Course Information
Course title
 Introduction to Real Analysis 
Semester
 111-2 
Designated for
 COLLEGE OF SOCIAL SCIENCES  GRADUATE INSTITUTE OF ECONOMICS  
Instructor
 JOSEPH TAO-YI WANG 
Curriculum Number
 ECON5200 
Curriculum Identity Number
 323EU0050 
Class
  
Credits
 3.0 
Full/Half
Yr.
 Half 
Required/
Elective
 Elective 
Time
 Monday 2,3,4(9:10~12:10) 
Remarks
 The upper limit of the number of students: 32. 
  
Course introduction video
 
Table of Core Capabilities and Curriculum Planning
 Table of Core Capabilities and Curriculum Planning
Course Syllabus
Please respect the intellectual property rights of others and do not copy any of the course information without permission
Course Description

[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).  

Course Objective
 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!  
Course Requirement
 Students are expected to know Calculus 1-3 prior to taking this course.  
Student Workload (expected study time outside of class per week)
 20 hours 
Office Hours
 Mon. 09:10~10:00 Note: Monday 9:10-10:00am in class or by email appointment 
Designated reading
 Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw Hill. 
References
 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 
Grading
  
No.
Item
%
Explanations for the conditions
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%. 
 
Adjustment methods for students
  
Teaching methods
 Assisted by recording, Assisted by video, Provide students with flexible ways of attending courses
Assignment submission methods
Exam methods
Others
Progress
Week
Date
Topic
Week 1
 2/20  Lecture 01: Constructing the Rational Numbers (Lecture note 01)
Lecture 02: Properties of Q (Lecture note 02) 
Week 2
 3/6  Lecture 03: Construction of R (Lecture note 03)
Lecture 04: The Least Upper Bound Property (Lecture note 04) 
Week 3
 3/13  Lecture 05: Complex Numbers (Lecture note 05)
Lecture 06: The Principle of Induction (Lecture note 06)  
Week 4
 3/20  Lecture 07: Countable/Uncountable Set (Lecture note 07)
Lecture 08: Cantor Diagonalization, Metric Space (Lecture note 08)  
Week 5
 3/27  Lecture 09: Limit Points (Lecture note 09)
Lecture 10: Relationship between Open and Closed Sets (Lecture note 10) 
Week 6
 4/10  Lecture 11: Compact Sets (Lecture note 11)
Lecture 12: Relationship between Compact, Closed Sets (Lecture note 12) 
Week 7
 4/17  Lecture 13: Compactness, Heine-Borel Theorem (Lecture note 12 & 13)
Lecture 14: Connected Sets, Cantor Sets (Lecture note 13, Lecture note 14) 
Week 8
 4/24  Lecture 15: Convergence of Sequences (Lecture note 15)
Lecture 16: Subsequences, Cauchy Sequences (Lecture note 16 & 17) 
Week 9
 5/1  Lecture 17: Complete Spaces (Lecture note 18)
Lecture 18: Series (Lecture note 19) 
Week 10
 5/8  Lecture 19: Series Convergence Tests (Lecture note 20)
Lecture 20: Functions - Limits and Continuity (Lecture note 21) 
Week 11
 5/15  Lecture 21: Continuous Functions (Lecture note 22)
Lecture 22: Uniform Continuity (Lecture note 23) 
Week 12
 5/22  Lecture 23: Discontinuous Functions (Lecture note 24)
Lecture 24: The Derivative, Mean Value Theorem (Lecture note 25) 
Week 13
 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) 
Week 14
 6/5  Final Exam (In-person)