課程資訊

Introduction to Real Analysis

111-2

ECON5200

323EU0050

3.0

[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).

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!

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

20 hours
Office Hours

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

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

(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%.

 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)