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。
Tuning mainly explores the unchanging properties of spaces under continuous changes, and has important applications in many fields. This course will first introduce the concepts of basic point set expansion theory, including concepts such as expansion space, Ou's expansion, homogeneity, continuous mapping, measurement space and tightness. Then, we will explore related applications such as structural theory, basic group, and surface. The main purpose of not only allowing students to understand the basic theories and related knowledge of the tuning of the tuning, but also learning the application of tuning in other mathematical fields.
During the course, conceptual practice, expert lectures, and off-campus visits will also be arranged. In order to improve the cooperative learning and presentation ability of students in the course, the course will also design a briefing group discussion, oral publication, and produce academic posters to improve 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 online) 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 a password to the original author according to the regulations of the website listed above, and the password protection regulations must be followed. In addition, there are also simple Chinese versions in Chapters 1 to 5.)
(It can be downloaded for free from the on-campus e-book resources) 2. John B. Conway, Course in Point Set Topology, Springer International Publishing, 2014.
(It can be downloaded for free from the on-campus e-book resources) 3. David S. Richeson, Euler's gem : the polyhedron formula and the birth of topology, Princeton University Press, 2008.
(You can download free of charge from the on-campus e-book resources) 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 Declaration |
20 | 包含口頭報告及海報發表（細節將於課堂說明）。 |
| 平時成績平時成績 Regular achievements |
30 | 包括：出席成績、學習單作業、課堂表現等。 |
