本課程是以微積分及線性代數的知識為基礎，介紹空間中之曲線與曲面的相關理論，以及它們的應用。主要的目的在於使同學瞭解如何掌握『彎曲』的概念，以及彎曲空間中 （正如我們所生存的地球）的幾何（例如什麼是『直線』等等）。為了深入探究這些數學理論，我們也將藉由較宏觀的角度，介紹整個幾何理論發展的歷史，使同學更進一步認識幾何學對於人類文明的影響，並瞭解我們所講授的課程內容在整體發展過程中的重要性。

（第17、18週自主學習相關事項將於課堂說明。）

This course is based on the knowledge of calculus and linear algebra, and introduces the related theories of curves and surfaces in space, as well as their applications. The main purpose is to enable students to understand how to grasp the concept of "curvature" and the geometry (such as what is a "straight line", etc.) in curved space (just like the earth we live on). In order to explore these mathematical theories in depth, we will also introduce the history of the development of the entire geometric theory from a macro perspective, so that students can further understand the impact of geometry on human civilization and understand the importance of the course content we teach in the overall development process.

(Matters related to independent learning in weeks 17 and 18 will be explained in class.)

1. 課程講義資料

2. A. Pressley, Elementary Differential Geometry, Springer 2003.

3. A. Pressley, Elementary Differential Geometry (second edition), Springer 2010.

1. Course handouts

2. A. Pressley, Elementary Differential Geometry, Springer 2003.

3. A. Pressley, Elementary Differential Geometry (second edition), Springer 2010.