Introduction to Quantitative Methods (Online Math Camp 數量方法入門)

NTU (Fall 2024)

Course Syllabus

TA: Wei-Fu Tseng (曾暐富) (Office hour by email appointment)

Textbook and Recommended Reading:

    1. Rudin, Principles of Mathematical Analysis, 3rd ed., McGraw Hill. (Textbook)
    2. Ok, Real Analysis with Economic Applications, Princeton University Press. (Chapter A)
    3. Tao, Analysis I: Third Edition, Springer. (e-book available through NTU library)
    4. Interactive Real Analysis. (online book)

Online Resources:

1. Su's Lecture Videos

2. Su's Lecture Notes

3. Past TA Session Videos

4. Richard Hammack, Book of Proof, 3rd ed.

Class Topics:

 1. [8/12] Lecture 01: Constructing the Rational Numbers (Lecture note 01)
                 Lecture 02: Properties of Q (Lecture note 02)
                 Exercise 1 and its solution
                 Lecture 1-2 Review (old video 1-2)
                 Quiz 1 and its solution

 2. [8/16] Lecture 03: Construction of R (Lecture note 03)
                 Lecture 04: The Least Upper Bound Property (Lecture note 04)
                 Exercise 2 and its solution (notes, video)
                 Lecture 3-4 Review (old video 3-4)
                 Quiz 2 and its solution
         

 3. [8/19] Lecture 05: Complex Numbers (Lecture note 05)
                 Lecture 06: The Principle of Induction (Lecture note 06)
                 Exercise 3 and its solution (notes, video1, video2)
                 Lecture 5-6 Review (old video 5-6)
                 Quiz 3 and its solution
  

 4. [8/22] Lecture 07: Countable/Uncountable Set (Lecture note 07)  [At Social Sciences 101]
                 Lecture 08: Cantor Diagonalization, Metric Space (Lecture note 08)
                 Exercise 4 and its solution (notes, video)
                 Lecture 7-8 Review (old video 7-8)
                 Quiz 4 and its solution
  

 5. [8/26] Lecture 09: Limit Points (Lecture note 09)
                 Lecture 10: Relationship between Open and Closed Sets (Lecture note 10)
                 Exercise 5 and its solution (notes, video)
                 Lecture 9-10 Review (old video 9-10)
                 Quiz 5 and its solution

 o. [8/30] Exam 1 (solution) [You pass the course if you "pass" this exam!]

 6. [9/ 3 ] Lecture 11: Compact Sets (Lecture note 11)
                 Lecture 12: Relationship between Compact, Closed Sets (Lecture note 12)
                 Exercise 6 and its solution (notes, video)
                 Lecture 11-12 Review (old video 11-12)
                 Quiz 6 and its solution

 7. [9/10] Lecture 13: Compactness, Heine-Borel Theorem (Lecture note 13/Su's Lecture note 12, 13)
                 Lecture 14: Connected Sets, Cantor Sets (Lecture note 14/Su's Lecture note 13, 14)
                 Exercise 7 and its solution (notes, video)
                 Lecture 13-14 Review (old video 13-14)
                 Quiz 7 and its solution

 o.[ 9/17] Holiday (Mid-Autumn Festival)

 8. [9/24] Lecture 15: Convergence of Sequences (Lecture note 15)
                 Lecture 16: Subsequences, Cauchy Sequences (Lecture note 16)
                 Exercise 8 and its solution
                 Lecture 15-16 Review (old video 15-16)
                 Quiz 8 and its solution

 o. [10/1] Review Session

 9. [10/8] Lecture 20: Functions - Limits and Continuity (Lecture note 20)
                 Lecture 21: Continuous Functions (Lecture note 21)  
                 Exercise 9-1 and its solution (Ignore questions on Lecture 19)
                 Exercise 9-2 and its solution (Ignore questions on Lecture 22)
                 Quiz 9 and its solution

10.[10/15] Lecture 22: Uniform Continuity (Lecture note 22)
                 Lecture 23: Discontinuous Functions (Lecture note 23)
                 Exercise 10-1 and its solution (Ignore questions on Lecture 21)
                 Exercise 10-2 and its solution (Ignore questions on Lecture 24)
                 Quiz 10 and its solution  

o.[10/22] Review Session

o.[10/29] Exam 2 (In-person)