Here is a list of topics and a dynamic listing of what was actually planned and covered in the lecture. Parentheses indicate a topic was not covered or not covered in much detail.

   Date    Chapter.Section/Topics   or   Page/Problems

M   Jan 12  Lecture 1  Introduction: (Alexandrov's theorem)
                                     Surface definitions
                                     Definitions A and B
  
W    14     Lecture 2  (calculus; inverse function theorem)
                       meaning of Definitions A and B
                       (overlapping parameterizations theorem)
                       Statement of the pillbox theorem
                       (Properties of surfaces)

M    19     Holiday (MLK)

W    21     Lecture 3  project suggestions 
                       -higher order reflection/extension
                       -calculus: inverse function thm, Taylor's thm
                       -Banach space calculus (Hörmander, Analysis of Linear Partial Differential Operators Vol. 1) 
                           -inverse function theorem
                           -higher order derivatives and multilinear maps
                           -extension theorems
                           -Whitney extension theorem
                       -improve results in my notes
                       -C^k embedded surface in R^n (Osserman, Survey of Minimal Surfaces)
                       start of proof of pillbox theorem
M   26      Lecture 4  proof of the pillbox thm (snow day---postponed)
W   28      Lecture 4  proof of the pillbox thm
M  Feb 2    Lecture 5  first order geometry in the tangent plane
W    4      Lecture 6  first order geometry in the parameter tangent plane
M    9      Lecture 7  the elliptical image and the unit circle
W   11      Lecture 8  angles
                       Quiz 1   
M   16



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W  Apr 1    Lecture 21 


	    
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M  27       Last class meeting

	    

F  May 1    (scheduled final exam time 11:20 AM - 2:10 PM)