拓樸學主要是探討空間在連續變換之下不變的性質，在許多領域中都有重要的應用。本課程首先將介紹基本點集拓樸理論，包括拓樸空間、歐氏拓樸、同胚、連續映射、度量空間及緊緻性等概念，之後將探討相關應用例如結理論、基本群、曲面分類等概念，以及基本的Hausdorff維度與碎形以及宇宙的拓樸等等，主要目的除了讓同學瞭解拓樸學的基本理論與相關知識外，也能學習到拓樸學在其他數學領域的應用。
課程中也將安排概念實做、專家演講、以及視情況安排校外參訪活動。而為了增進修課同學間的合作學習與發表能力，課程中也將設計引討小組討論、口頭發表、以及製作學術海報，從而增進學習成效。
Topology mainly explores the invariant properties of space under continuous transformation, and has important applications in many fields. This course will first introduce the basic point set topology theory, including concepts such as topological space, Euclidean topology, homeomorphism, continuous mapping, metric space, and compactness. Later, it will explore related applications such as knot theory, basic groups, and surfaces. Concepts such as classification, as well as basic Hausdorff dimensions and fractals, topology of the universe, etc. The main purpose is not only to let students understand the basic theory and related knowledge of topology, but also to learn the application of topology in other mathematical fields.
The course will also arrange concept implementation, expert lectures, and off-campus visits as appropriate. In order to enhance the cooperative learning and presentation skills among course students, the course will also design introductory group discussions, oral presentations, and the production of academic posters to enhance learning effectiveness.
（可於網路免費下載）1. Sidney A. Morris, Topology without tears (version of Feb. 20, 2012) ,
http://uob-community.ballarat.edu.au/~smorris/topology.htm
（本書需先依上列網站的規定E-Mail給原作者取得密碼後，才能下載可列印的版本，同時需遵守密碼保護規定。另外，第一到第五章亦有簡體中文版本。）
（可於校內圖書館電子書資源免費下載）2. John B. Conway, Course in Point Set Topology, Springer International Publishing, 2014.
（可於校內圖書館電子書資源免費下載）3. David S. Richeson, Euler's gem : the polyhedron formula and the birth of topology, Princeton University Press, 2008.
（可於校內圖書館電子書資源免費下載）4. David Gay, Explorations in Topology: Map Coloring, Surfaces and Knots, Elsevier Science & Technology Books, 2013.
(Available for free download on the Internet) 1. Sidney A. Morris, Topology without tears (version of Feb. 20, 2012) ,
http://uob-community.ballarat.edu.au/~smorris/topology.htm
(This book must first obtain the password from the original author by email according to the regulations of the above-mentioned websites before downloading the printable version. At the same time, password protection regulations must be followed. In addition, Chapters 1 to 5 are also available in simplified Chinese.)
(Can be downloaded for free from e-book resources in the campus library) 2. John B. Conway, Course in Point Set Topology, Springer International Publishing, 2014.
(Can be downloaded for free from e-book resources in the campus library) 3. David S. Richeson, Euler's gem: the polyhedron formula and the birth of topology, Princeton University Press, 2008.
(You can download it for free from e-book resources in the campus library) 4. David Gay, Explorations in Topology: Map Coloring, Surfaces and Knots, Elsevier Science & Technology Books, 2013.
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 期中考（第一次考試）期中考（第一次考試） Midterm exam (first exam) |
25 | |
| 第二次考試第二次考試 second exam |
25 | 時間約於第13～14週 |
| 課堂發表課堂發表 Class presentation |
20 | 包含口頭報告及海報發表（細節將於課堂說明）。 |
