“For math, unless academia is the end target, you’ll be good at any top 50 college.”
I think that in some ways this is less true for math than almost any other subject. Yes any top 50 college will have competent math professors, whereas some colleges may not have depth in certain less popular subjects, but the peer experience in math differs significantly all the way up the scale. A good example is Hardy’s “A Mathematician’s Apology” where he explains (as one of the top mathematicians in the world) how much he was outclassed by Ramanujan. At Cambridge, the experience at my college was qualitatively different to other colleges due to the peer group.
That may not matter for some people, but it’s not only those targeting academia that would care. OP should think about whether it matters to him.
I am in Texas, and my unweighted GPA is 3.9/4.0. Hmm, from what I have heard, UT basically accepts top 10% unofficially from my school (which I shall not reveal for privacy reasons) because of its competitiveness; top 10% at my school is basically top 5 at most other schools. Also, from what I heard, it is not that hard to get into UT if you are a decent instate student (which, at the risk of sounding overconfident or my abilities, I think I am) but not at all easy to get the major of your choice. And I suppose that doesn’t do much good for me. In any case I still have UTD, SMU as safety schools. I will certainly apply for the Turing and Deans scholarships at Austin.
Academia is certainly not the end goal for me (at least, it does not appeal to me that much right now).
@Twoin18 makes a valid point; the quality of education might be equivalent at any top-50 university, but the skill level of peers will certainly not. For pretty much my entire life I have been surrounded by people just as smart, if not significantly more, than me, due to living in one of the top intellectual hubs in the country; I think that this brings out the best in me and makes me more motivated to achieve success.
If your class rank is top 7.5%, then it would appear that you are also surrounded by mostly people who are not quite as high achieving in high school as you are (92.5% of your high school classmates).
As was said above, it makes sense for you to check the offerings in the math departments of the schools you’re considering, to make sure there’s enough upper-level math to cover what you want to learn and keep you challenged.
Since Northwestern was mentioned above, here are the offerings for the upcoming fall semester in math (you’d be looking at courses numbered above 290-1, I think): https://www.northwestern.edu/class-descriptions/4760/WCAS/MATH/index.html
You’d want to look at the topics covered in the courses rather than just the course titles, as some upper-level courses have deceptively simple names. It would be wise to also look at the requirements for the math major at the schools you’re considering, as those may show what upper-level courses are typically part of the major (and could also list basic foundational courses that you may well place out of). Here’s Northwestern’s as an example: https://catalogs.northwestern.edu/undergraduate/arts-sciences/mathematics/mathematics-major/
What’s difficult to know is the SCEA chances at Princeton of a student who is not just strong in math, but one of the top 100 seniors in the country in math. And it does seem from the Putnam results posted above that some universities including Princeton have many more students participating in the highest level of math competitions in college.
@ucbalumnus yes, but my school is segregated between “top 15%” and “rest”. Like there is a literal segregation between the honors and regular classes. As a result, most of the people around me (also due to friend group choice) is as good if not better than me. Moreover, I have attended many math camps in which my skills are the norm or below the norm. I find myself performing the best in these situations. It is motivating and refreshing being able to continually discuss complex topics and issues with people just as passionate as me in math/science. Of course, “peer pressure” (ensuring that I do not look like an idiot) is also, to an extent, motivating as well.
@Genevieve18 yeah, I will look into Northwestern and other similar schools. I too am not sure how much of a boost USAMO is on college apps, but I’d wager its not that significant for a place like Princeton, especially when there are MOPpers and IMO-ers aplenty (I was aiming for MOP this year but unfortunately came up short on both days ) . On the other hand, everyone I know who has qualified for USAMO also got into Rice RD, but they all had strong resumes in the first place without USAMO (our school had some 18-20 students get accepted into Rice).
Speaking as someone who was a math major for a couple years at a top 5 math school, if you have any intention of going to grad school in math (or if you think you might eventually), you want to go to the best math program you can get into. There is a huge qualitative difference at the top end of schools. The difference between a Princeton and a Rice is huge.
If you don’t want to pursue grad school, just try to go to a school with a top 25-30 grad program in math. If they have a decent grad program, they will certainly have enough classes to keep you busy. (Also: multivariable, linear algebra, and differential equations aren’t the math classes a real math major at a top school generally takes–though having taken them already should be helpful. It’s generally more like some calc, analysis, algebra, and some miscellaneous other stuff.)
If I were you and I couldn’t get into one of those reaches, I’d probably just go to UT Austin if I were thinking about things from a purely academic perspective. They have a great faculty in most academic fields (better than some of your reaches). Of course, there is something to be said about the environment, socially and intellectually, of a more selective school regardless of whether the faculty is worse–although if you get into the honors program then socially and intellectually things should be a bit better.
Regarding whether Rice represents a reach for all, there’s a fair amount of opinion in that assessment. Yes, Rice would be a challenging admit for many potential applicants. However, with a sufficiently impressive application, things begin to change. Even if your chances at Rice can only be estimated at fair to good, then it could still serve as a match of some type for you.
Looking further into the future, irrespective of the college you choose, you may want to consider a semester in Budapest as well as an REU in order to acquire extra preparation for graduate school along with an opportunity to broaden your general exposure to mathematics.
Actually, these are commonly included or assumed lower level courses for math majors, though (a) honors versions (with more theory and proofs) may be offered and commonly taken by math majors, and (b) some math majors may have completed them while in high school and choose to skip them entirely after matriculating to a college.
Linear algebra (irrespective of when taken) tends to serve as a gateway course into college mathematics. Other than in reply #26, I’ve never heard otherwise.
) . On the other hand, everyone I know who has qualified for USAMO also got into Rice RD, but they all had strong resumes in the first place without USAMO (our school had some 18-20 students get accepted into Rice).