課程大綱

課程資訊

課程名稱

分析導論
Introduction to Real Analysis

開課學期

111-2

授課對象

社會科學院經濟學系

授課教師

王道一

課號

ECON5200

課程識別碼

323EU0050

班次

學分

3.0

全/半年

半年

必/選修

選修

上課時間

星期一2,3,4(9:10~12:10)

上課地點

社科研609

備註

本課程以英語授課。英文考試。
總人數上限：32人

課程簡介影片

核心能力關聯

核心能力與課程規劃關聯圖

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

[Please visit the course website for more details: https://homepage.ntu.edu.tw/~josephw/mathcamp_23S.htm ]
This is a flipped online course to help you go through the introduction of (undergraduate) real analysis, focusing on the first five chapter of Rudin’s Principles of Mathematical Analysis. The purpose is to introduce economics students to point-set topology which forms the foundation of Advanced Calculus, so they can study abstract mathematics required for graduate studies in economics. Note this course cannot substitute “Introduction to Real Analysis I” (5 units).

課程目標

Students are expected to:
1. Watch Lecture Videos Online: Such as 高等微積分@NTU OCW or Francis Su at Harvey Mudd College: http://analysisyawp.blogspot.com/2013/01/lectures.html
2. Participate In-Class: Take weekly quizzes of 50 minutes each, which solutions are discussed immediately. Come and ask questions in office hours before the quiz!

課程要求

Students are expected to know Calculus 1-3 prior to taking this course.

預期每週課後學習時數

20 hours

Office Hours

每週一 09:10~10:00 備註： Monday 9:10-10:00am in class or by email appointment

指定閱讀

Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw Hill.

參考書目

Tao, Analysis I: Third Edition, Springer. (e-book available through NTU library: https://link.springer.com/book/10.1007/978-981-10-1789-6)
Protter and Morrey, A First Course in Real Analysis, 2nd ed., Springer.
Interactive Real Analysis: https://mathcs.org/analysis/reals/index.html

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Weekly Quizzes	50%	5% each for 10 highest. When a quiz is taken online, it counts for only 1%; the remaining 4% will be replaced by the final exam, so if all quizzes are taken online, final exam will count as 90%.
2.	Final Exam	50%	6/5 (during finals week). When a quiz is taken online, it counts for only 1%; the remaining 4% will be replaced by the final exam, so if all quizzes are taken online, final exam will count as 90%.

針對學生困難提供學生調整方式

上課形式	以錄音輔助, 以錄影輔助, 提供學生彈性出席課程方式
作業繳交方式
考試形式
其他

課程進度

週次	日期	單元主題
第1週	2/20	Lecture 01: Constructing the Rational Numbers (Lecture note 01) Lecture 02: Properties of Q (Lecture note 02)
第2週	3/6	Lecture 03: Construction of R (Lecture note 03) Lecture 04: The Least Upper Bound Property (Lecture note 04)
第3週	3/13	Lecture 05: Complex Numbers (Lecture note 05) Lecture 06: The Principle of Induction (Lecture note 06)
第4週	3/20	Lecture 07: Countable/Uncountable Set (Lecture note 07) Lecture 08: Cantor Diagonalization, Metric Space (Lecture note 08)
第5週	3/27	Lecture 09: Limit Points (Lecture note 09) Lecture 10: Relationship between Open and Closed Sets (Lecture note 10)
第6週	4/10	Lecture 11: Compact Sets (Lecture note 11) Lecture 12: Relationship between Compact, Closed Sets (Lecture note 12)
第7週	4/17	Lecture 13: Compactness, Heine-Borel Theorem (Lecture note 12 & 13) Lecture 14: Connected Sets, Cantor Sets (Lecture note 13, Lecture note 14)
第8週	4/24	Lecture 15: Convergence of Sequences (Lecture note 15) Lecture 16: Subsequences, Cauchy Sequences (Lecture note 16 & 17)
第9週	5/1	Lecture 17: Complete Spaces (Lecture note 18) Lecture 18: Series (Lecture note 19)
第10週	5/8	Lecture 19: Series Convergence Tests (Lecture note 20) Lecture 20: Functions - Limits and Continuity (Lecture note 21)
第11週	5/15	Lecture 21: Continuous Functions (Lecture note 22) Lecture 22: Uniform Continuity (Lecture note 23)
第12週	5/22	Lecture 23: Discontinuous Functions (Lecture note 24) Lecture 24: The Derivative, Mean Value Theorem (Lecture note 25)
第13週	5/29	Lecture 25: Taylor's Theorem (Lecture note 25) Lecture 26: Sequences of Functions (In-person) (Lecture note 26) Lecture 27: Brower’s Fixed-Point Theorem (In-person) (Lecture note 27)
第14週	6/5	Final Exam (In-person)