<p>Another interesting way to compare the strength of the math departments at various universities besides looking at the quality of the research done at the graduate level and the course offerings provided is to see which programs enroll the best students. The Putnam is an annual mathematics competition in which teams of 3 from universities all over America compete on a rigorous exam. It goes to follow that consistent excellence in the Putnam requires that a university draw the strongest students year in and year out. Most math departments are small enough where even looking at the 3 best math students can be reflective of the undergraduate caliber of the math program at the university.</p>
<p>Here are the top performing universities historically:</p>
<p>Most Top 5 Finishes Since 1990
1. Harvard: 20
2. MIT: 15
3. Princeton: 13
4. Duke: 12
5. University of Waterloo: 9
6. Caltech: 8
7. Stanford: 6
8. Toronto: 4
9. Cornell, Berkeley, Wash U and UC Berkeley: 3
10. Michigan, Yale, Harvey Mudd and Chicago: 2</p>
<p>The actual winner of the Putnam has been the Harvard team boasting 27 victories followed in the far distance by Caltech and MIT with 10 and 6 wins a piece.</p>
<p>^The Putnam exam has nothing to do with the strength of math department. I sat at the training sessions for a while (when I was at WashU) and none of the stuff is related to what you learn in class. In fact, you don’t need to have anything beyond Calclus I/II to compete. The training was all about creative tricks and practicing problems from the past. What’s good about WashU’s camp was they got an incredibly talent and funny professor that’s very good at solving these kind of problems AND commiting to be the coach; whereas in many schools, the camp was just a student-run camp with no faculty involved. Part of it is that many math professors can’t solve them either. Your brain has to be wired in some ways to "see’ the solution. That’s where the difference lies. The professor at WashU was not even from the math department but in the physics department and he’s the leading world expert in quantum physics and applied math. Also, the students don’t have to be math majors either. Like I said, you don’t need much math to compete, though many members are already taking graduate level courses.</p>
<p>When I was at WashU, it was the last time they were in the top-5. WashU hasn’t done as well in the last decade even though it’s much tougher to get into WashU these days. The prof is in his late 60s now and I suspect he might have retired from coaching the training sessions in recent years. Having a coach that can teach you all the tricks you need makes a world of difference.</p>
<p>^also, schools like Harvard/MIT will always be there even if their coaches aren’t the best. The sheer talents may just be enough because they get former IMO gold medalists matriculating there and Putnam is very much like the college version of IMO. For other schools, the success will definitely rely on whether they have great coaches from the faulty; that’s why you see some schools that were consistent for a certain period and then just kinda disappear and some schools that didn’t do well before and all of a sudden have become major players in recent years.</p>
<p>The best Putnam performers are usually the same people who did well in high school math competitions, ie. they were already good before they entered undergrad. They learned the skills necessary to do well at Putnam in years of high school competition, and it’s definitely possible to do well on Putnam without learning advanced college mathematics topics (depending on the subject distribution that year). Putnam standings are very loose indicators of the strength of math programs, though certainly they must be attracting the best math students for some reason.</p>
<p>The current professors leading the WashU sessions are quite knowledgeable, but I haven’t found them to have the most engaging teaching style (read: they’re kinda boring to listen to).</p>