Math 403H     Fall 2017   Schedule

Lec. Date Chapter Topic
  1   8/21       2     Countable and uncountable sets.  
  2   8/23       2     Cantor set and Cantor function.  
  3   8/25     1, 2   Monotone functions. More on Cantor function.  
  4   8/28       3     Metric spaces.  
  5   8/30       3     More on metrics. Bounded sets.  
  6   9/1       3     Normed vector spaces.  
  -   9/4       -     Labor Day - No Classes  
  7   9/6       3     Limits in metric spaces.  
  8   9/8       3     Cauchy sequences. "Coordinatewise" convergence.  
  9   9/11       4     Open sets.  
  10   9/13       4     Closed sets.  
  11   9/15       4     Interior and closure. Dense sets.  
  12   9/18     4, 5     Relative metric.  Continuous functions.  
  13   9/20       5     Continuous functions.  
  14   9/22       5     Homeomorphisms.
  15   9/25       5     Isometries.  Distance to a set.  
  16   9/27       5     Continuous real-valued functions.  
  17   9/29         Problems   pdf  
  18   10/2         Exam 1  covering Chapters 2-5.  Study guide  pdf  
  19   10/4       6     Connectedness.  
  20   10/6       6     Connectedness.
  21   10/9    
    7  
  Review: Continuous functions on [a,b].
  Boundedness vs total boundedness.  
  22   10/11       7     Total boundedness.  
  23   10/13       7     Completeness.
  24   10/16       7     Nested closed sets.   Contractions.  
  25   10/18       7     Completions.  
  26   10/20       7, 8     More on completions.  Compactness.
  27   10/23       8     Continuous functions on compact metric spaces.  
  28   10/25       8     Compactness via open covers.  
  29   10/27       8     Uniform continuity.
  30   10/30       8     Properties of uniformly continuous functions.  
  31   11/1         Uniform continuity — problems   pdf    
  32   11/3         Chapter 8 — problems   pdf
  33   11/6         Exam 2  covering Chapters 6-8.  Study guide  pdf  
  34   11/8       9     Exam 2 discussion.   Open dense sets.  
  35   11/10       9     Baire Category Theorem.
  36   11/13      10     Pointwise and uniform convergence.  
  37   11/15      10     Consequences of uniform convergence.  
  38   11/17      10     Uniform convergence of derivatives.
  Spaces of bounded and continuous functions.
11/19-25   Thanksgiving Holiday - no classes
  39   11/27     10     Weierstrass M-test. Power series.  
  40   11/29     11     Equicontinuity.  
  41   12/1     11     The Arzela-Ascoli Theorem.
  42   12/4     12     The Stone-Weierstrass Theorem.  
  43   12/6     9,11     Discontinuities.  
  44   12/8         Chapters 9,10,11 — problems   pdf

  The Final Exam will be on Monday, Dec. 11, 4:40-6:30 p.m. in 107 Willard.