Introduction to Real Analysis Saturday, August 31, 2024

This semester (Fall 2024), I am taking (introductory) real analysis at UNC (Math 653). My sources for my material (in general) are (in no particular order):

1. Andrew Browder’s Mathematical Analysis: An Introduction
2. Walter Rudin’s Principles of Mathematical Analysis
3. Stephen Abbott’s Understanding Analysis
4. Professor Mark William’s Math 653 (UNC) lectures
5. Professor Robert E. Greene’s Math 131ABH (UCLA) lectures

Notes

1. Metric Spaces and Sequences I (Overview)
   Aug 31, 2024

   A guided tour and introduction to metric spaces in real analysis.
2. Metric Spaces & Sequences II (Completeness)
   Sep 11, 2024

   Are Cauchy sequences convergent? Yes! But also no.
3. Topology & Continuity I (Open sets)
   Sep 13, 2024

   What defines the shape of a metric space?
4. Topology & Continuity II (Continuous functions)
   Sep 15, 2024

   A study of pen-lifting, or the lack thereof.