How do they compare to those in the U.S.?
Pure math in particular.
I know U Toronto is strong, McGill as well I believe. I don't think any of them are quite on par with the very top U.S. schools but to my knowledge there are definitely a few strong departments.
So U Waterloo is stronger than U Toronto in your estimation?
I've never heard of that before. In terms of math grad school, I've only seen UToronto considered top 50 in the world consistently.
UWaterloo is excellent for pure math, it's better than UT.
Look at the Putnam scores
2000 Duke MIT Harvard Caltech Toronto
2001 Harvard MIT Duke UC Berkeley Stanford
2002 Harvard Princeton Duke UC Berkeley Stanford
2003 MIT Harvard Duke Caltech Harvey Mudd
2004 MIT Princeton Duke Waterloo Caltech
2005 Harvard Princeton Duke MIT Waterloo
2006 Princeton Harvard MIT Toronto Chicago
2007 Harvard Princeton MIT Stanford Duke
2008 Harvard Princeton MIT Stanford Caltech
2009 MIT Harvard Caltech Stanford Princeton
2010 Caltech MIT Harvard UC Berkeley Waterloo
Waterloo has 3, UT has 2 but the last time they did well was 2006. UW had a strong performance in 2010 and I think they'll do better because they recruited some talented people. But the US is unfair anyway since they draft from IMO. MIT views UW as it's equal in Canada, plenty of MIT researchers are at UW. If you want to go to MIT then definitely go to UW.
Of course, Putnam performance isn't the best measure of strength in math (unless you really want to claim Duke has a better math program than UC Berkeley) and especially for PhD programs. It might be a reasonable measure of undergraduate student quality. That said, UW definitely looks like a strong program.
In Toronto, there is Fields Institute associated with UofT. It constantly has thematic programs and seminars. People all over the world come there to talk.
For example, thematic program on Operator Algebra is ongoing in Fields.In Fall 2012 it will be Forcing. And in Winter/Spring 2012 it will be Galois Representations.
It also depends in what particular field of pure math your are interested. Toronto is probably the best place for set theoretic topology. The groups by subject are usually across the Universities (York,UofT, Fields) and work together. So it does not really matter which university you will enroll, the most important is the subject and research group that associated with it.
I know that all major math competition in high school is funded by waterloo and they have very good scholarship for math students there
and of course they have always been known for computer math and engineering school
toronto on the other hand, they are generally good on most of the majors
so it won't hurt to do any of them but if you are going back to U,S for jobs i recommend toronto
if you are thinking of getting a job in finance, engineering, computing or any other industries waterloo would be my answer
I know Bill Gates hires the majority of his students from Waterloo out of any university in North America and many of the CS, math and engineering students end up working at Microsoft in software development or at Microsoft Research. Google and RIM (which is doing pretty bad right now) and other technology companies have their main Canadian offices in Waterloo. Most major finance companies are in Toronto.
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