Will, 

     Your paper on Chinese contributions to algebra is good as far as 
   it goes, although there are a few points where your chronology is not 
   exactly right.  For example, the Suan shu shu in China was compiled 
   long before the time of Euclid (300 BCE) and Apollonius (roughly 250BCE) 
   in Greece.  Also, there actually was a systematic form of writing that 
   was used in the Mycenean period in Greece (up to about 1200 BCE), but 
   it died out and the Greeks only returned to written records around the 
   time of Homer.

   The main issue I have, though, is that the paper just sort of "peters 
   out" right when you are getting to a very interesting topic (and one 
   that is certainly closer to algebra than some of the other topics you 
   do discuss).  I'm referring to your discussion of the Chinese approach 
   to solving simultaneous systems of linear equations, and the similarities 
   between what they did and what we do know with Gaussian elimination, 
   matrices, and so on.  I think this would have been an accessible topic 
   to say more about, since I'm sure you did something similar in high 
   school mathematics at some point.  The idea is that you can add multiples 
   of one equation in a system to another equation repeatedly to eliminate 
   variables and then solve the system.

   Here's a simple example.  Suppose you want to solve for x, y, z in the 
   equations 

                 x +  y +  z = 1
                2x -  y + 5z = 1
                4x + 3y + 2z = 0

   If you subtract 2 times the first equation from the second and four
   times the first equation from the third, you get a new system
   in which only the first equation contains the variable x:

                 x +  y +  z = 4
                    -3y + 3z = -1
                     -y - 2z = -4

   Then you could continue to eliminate the y in either the second
   or third equation using the other of those two equations.  

     The point is that the Chinese were doing almost exactly the 
   same calculations, in a similar format in the "Nine Chapters."
   Katz and Parshall discuss this via an example on pages 87-89, so
   you had a good source to get started with including more details
   on this.  Was there a reason you chose not to?  That would have 
   rounded out your paper and brought you up to the required length
   too.  As it is, you only have about 5 pages.

   Grade:  B