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 15: Convergence of Sequences (MATH 131)
This session formally defines the convergence of sequences in metric spaces using epsilon-delta arguments, exploring properties like uniqueness of limits and boundedness of convergent sequences.
Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Playlist, FAQ, writing handout, notes available at: http://analysisyawp.blogspot.com/
Lecture 14: Connected Sets, Cantor Sets (MATH 131)
Next · Lecture 16Lecture 16: Subsequences, Cauchy Sequences (MATH 131)