Su老师讲的实分析视频，爆好好哦！逻辑、概念、背景、思路等讲得异常清晰形象。Su老师已经开始研究博弈论和社会选择，看来他要踏入经济学领域了。他的实分析课程分两部分，用RUDIN的教材。

教授：Professor Francis Su

Goals of the course:

• Learn the content of real analysis.
• Learn to read and write rigorous proofs.
• Learn good mathematical writing skills and style.
  

Required Text: Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill. We will cover Chapters 1 through 5.


Lecture 1: Constructing the rational numbers
Lecture 2: Properties of Q
Lecture 3: Construction of R
Lecture 4: The Least Upper Bound Property
Lecture 5: Complex Numbers
Lecture 6: The Principle of Induction
Lecture 7: Countable and Uncountable Sets
Lecture 8: Cantor Diagonalization, Metric Spaces
Lecture 9: Limit Points
Lecture 10: Relationship b/t open and closed sets
Lecture 11: Compact Sets
Lecture 12: Relationship b/t compact, closed sets
Lecture 13: Compactness, Heine-Borel Theorem
Lecture 14: Connected Sets, Cantor Sets
Lecture 15: Convergence of Sequences
Lecture 16: Subsequences, Cauchy Sequences
Lecture 17: Complete Spaces
Lecture 18: Series
Lecture 19: Series Convergence Tests
Lecture 20: Functions - Limits and Continuity
Lecture 21: Continuous Functions
Lecture 22: Uniform Continuity
Lecture 23: Discontinuous Functions
Lecture 24: The Derivative, Mean Value Theorem
Lecture 25: Taylor's Theorem
Lecture 26: Ordinal Numbers, Transfinite Induction

http://www.math.hmc.edu/~su/math131/

RUDIN原理的后半本书：

http://www.math.hmc.edu/~su/math132/