Real Analysis, Lecture 1: Constructing the Rational Numbers
1:02:05Real Analysis, Lecture 2: Properties of Q
1:07:38Real Analysis, Lecture 3: Construction of the Reals
1:15:29Real Analysis, Lecture 4: The Least Upper Bound Property
1:12:04Real Analysis, Lecture 5: Complex Numbers
1:07:57Real Analysis, Lecture 6: Principle of Induction
1:11:58Real Analysis, Lecture 7: Countable and Uncountable Sets
1:13:16Real Analysis, Lecture 8: Cantor Diagonalization and Metric Spaces
1:16:27Lecture 9: Limit Points (MATH 131)
1:12:11Lecture 10: The Relationship Between Open and Closed Sets (MATH 131)
1:13:02Lecture 11: Compact Sets (MATH 131)
1:10:54Lecture 12: Relationship of Compact Sets to Closed Sets (MATH 131)
1:15:55Lecture 13: Compactness and the Heine-Borel Theorem (MATH 131)
1:09:29Lecture 14: Connected Sets, Cantor Sets (MATH 131)
1:03:52Lecture 15: Convergence of Sequences (MATH 131)
59:00Lecture 16: Subsequences, Cauchy Sequences (MATH 131)
1:08:01Lecture 17: Complete Spaces (MATH 131)
1:05:23Lecture 18: Series (MATH 131)
1:11:06Lecture 19: Series Convergence Tests, Absolute Convergence (MATH 131)
1:02:58Lecture 20: Functions - Limits and Continuity (MATH 131)
1:04:26Lecture 21: Continuous Functions (MATH 131)
48:19Lecture 22: Uniform Continuity (MATH 131)
1:10:22Lecture 17: Complete Spaces (MATH 131)
This session defines complete metric spaces as those where every Cauchy sequence converges within the space, illustrating the importance of completeness for foundational theorems like the Contraction Mapping Principle.
Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Playlist, FAQ, writing handout, notes available at: http://analysisyawp.blogspot.com/
Lecture 16: Subsequences, Cauchy Sequences (MATH 131)
Next · Lecture 18Lecture 18: Series (MATH 131)
Seminar notes & discussion
No public seminar notes on this lecture yet.