Northwestern vs. WUSTL vs Rice vs. UChicago for Math Major

[Pphhiilliipp]

Hi everyone,

I am a rising senior who is starting to narrow down his college list for where I plan to do ED. I go to a rigorous boarding school and my college counselor has helped me based on my stats a few T20s that he thinks I would have a legitimate shot at based on my stats and the profiles of previously accepted students from our school. He thinks that I’d have about the same chance for all of these schools.

How do the math programs for these 4 schools compare in terms of specific strengths? Do any of them have standout subfields, like maybe a school could have a notably strong stable of PDE faculty? Any specific nuances would be appreciated!

[hebegebe]

UChicago has one of the nation’s best math programs. It is notably stronger than the rest on your list. Note that it also has the most selective admissions among these four as well. I have a child attending there and can attest they have many different levels of math that a freshman can take, including Honors Real Analysis that can challenge the nation’s most capable students.

In terms of a match school, you should also consider applying EA to Michigan, which is stronger in math than every school on your list besides UChicago.

[Pphhiilliipp]

@hebegebe thanks. UMich is a bit too large for my liking. How is the math program at an LAC like Bowdoin? (them specifically because I am being recruited there for a sport and thinking of doing ED2 there assuming my ED1 doesn’t work out).

How is the math program at a place like Notre Dame? My college counselor has designated it as a ‘semi-target’ because, over the past 5 years, 8/11 of kids with my statistic profile from my school got in RD, so he thinks if I applied SCEA I’d have a great shot.

[hebegebe]

First of all, I hear Bowdoin is great. I can’t specifically tell you anything about Bowdoin’s strength in math, but I have tagged @homerdog who has a child at Bowdoin and might be able to help more.

But in terms of math education, any top 50 university or top 20 LAC (which includes Bowdoin) offers more challenging courses than the vast majority of students can handle. Are you roughly at the 1% in terms of math skills? If so, Bowdoin can meet your needs just fine. But it is when start going further into the top 1% that you need to evaluate further. And in terms of this, there are two separate things to consider.

The first is depth of courses. For example, if you have completed Linear Algebra in your senior year of high school, you will want to look at the college course catalog and verify that there are enough courses that will keep you engaged for all four years of college. Just about any university can do that, but not all LACs can.

The second is peer group. You don’t want to be much stronger than just about everyone in your class for two reasons. First, it means that you won’t learn much from your peers, which is an essential part of the college experience. This is much more likely to happen at an LAC with 500 students in the class than a university with 3000+ students per class. Second, being much stronger than everyone in your class means that few of the classes will challenge you because they are geared at a different level.

So when does this start to matter? If you tell me that you got an A in Linear Algebra but had to work for it, or that you barely qualified for AIME, then a place like Bowdoin is still fine as long as they have the courses for all four years. If instead you tell me that you took Linear Algebra but got an easy A, or that you got a 7+ on AIME, then you probably won’t have true peers at Bowdoin. On the other hand, you will probably have a handful at Notre Dame just because there are more students there. Finally, if you have qualified for USAMO or published mathematics research papers, you should probably look beyond both Bowdoin and Notre Dame as your reach schools.

[Pphhiilliipp]

@hebegebe Thank you very much for the feedback on this. I should have given a bit more of a qualification to my math abilities. I finished up Linear Algebra last year and will be taking a ‘special topics’ course this year (probably an intro to PDE, real analysis, applications), and I got a 102 on the AMC 12 and a 10 on AIME.

How is the math program at Harvey Mudd viewed compared to the top math programs at national research universities? Or Pomona–I wouldn’t have much of an in through athletics but I’ve heard that their math program is quite rigorous. The reason why I chose those research universities to consider is that I am originally from the Midwest and I wouldn’t have to travel all too far from home to go there (Rice would be the furthest).

[hebegebe]

That helps a great deal with context. I think that places you roughly in the top 500 math students applying for college. There aren’t that many places that have a handful of true peers. Off the top of my head those will include UChicago, every HYPSM, Michigan, CalTech, and Berkeley. Probably missing a few. It might also include HMC, as it is a standout among LACs.

I think you will still learn quite a bit at places like Northwestern, WUSTL, and Rice. Much less so at Bowdoin and Notre Dame.

I will think about this some more, but am tagging @RichInPitt and @yearstogo as they might be able to add perspective re elite math programs as well. Not sure if they will join right away as it’s the holiday weekend.

[Pphhiilliipp]

@hebegebe You have been a great help for me! Thank you.

I am hesitant to put a lot of effort into looking into HYPSM-level schools because I have a very weak EC profile and understand that the main reason why I have a chance at these T20s are because of my stats. Especially with schools going test-optional, I am afraid that my high scores across ACT, SAT, and SAT subject tests will be greatly diminished, and there will be greater emphasis on ECs and more subjective principles. MIT is actually going SAT II-blind; they won’t even look at them if you submit them. There isn’t a whole lot of rhyme or reason in Naviance for the students accepted to those places from my school, and my CC expresses that after a certain level of stats to those places, it comes down to subjectivity and personality.

Our school’s acceptance data suggests that the colleges I listed are more prone to ‘brute force’ acceptance if need be–in this I mean if your overall stats are high enough its harder for them to say ‘no’ and having a 1600 vs a 1570 on the SAT seems to hold some degree of marginal benefit.

Apologies for that digression! Berkeley is quite an interesting one. Their math program speaks for itself, but again it might be a bit too big for me and it might be difficult to generate connections with the many talented faculty they have. I was thinking more for graduate school (because if there’s one place to do doctorate math work, its there). If I did my undergrad there, would it give me a leg up when I do graduate work there? If so, it might be worth a few years of massive lecture halls, non-guaranteed housing, and strong politics.

[collegemom3717]

Would you consider- and would finances allow for- going to the UK? Oxford or Cambridge would let you do all math all the time, and they don’t care about ECs. Check out the course at Oxford:

http://www.ox.ac.uk/admissions/undergraduate/courses-listing/mathematics

(there are also Maths+ Philosophy, Math + Stats, and Math + CompSci options, the last of which is what @HazeGrey’s son is doing (just finished year 2)

And the maths admissions test (MAT):

https://www.maths.ox.ac.uk/system/files/attachments/test19.pdf

(solutions: https://www.maths.ox.ac.uk/system/files/attachments/websolutions19.pdf)

[Pphhiilliipp]

It hadn’t really dawned on me to study internationally. But, I know that it is a very strong school and there is a specific emphasis on one specific subject area to study. I will definitely look into it now. How does the selectivity of Oxford/Cambridge compare to the top US universities?

[Pphhiilliipp]

@collegemom3717 And do you think because of COVID-19, their testing requirements may shift?

[collegemom3717]

Paging @Twoin18, who is the resident expert on Math in the UK (he is a Trinity College, Cambridge PhD- the ne plus ultra of math credentials).

Selectivity is a different animal in the UK, as it relates solely to your strengths in that particular subject. Go take a look at the MAT to see how. they test HS students for aptitude

[MWolf]

In general, if you prefer math theory, a university with a strong liberal arts background, like UChicago, can often be better than one with a more applied bent, like Caltech, though MIT is still one of the very best.

UCLA has an excellent math program, and, while they have somewhat holistic admissions, stats are more important (my nephew was accepted recently, pretty weak ECs, but superb stats).

Oxbridge is indeed an excellent choice for mathematics.

Rice and Northwestern have excellent math programs, though not as good as some public universities (what is your state of residence?), and WashU wouldn’t be my forst choice for math.

Among LACs, Carleton has a really good math program, HMC was mentioned, Pomona is also great, as are Williams, Amherst, and Colgate.

[yearstogo]

Hi @Pphhiilliipp

DS also scored a 10 on the AIME but is probably leaning more towards physics or CS than math. (Ideally he would like to do some sort of combination of all three…) I do not have too much to add to the list…DS is most interested in Caltech, HMU or MIT but realizes the chances are quite slim. Obviously any of those top schools would be a great, challenging experience for everyone. We are in NC, so DS’ instate options are decent with NCSU and UNC. We will definitely be interested in some of the responses you get so thanks very much for starting this thread.

By the way, DS also attends a fairly rigorous BS and one of the strongest benefits he has there is the cohort and while certainly all schools will have a group of top kids, as @hebegebe indicated, your scores place you highly in math and I think it adds a different set of challenges/considerations than most other HS kids.

Best of luck!!

[hebegebe]

Circling back after the weekend. Here are some other colleges for you to consider:

1. NYU Courant: People often don't think of NYU when it comes to top math programs, and that's a mistake. The Courant Institute is one of the nation's best math centers. You have a good chance of admission there particularly with a "Why NYU" essay that recognizes the strengths of Courant. But there are two things to think about. First, you will again be one of the strongest undergrad math students there altough you might have a few peers. Second, it is right in NYC, and you have to decide if that's where you want to live. But there is no worry about the strength of the faculty or running out of material.
2. CMU: Like MIT and CalTech, CMU also explicitly asks for AMC scores, so they value it. Note that CMU explicitly used to say that they cared about demonstrated interest. They don't say that anymore, but I suspect it still matters. The culture of CMU didn't seem to fit either of my kids, so check to see if it fits you.
3. Vanderbilt: Among the top-20 schools, Vanderbilt is the most stats-based one around. Our school sends a lot of kids there and from our Naviance scattergram it's a pretty clear demarcation between those don't get in vs those that do. Above a certain GPA and SAT, admit rates are roughly 80%.
4. U of Toronto and McGill: These Canadian colleges do not practice holistic admissions so your stats will serve you well here. Because they get most of Canada's best students, I expect you will find your math peers there. You have to decide if the size is an issue.

[ucbalumnus]

@hebegebe

The second is peer group. You don’t want to be much stronger than just about everyone in your class for two reasons. First, it means that you won’t learn much from your peers, which is an essential part of the college experience. This is much more likely to happen at an LAC with 500 students in the class than a university with 3000+ students per class. Second, being much stronger than everyone in your class means that few of the classes will challenge you because they are geared at a different level.

That is basically an argument that colleges which are safeties for admission, or those where you receive the largest merit scholarships, are unsuitable.

While this may be more true for smaller colleges, huge state flagships (perhaps your own) do tend to have a significant number of top-end students (at least in comparison to their state populations); their absolute numbers may be non-trivial, even if they may be only a small percentage of the student population. But they may provide enough numbers for there to be the kind of peer group advocated above, and give departments incentive to offer more rigorous options or honors courses.

[ucbalumnus]

@Pphhiilliipp

@hebegebe Thank you very much for the feedback on this. I should have given a bit more of a qualification to my math abilities. I finished up Linear Algebra last year and will be taking a ‘special topics’ course this year (probably an intro to PDE, real analysis, applications),

Colleges typically have catalogs, schedules, and faculty rosters online. You can look at them to get an idea of:

A. What upper level (and graduate level) math courses are offered, and how often.
B. How many faculty there are, and which subareas they are in.

Note that upper level math courses are mostly held in smaller class sizes (unlike huge lower level math courses that many other majors need), but you can check this on the class schedules of most colleges.

Note also that some colleges’ math departments include statistics, operations research, and/or computer science, while others have these as separate departments (or operations research within industrial engineering). Be aware when checking out math department course offerings and faculty rosters on college web sites.

The other question you need to consider: can you and your parents afford all of the colleges on your list (based on net price calculator results if you cannot afford list price)?

[merc81]

With respect to smaller colleges, which appear to be of interest to you — and which offer an excellent alternative to universities if you would like to study in a purely undergraduate-focused environment — Harvey Mudd, Pomona, Haverford, Amherst, Williams, Hamilton, Bowdoin, Reed and Carleton are among those that appear in a Princeton Review sampling, “Great Schools for Mathematics Majors.” From your core group of four schools, the University of Chicago and Rice also appear.

[ucbalumnus]

@merc81

With respect to smaller colleges, which appear to be of interest to you — and which offer an excellent alternative to universities if you would like to study in a purely undergraduate-focused environment — Harvey Mudd, Pomona, Haverford, Amherst, Williams, Hamilton, Bowdoin, Reed and Carleton are among those that appear in a Princeton Review sampling, “Great Schools for Mathematics Majors.”

Perhaps you did not notice that the OP is highly advanced in math (linear algebra completed already), so that many LAC math departments would have insufficient advanced or graduate-level offerings for the OP. Math major for a highly advanced in math student is pretty much the worst case major (within the realm of those offered) for choosing a LAC.

[merc81]

@ucbalumnus

Perhaps you did not notice that the OP is highly advanced in math (linear algebra completed already), so that many LAC math departments would have insufficient advanced or graduate-level offerings for the OP.

LACs with strong math departments may offer ~20 courses beyond the level of linear algebra, which includes sophomore level topics such as linear optimization and differential equations, for which linear algebra serves as a prerequisite. Beyond that, the OP expressed a specific interest in information on schools such as Bowdoin, Harvey Mudd and Pomona.

[bookworm]

OP, have you been accepted into any of these schools?