課程資訊
課程名稱
分析一
Analysis(Honor Program)(Ⅰ) 
開課學期
108-1 
授課對象
理學院  數學系  
授課教師
沈俊嚴 
課號
MATH5232 
課程識別碼
221 U6540 
班次
 
學分
5.0 
全/半年
半年 
必/選修
選修 
上課時間
星期二2,3,4(9:10~12:10)星期四3,4(10:20~12:10) 
上課地點
天數101天數302 
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:30人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1081MATH5232_ 
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

Mathematical analysis is a fundamental course that aims to provide us advanced theorems and prepare us writing rigorous mathematical theorems. The main contents of this course in the first semester will cover most of the materials in the textbook. The contents in the second semester will cover some selected advanced analysis topics such as Lebesgue theory, Fourier analysis, Oscillatory integrals and their connections and applications to combinatorics and number theory. In particular, you will see explicitly how the Green's theorem that you learn in Calculus courses and contour integrals in complex analysis courses are used while establishing the connections from Analysis to combinatorics and number theory.  

課程目標
Develop abstract and logical thinking
Write rigorous mathematical statements and proofs 
課程要求
待補 
預期每週課後學習時數
 
Office Hours
 
參考書目
Real Analysis by E. Stein and R. Shakarchi
Mathematical Analysis by T. Apostol  
指定閱讀
Real Mathematical Analysis by Charles C. Pugh (It can be downloaded with NTU IP) 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Midterm exam  
25% 
 
2. 
Final exam  
30% 
 
3. 
Homework  
45% 
Homework will be assigned every week 
 
課程進度
週次
日期
單元主題