This is surely controversial enough to be discussed. Recently, we received the results from the Waterloo math competitions. Of course, participation is what matters but we would have liked to see our school's name a bit higher in the rankings. Being a relatively small school, we can use the excuse that it easier to find 3 math wizards in a school with 200 grade 9 students than in a school with 30 grade 9 students.From David Dymov, May 28, 1997:
The topic that I propose for discussion is "How much does the size of a school influence its rank in (say) the Pascal contest?"
I did a little research on my own by "playing" with order statistics in normally generated samples and I found out that increasing the size of our school 3 times would have improved our Cayley score from 309 to about 340. Increasing the size 7 times would have brought it only up to 350. It seems to matter if the school is really small but after a certain size it does not seem to matter as much as I would have expected it.
Has anybody given this topic a thought?
I think it doesn't matter how many students there are. What is more important is the quality of the teaching staff.From Dorian Smith, Arizona State University, November 14, 1997:
Are there any competitions above the high school level?(From Philip Spencer, University of Toronto) Yes, there is the William Lowell Putnam Mathematics Competition. You can find more information at http://www.maa.org/past/putnam.html