Nicole McDonald -- The Max Flow-Min Cut Theorem

  Your presentation on the max flow-min cut theorem was excellent -- clear, 
  detailed, well structured.  I think it was actually one of the best of
  all of the presentations from the projects in our class.  

  The paper follows the presentation pretty closely, which is OK.  However,
  I think it shows the effects of your being somewhat rushed for time to complete
  the project.  Around page 5 you stopped footnoting sources.  You really need 
  to do that in work like this, especially when you use a graphic from one of 
  them.  Copying and pasting an image is equivalent to using a direct quotation, 
  so those MUST be footnoted in the formal paper.  Ideally you would do that
  in the presentation slides too, but I wasn't so picky about that.  I'm not 
  going to treat this as a violation of academic integrity because I do not 
  think you're trying to represent those images as your own work.  But you need 
  to be more careful about this.

  I would also have liked to see some more details about the proofs of 
  Lemma I, Corollary II, and Lemma III on page 9.  It was perfectly OK to
  do what you did in the presentation.  But the paper is the place to 
  say more about why those results are true.  

  Some specific comments

  1)  Page 3 -- Usually mathematicians would reserve the word "symmetric" for
      a relation that is symmetric as a whole (in your terms, EVERY arc has
      a corresponding arc in the opposite direction, not just one as in your
      example).

  2)  Page 7 -- It would have been good to say exactly which arcs are in a minimum
      cut here -- it's the arcs (7,t), (3,6) and (s,2).  Recall that you have
      stated a certain definition of what a cut is -- a collection C of arcs
      in the network such that every path from s to t includes one of the 
      edges in C.  The diagrams you are using to illustrate the example
      might be based on a different, equivalent way to think about the definition.

  3)  Page 13 -- I'm sorry to see that the example you did in the presentation
      (or one like it) where you use the Ford-Fulkerson algorithm to find a
      maximum flow did not make it into the paper.  

   Final Project Grade Computation 
 
   Bibliography:   9/10  (late penalty)

   Paper:         49/60

   Presentation:  30/30

   Total:        88/100