Course Syllabus

Course Information：

Year-Semester Course Number Course Name Phase Credits Hours Required/Elective Instructor Class Student NO. Withdraw Note

Spring Semester
Year 2026 360195 Topics of Mathematics 1 2.0 2 △ Kuo Ann Liu Core Curriculum (III) 41 0 自然與科學向度

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	360195	Topics of Mathematics	1	2.0	2	△	Kuo Ann Liu	Core Curriculum (III)	41	0	自然與科學向度

Course Plan：

Instructor Kuo Ann Liu

Email mathman@ntut.edu.tw

Last Updated 2026-02-24 10:53:32

Course Objective 數學的發展多是為了解決自然科學上的問題，其研究動機結果大都有蛛絲馬跡脈絡追尋。千百年來累積了相當多有益且有意義的故事，追尋前人的足跡，可欣賞數學之美，更可體察定理背後的真實用意。本課程收集很多數理發展史上具代表性的例子，借古鑑今，能體會所學的來龍去脈，更感覺數學的踏實。 Most theorems in Mathematics are used to solve the problem of sciences, so that the traces and their researched motivation is worth pursuing. Many beneficial and significant examples have accumulated throughout the history of the human being. Following the footprints of predecessors, we can appreciate the beauty of the theorems and savor the purports of them. In this course, we will bring some representative examples to show the beginning and subsequent development of theorems, hoping that our students can feel the concreteness of Mathematics.

Course Schedule 第1,2週: 除法原理,餘式定理,因式定理第3,4週: 根與係數關係第5,6週: 數列,級數,階差第7,8週: 遞迴,差分方程,生成函數第9週: 期中考第10,11週: V-E+F=2,正多面體第11,12週: 圓錐截痕(古典與現代錐線) 第13,15: 阿基米德拋物線公式,錐的體積公式第16週: 懸鏈線第17,18: 最速曲線與等時曲線

Evaluation and grading policy 1. 出缺勤 30% 2. 期中考 30% 3. 期末報告(作業) 40%

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:No
自編講義

The access to curricular consultation email, line群組

Expanding teaching and resources ● 參與式創新教學 (Participatory & Innovative Teaching)
強調學生參與與產出，導入翻轉、PBL/專題、設計思考或遊戲化等策略。
Emphasizes student engagement and outcomes by adopting strategies such as Flipped Classroom, PBL (Problem/Project- Based Learning), Design Thinking, or Gamification.
● 數位科技融入 (Digital Technology Integration)
運用生成式AI、VR/AR、IoT、IRS等新興科技輔助教學與評量。
Utilizes emerging technologies such as Generative AI, VR/AR, IoT, and IRS (Interactive Response Systems) to facilitate teaching and assessment.

The course corresponds to the SDGs SDG4：優質教育（Quality Education）
SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）

Does the course incorporate AI ● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process）
● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）

Note
基礎1: 中學數學
基礎2: 懸鏈線,最速曲線與等時曲線需微積分與工程數學基礎

Instructor	Kuo Ann Liu
Email	mathman@ntut.edu.tw
Last Updated	2026-02-24 10:53:32
Course Objective	數學的發展多是為了解決自然科學上的問題，其研究動機結果大都有蛛絲馬跡脈絡追尋。千百年來累積了相當多有益且有意義的故事，追尋前人的足跡，可欣賞數學之美，更可體察定理背後的真實用意。本課程收集很多數理發展史上具代表性的例子，借古鑑今，能體會所學的來龍去脈，更感覺數學的踏實。 Most theorems in Mathematics are used to solve the problem of sciences, so that the traces and their researched motivation is worth pursuing. Many beneficial and significant examples have accumulated throughout the history of the human being. Following the footprints of predecessors, we can appreciate the beauty of the theorems and savor the purports of them. In this course, we will bring some representative examples to show the beginning and subsequent development of theorems, hoping that our students can feel the concreteness of Mathematics.
Course Schedule	第1,2週: 除法原理,餘式定理,因式定理第3,4週: 根與係數關係第5,6週: 數列,級數,階差第7,8週: 遞迴,差分方程,生成函數第9週: 期中考第10,11週: V-E+F=2,正多面體第11,12週: 圓錐截痕(古典與現代錐線) 第13,15: 阿基米德拋物線公式,錐的體積公式第16週: 懸鏈線第17,18: 最速曲線與等時曲線
Evaluation and grading policy	1. 出缺勤 30% 2. 期中考 30% 3. 期末報告(作業) 40%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:No 自編講義
The access to curricular consultation	email, line群組
Expanding teaching and resources	● 參與式創新教學 (Participatory & Innovative Teaching) 強調學生參與與產出，導入翻轉、PBL/專題、設計思考或遊戲化等策略。 Emphasizes student engagement and outcomes by adopting strategies such as Flipped Classroom, PBL (Problem/Project- Based Learning), Design Thinking, or Gamification. ● 數位科技融入 (Digital Technology Integration) 運用生成式AI、VR/AR、IoT、IRS等新興科技輔助教學與評量。 Utilizes emerging technologies such as Generative AI, VR/AR, IoT, and IRS (Interactive Response Systems) to facilitate teaching and assessment.
The course corresponds to the SDGs	SDG4：優質教育（Quality Education） SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）
Does the course incorporate AI	● 使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process） ● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
Note	基礎1: 中學數學基礎2: 懸鏈線,最速曲線與等時曲線需微積分與工程數學基礎