課程資訊
課程名稱
幾何學導論
Introduction to Geometry 
開課學期
105-1 
授課對象
理學院  數學系  
授課教師
崔茂培 
課號
MATH5356 
課程識別碼
221 U6580 
班次
 
學分
全/半年
半年 
必/選修
必修 
上課時間
星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) 
上課地點
新202新103 
備註
此課程研究生選修不算學分。
限學士班學生
總人數上限:100人
外系人數限制:30人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1051MATH5356_ 
課程簡介影片
 
核心能力關聯
本課程尚未建立核心能力關連
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

This course is an introduction to the local and global geometry of curves and surfaces􏰑.
In this course, we will apply tools of multivariable and vector calculus to study geometric properties of curves and surfaces in 3-dimensional space. Our course will focus on the concept of "curvature", "surface" and the interplay between them.  

課程目標
We will cover the following three topics
1. Local and global geometry of plane curves
2. Local geometry of surfaces
3. Global geometry of surfaces

If time permits, we will also discuss the application of geometrical ideas in data science or other applied areas.
 
課程要求
1. You are expected to turn in homework regularly.
2. You are expected to understand the proof and the application of the Theorem presented in this class.
3. You are expected to think a lot and discuss the topics with classmates and instructor. 
預期每週課後學習時數
 
Office Hours
另約時間 
參考書目
J. Oprea, Di erential Geometry and its Applications, 2nd edition, 2007.  
指定閱讀
DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces
byTheodore Shifrin 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework 
30% 
 
2. 
Midterm 
30% 
 
3. 
Final exam 
35% 
 
4. 
Class participation 
5% 
 
 
課程進度
週次
日期
單元主題
第1週
9/14,9/16  The Geometry of Curves
ShifrinDiffGeo.pdf is the textbook

HW1 due Friday, September 23
Exercise 1.1 p8 problem 1, 2, 5
 
第2週
9/21,9/23  The Geometry of Curves
9-23-2016.pdf is today's lecture note


 
第3週
9/28,9/30  Fundamental Theorem of Space Curves 
第4週
10/05,10/07  Surfaces 
第5週
10/12,10/14  Curvatures 
第6週
10/19,10/21  Curvatures 
第7週
10/26,10/28  Constant Mean Curvature Surfaces

Sage software download
http://www.sagemath.org/index.html

You can download the program at "download"

Make sure you have java and java jdk

https://www.java.com/zh_TW/download/help/index_installing.xml

http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html
 
第8週
11/02,11/04  Constant Mean Curvature Surfaces
Midterm on November 5
(Saturday 2pm at 101 Astro-Math building)
Topics: Ch1, 2.1, 2,2 and 2.3
 
第9週
11/09,11/11  Geodesics, Metrics and Isometries
 
第10週
11/16,11/18  自主學習週 
第11週
11/23,11/25  Geodesics, Metrics and Isometries 
第12週
11/30,12/02  Holonomy and the Gauss-Bonnet
Theorem 
第13週
12/07,12/09  Holonomy and the Gauss-Bonnet
Theorem 
第14週
12/14,12/16  Holonomy and the Gauss-Bonnet
Theorem 
第15週
12/21,12/23  A Glimpse at Higher Dimensions 
第16週
12/28,12/30  Application! 
第17週
1/04,1/06  Application!

期末考:
星期三 January 11 1:20-3:20 pm