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課程名稱 |
幾何學導論
Introduction to Geometry |
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開課學期 |
105-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
崔茂培 |
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課號 |
MATH5356 |
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課程識別碼 |
221 U6580 |
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班次 |
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學分 |
4 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) |
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上課地點 |
新202新103 |
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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 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1051MATH5356_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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. |
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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.
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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. |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
DIFFERENTIAL GEOMETRY: A First Course in Curves and Surfaces
byTheodore Shifrin |
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參考書目 |
J. Oprea, Di erential Geometry and its Applications, 2nd edition, 2007. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
30% |
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2. |
Midterm |
30% |
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3. |
Final exam |
35% |
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4. |
Class participation |
5% |
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週次 |
日期 |
單元主題 |
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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
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第2週 |
9/21,9/23 |
The Geometry of Curves
9-23-2016.pdf is today's lecture note
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第3週 |
9/28,9/30 |
Fundamental Theorem of Space Curves |
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第4週 |
10/05,10/07 |
Surfaces |
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第5週 |
10/12,10/14 |
Curvatures |
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第6週 |
10/19,10/21 |
Curvatures |
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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
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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
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第9週 |
11/09,11/11 |
Geodesics, Metrics and Isometries
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第10週 |
11/16,11/18 |
自主學習週 |
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第11週 |
11/23,11/25 |
Geodesics, Metrics and Isometries |
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第12週 |
11/30,12/02 |
Holonomy and the Gauss-Bonnet
Theorem |
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第13週 |
12/07,12/09 |
Holonomy and the Gauss-Bonnet
Theorem |
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第14週 |
12/14,12/16 |
Holonomy and the Gauss-Bonnet
Theorem |
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第15週 |
12/21,12/23 |
A Glimpse at Higher Dimensions |
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第16週 |
12/28,12/30 |
Application! |
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第17週 |
1/04,1/06 |
Application!
期末考:
星期三 January 11 1:20-3:20 pm |
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