Schools What sort of schools should I be looking at?

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The discussion centers around a student in Canada completing their third year in a Math and Physics program, expressing anxiety about academic performance and graduate school prospects. Despite maintaining a solid GPA of 3.7 and receiving a renewable entrance scholarship, the student feels inadequate compared to peers and struggles with exams. They have participated in research experiences, including a summer program with a professor, and are considering a fifth year to enhance their research credentials and obtain stronger reference letters. The student seeks advice on potential graduate schools to apply to, factoring in their GPA, research experience, and the importance of the reputation of their undergraduate institution. Participants in the discussion affirm that a 3.7 GPA is commendable, especially from a top university, and emphasize that strong references and GRE scores can significantly impact graduate school applications.
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Hello PF. I am finishing my third year of a Math and Physics program in Canada. I am getting very anxious about my marks and grad school, and what sorts of schools I should look into applying to / expect to actually get into. I'm asking partially because my friends always seem to be doing significantly better than me, so I'm really doubting whether I should even stay in the field. I really do enjoy mathematical physics and I want to study it (for a living if things work out), but I'm worried I'm just not good enough to get anywhere. I feel like no matter how hard I try, I am simply horrible at tests/exams and do poorly on them. So:

My GPA has been a consistent 3.7 throughout the years. I've been receiving a renewable entrance scholarship each year (if that is relevant). I worked with a professor in a math REU-type thing last summer (but we didn't do any serious research). This year I will be working for a physics prof and it will probably be more serious (math is hard to do anything in really as an undergrad).

I'm considering taking a 5th year, to get more research experience/ better reference letters (comments on whether this is a good idea would also be appreciated).

So the question is, am I doomed? What sort of schools might I expect to get into (assuming I get a good GRE score -- probably in math actually, in which case I'd be applying for mathematical physics) with this kind of GPA and three consecutive summers of research (with possibly research courses in the next two school years). Which schools are longshots? Which ones are impossible?
 
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I guess it depends on how good your undergraduate university is considered. You haven't really said anything about that. I'd suspect that getting a 3.7 at a top university and getting positive references from professors well known in your field.

Also Isn't 3.7 very good? I'm from Australia so our grading system is different, but I thought that 3.7 was good.
 
Hi, I just wanted to ask which school are you in I'm guessing one of McGill, Waterloo, Toronto
 
Yes I wanted to try to stay a bit anonymous but it's one of the top schools in math and physics here.
 
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