Constructing the Rational Numbers
1:02:05Properties of Q
1:07:38Construction of the Reals
1:15:29The Least Upper Bound Property
1:12:04Complex Numbers
1:07:57Principle of Induction
1:11:58Countable and Uncountable Sets
1:13:16Cantor Diagonalization and Metric Spaces
1:16:27Limit Points
1:12:11The Relationship Between Open and Closed Sets
1:13:02Compact Sets
1:10:54Relationship of Compact Sets to Closed Sets
1:15:55Compactness and the Heine-Borel Theorem
1:09:29Connected Sets, Cantor Sets
1:03:52Convergence of Sequences
59:00Subsequences, Cauchy Sequences
1:08:01Complete Spaces
1:05:23Series
1:11:06Series Convergence Tests, Absolute Convergence
1:02:58Functions - Limits and Continuity
1:04:26Continuous Functions
48:19Uniform Continuity
1:10:22Properties of Q
Benediktsson-Karwa Professor of Mathematics
This lecture delves into the axiomatic properties of the rational numbers (Q) as a field, specifically examining their order structure and limitations in representing certain real numbers. It establishes foundational concepts for formal real analysis.
Real Analysis, Spring 2010, Harvey Mudd College, Professor Francis Su. Playlist, FAQ, writing handout, notes available at: http://analysisyawp.blogspot.com/