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課程名稱 |
幾何學導論
Introduction to Geometry |
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開課學期 |
108-1 |
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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 |
4.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
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上課地點 |
普503普503 |
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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：70人
外系人數限制：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081MATH5356_ |
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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 |
Applying basic calculus and linear algebra to study the surface inside 3 dimensional space gives fruitful results and forms the basis of modern differential geometry, which, in turns, provide the framework of general relativity and quantum field theory.
Our course would concentrate on the concept of "curvature", "surface" and the interplay between them. We shall conduct a course from the local behavior of a surface to the global property of it. |
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課程目標 |
1. Curvature of Curves.
2. Curvature of Surfaces.
3. Internal Curvature of Surfaces.
4. Curvature and Global Property of Surfaces |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Elementary Differential Geometry ,Second Edition
by Andrew Pressley
It is available from Springer link (it can be downloaded from NTU IP)
https://link.springer.com/book/10.1007%2F978-1-84882-891-9
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參考書目 |
J. Oprea, Differential 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. |
Midterm |
35% |
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2. |
Final |
35% |
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3. |
Homework |
20% |
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4. |
Quiz |
10% |
Average from best three quizzes |
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週次 |
日期 |
單元主題 |
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第1週 |
9/11,9/13 |
9/11 Ch 1 . Curves in the plane and in space
Software to graph parametric curve
https://www.desmos.com/calculator/ksjcpazwa9
Software to draw level curve
https://www.desmos.com/calculator/scxe341uyn
13日 中秋節(放假日)
Elementary Differential Geometry ,Second Edition
by Andrew Pressley
It is available from Springer link (it can be downloaded from NTU IP)
https://link.springer.com/book/10.1007%2F978-1-84882-891-9 |
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第2週 |
9/18,9/20 |
9/18 More on Ch 1 . Curves in the plane and in space
& 2.1 Curvature
9/19 2.2 Plane curves 2.3 Space curves
I updated the lecture to fix some typos in the note.
HW1-1.pdf and HW1-2.pdf are the HW problems from the book. |
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第3週 |
9/25,9/27 |
9/25 2.3 Space curves
9/27 2.3 Space curves 4.2 Smooth surfaces (Regular surfaces)
You can use
https://www.geogebra.org/3d
to graph the parametric surface. Please see the lecture note on Sep 27 for more detail. |
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第4週 |
10/02,10/04, 10/05 |
10/2 4.1 What is a surface? 4.2 Smooth surfaces
10/4 4.1 What is a surface? 4.2 Smooth surfaces 4.4 Tangents and derivatives
10/5 Make up class for Oct 11
4.4 Tangents and derivatives
4.3 Smooth maps
4.5 Normals and orientability
6.1 First fundamental form
video of Mobius band at https://youtu.be/gibTQyDmQPQ
If you are interested learning more about topology, you can take a look at this book "Introduction to Topological Manifolds by John M. Lee."
https://link.springer.com/book/10.1007%2F978-1-4419-7940-7 You can download this book form NTU IP.
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第5週 |
10/09,10/11 |
10/9 6.1 Lengths of curves on surfaces
6.2 Isometries of surfaces
11日 國慶紀念日調整放假 |
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第6週 |
10/16,10/18 |
0/16 6.3 Conformal mappings of surfaces
6.4 Equiareal maps and a theorem of Archimedes
10/18 7.1 The second fundamental form 7.2 The Gauss and Weingarten maps
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第7週 |
10/23,10/25 |
10/23
Quiz on Oct. 23 TA session
7.2 The Gauss and Weingarten maps
7.3 Normal and geodesic curvatures
10/25
7.3 Normal and geodesic curvatures
8.1 Gaussian and mean curvatures
8.2 Principal curvatures of a surface |
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第8週 |
10/30,11/01 |
10/30 8.2 Principal curvatures of a surface 7.4 Parallel transport and covariant derivative
9.1 Definition and basic properties
11/1 TA session |
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第9週 |
11/06,11/08 |
11/06 9.2 Geodesic equations 9.5 Geodesic coordinates
11/08 First Midterm |
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第10週 |
11/13,11/15 |
Midterm Break (No class)
15日 本校校慶(停課一天) |
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第11週 |
11/20,11/22 |
11/20 10.1 The Gauss and Codazzi–Mainardi equations 10.2 Gauss’ remarkable theorem
11/22 13.1 Gauss–Bonnet for simple closed curves 13.2 Gauss–Bonnet for curvilinear polygons
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第12週 |
11/27,11/29 |
11/27 13.3 Integration on compact surfaces 13.4 Gauss–Bonnet for compact surfaces
11/29 13.6 Holonomy and Gaussian curvature 13.7 Singularities of vector fields |
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第13週 |
12/04,12/06 |
12/04,12/06 Abstract manifolds, Higher dimensional geometry |
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第14週 |
12/11,12/13 |
12/11,12/13 Higher dimensional geometry |
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第15週 |
12/18,12/20 |
12/25 12/27
Topics on discrete surface |
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第16週 |
12/25,12/27 |
12/25 12/27
Topics on discrete surface |
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第17週 |
1/01,1/03 |
1日 開國紀念日(放假日)
1/03 Topics on discrete surface |
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第18週 |
1/6-1/10 |
Final exam on Jan 8th (Wednesday) 10:20 a.m. - 1 pm |
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