I’m a math undergrad at Caltech. I’m applying to grad school soon and since I’m a Canadian citizen I’ll be applying to grad school in Canada. I’ll also be applying to some top programs in the United States, but I’m very unsure of my chances. The thing is, due to a combination of personal issues and the fact that I wasn’t as good of a student back then as I am now, there were several terms in late frosh year/early sophomore year where I didn’t do very well. That is why, despite the fact that my GPA has ranged between 3.5 and 3.9 for the last four terms, my overall is only 3.2, and there are some pretty ugly dents in the early part of my transcript. I’m quite sure I can get good letters of recommendation from my research mentors, since I am doing research this summer and it is going well. I’m hoping to be able to get into a top program in Canada for number theory/algebraic geometry. Am I likely to be accepted into somewhere like Waterloo or UofT or UBC for this? I’m less sure about Berkeley/MIT/Stanford etc. etc. My question is: -Will grad schools take into account this GPA improvement over time? -My GPA is also heavily slanted towards things that I like and am interested in. I’m leaning towards either number theory/algebraic geometry or descriptive set theory/mathematical logic. My GPA was damaged slightly by not doing very well in my undergraduate analysis requirement and the one term differential geometry requirement which I profoundly disliked, but I took five yearlong graduate classes in commutative algebra/algebraic number theory and class field theory/algebraic geometry/axiomatic set theory/mathematical logic and computability theory and the lowest grade I got in any one term of any of them was A-. Is this the sort of thing that grad schools are likely to take into account? Also, don’t Canadian grad schools expect students to do a Masters first, unlike in the US? If that is true, and presuming I did well enough in that, if I applied to a top PhD program in the US after that, would I have a decent chance of being accepted? By then, my full undergraduate transcript would be available, which means two extra terms of improved grades in Senior year to make up for a poor couple of terms frosh/sophomore year. Thanks, I apologize for the brick wall of text.