公式、高斯映射、高斯曲率與均曲率、曲面的基本形式、測地線、Gauss–Bonnet 定理等課題。
This course is designed to study the geometric properties of curves and surfaces. We will talk about curvatures and torsions of curves, Frenet–Serret formulas, Gauss map, Gaussian and mean curvatures, fundamental forms of surfaces, geodesics, Gauss–Bonnet Theorem, etc.

課程學習目標 Course Objectives

  • 掌握曲線幾何
  • 學習幾何觀點並用以處理曲面幾何
  • Gauss–Bonnet 定理
  • 課程進度 Course Outline

    週次 Week進度說明 Progress Description
    1Curves
    2Curves
    3Curves
    4Regular surfaces
    5Regular surfaces
    6Regular surfaces
    7The Geometry of the Gauss Map
    8The Geometry of the Gauss Map
    9The Geometry of the Gauss Map
    10The Geometry of the Gauss Map
    11The Intrinsic Geometry of Surfaces
    12The Intrinsic Geometry of Surfaces
    13The Intrinsic Geometry of Surfaces
    14The Intrinsic Geometry of Surfaces
    15The Intrinsic Geometry of Surfaces
    16The Intrinsic Geometry of Surfaces
    17Gauss-Bonet Theorem
    18Gauss-Bonet Theorem
     以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

    有關課程其他調查 Other Surveys of Courses

    1.本課程是否規劃業界教師參與教學或演講? 否
    Is there any industry specialist invited in this course? How many times? No
    2.本課程是否規劃含校外實習(並非參訪)? 否
    Are there any internships involved in the course? How many hours? No
    3.本課程是否可歸認為學術倫理課程?
    Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
    4.本課程是否屬進入社區實踐課程?
    Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?