課程資訊
課程名稱
深入基礎數學一
Basic Math from Advanced View Points (I)(Ⅰ) 
開課學期
106-1 
授課對象
理學院  數學系  
授課教師
于靖 
課號
MATH5058 
課程識別碼
221 U8060 
班次
 
學分
2.0 
全/半年
半年 
必/選修
選修 
上課時間
星期一A,B(18:25~20:10) 
上課地點
 
備註
總人數上限:15人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH5058_basicM 
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
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課程概述

This is a demanding course on all aspects of basic mathematics. We deliberately put challenges in front of students. We use Overleaf site to offer a platform for students to interact with each other (using TeX as tool). There will also be reading homeworks. Guiding students to gain more insights into mathematical thinking. 

課程目標
This course aims at developing deeper and through understanding. Contents touch upon : Linear Algebra, Algebra, Calculus, Analysis, Complex Analysis, and Topology. We will discuss those parts from standard textbooks which usually not enough time can be given to cover it in class room lectures. We emphasize also the connections between various basic math courses. Put all these math contents in thought-provoking atmosphere. Will prepare students on stronger backgrounds to support their individual studies later on. 
課程要求
Students should have English comprehension as compared to TOEFL 80. 
預期每週課後學習時數
 
Office Hours
另約時間 
參考書目
1. M. Artin, Algebra.
2. L. V. Ahlfors, Complex Analysis, 1979.
3. H. Cartan, Differential Calculus, 1971.
4. H. Cartan, Elementary Theory of Analytic Function in One and Several Complex Variables. 1963.
5. H. Cartan, Differential Forms.
6. R. Courant & F. John, Introduction to Calculus and Analysis, I, II-1, II-2.
7. N. Jacobson, Basic Algebra I.
8. S. Krantz, Essentials of Topology with applications, 2010.
9. D. Knuth, The Art of Computer Programing, Vol, 1, 2, 3, 4.
10. I. R. Shafarevich & A. O. Remizov, Linear Algebra and Geometry.
11. L. Schwartz. Mathematics for the Physical Sciences, 2013.
12. S. Winitzki, Linear Algebra via Exterior Products, 2010. 
指定閱讀
D. Cox, The Arithmetic-Geometric Mean of Gauss, L'enseignement Mathematique, 30(1984) January (can be obtained from the internet). 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Overleaf worksheets 
50% 
 
2. 
Report of projects  
50% 
 
 
課程進度
週次
日期
單元主題