MODERN ANALYSIS (FALL 2024) - CLASS NOTES

 Date      NOTES

Aug 20     Some history     Some more history       

Aug 22     Real number system    

Aug 27     Cauchy-Schwarz etc    

Aug 29     Induction and Cardinality       

Sep 3      Topology Definitions    

Sep 5      Hausdorff Axioms                                     

Sep 10     Compactness    

Sep 12     Homework Hints    

Sep 17     Sequential Convergence    

Sep 19     Subsequences / Cauchy Property                                      

Sep 24     Special sequences    

Sep 26     No notes    

Oct 1      Convergence Tests  

Oct 3      More Convergence Tests     

Oct 8      No notes    

Oct 10     No notes    

Oct 15     Review    

Oct 17     No Notes       

Oct 22     Conditional Convergence                                     

Oct 24     Continuity    

Oct 29     Uniform continuity    

Oct 31     Differentiation    

Nov 5        no class                                

Nov 7      Cauchy's MVT, Oscillation    

Nov 12     Multivariate Differentiation    

Nov 14         

Nov 19          

Nov 21         

Nov 26         

Nov 28      no class         

Dec 3          

Dec 5

Dec 10