Michigan has, um, a few more than 2000-3000 undergrads 
Awesome school, though!
Yeah haha that was the one thing it doesnât meet; you can never make a small school bigger, but you can always make a big school smaller!
[Here ya go](http://math.williams.edu/putnam-exam-dec-3/), @frontpage (cursorily Googled âWilliams Collegeâ Putnam).
@WildestDream â UIUC is (rightly) already on the OPs list.
@frontpage I mean, the only academic competition I had a chance to participate in was a competition called WYSE. I advanced to state in math, but you have probably never heard of that. It is only a statewide competition, doesnât go any wider than that. I really like math; I donât think I would be overwhelmed anywhere, but I think that most math majors at places like MIT and Princeton would be better than me. At the same time, I definitely think I could hold my own and succeed at a top schoolâs math program. I think the LACâs on my list have extensive math course offerings; If you disagree please let me know why. Of course Iâm just a 17 year old; I probably know very little about this stuff.
@marvin100 UIUC is a school that gains most of Itâs value for my from its location and its cost. UMich is a more selective, but shares many of the same characteristics that I dislike about UIUC without the benefits mentioned above.
@ManaManaWegi Try to check the syllabi of the math courses at the universities you are comparing. What textbooks do they use? Do they have a rigorous introductory proof based course based on Spivak, Apostol, or Courant? Google the syllabus for the analysis or abstract algebra course. What textbooks do they use How do the PSETs compare with those from MIT OCW or the honors courses at Berkeley? How much do they cover? How is the undergraduate math culture? At a place like MIT, Berkeley, or UIUC there are many math majors and the program accommodates and challenges good math students at all levels, while there is no less rigorous path at Chicago or Princeton. Until youâve taken super rigorous math courses, you canât be sure how prepared you will be for them.
These are questions youâd want to ask
@frontpage thanks
@ManaManaWegi - totally, which is why I said â(rightly)â
ManaManaWegi: I am concerned about your SAT subject tests. For someone who wants to major in math to have anything less than an 800 on the Math 2 is weak (not to mention your Physics score). Any of my students that have applied to Ivies have always had 800âs on the SAT subject tests and most of them have been rejected by the Ivies. Some of these students have taken their Math 2 and Physics while in 10th grade because the 800 has been such a sure thing (they have always left their regular SAT for 12th grade since an 800 in the verbal sections has not been a sure thing).
My most recent two students who went to Ivies (both to Princeton for math) ended up switching majors to math/comp sci related stuff. They both had AP Calc BC and 800âs across the board in their regular SAT and SAT subject tests, but found they could not keep up with the many Princeton math majors who arrived there with a couple of years or more of university-level math (linear algebra, multivariate calc, diff eq etc.). Both of these students were bright and hard working and had written the AIME several times and the USAMO a couple of times.
Aim high but be realistic about your chances of acceptance and your chances of success as a math major if admitted. Keep some safety schools in your list.
I concur with the suggestion of University of Waterloo and University of Toronto. They are both very strong in mathematics. Waterloo and U of T have more Putnam placings than most of the Ivies (certainly not more than Harvard and Princeton), but they are relatively easy to get into. I am fairly certain that you would gain admission to math at both of them. I favour Waterloo for math because it has a very wide range programs within math and a wide range of students: some merely very good at math and some world-class. I believe that Waterloo still has the largest faculty of math in the world. It has an excellent co-op program that would allow to gain work experience and money to help off-set tuition. The tuition at Waterloo in the math faculty is Can$26 882 (which is less than US$20 000) for international students.
@violindad I find it hard to believe that the deciding reason in my acceptance will be a 30 point difference in the math 2 subject test. Of course, 800 is better. Frankly, I donât care enough to take another standardized test. Thanks for the other comments though, they are appreciated.
I am very confident in my success as a math major, whether that is justifiable or not. My willpower is strong (very strongly supported in common app essay) and I have gone outside my schoolâs curriculum to take enhanced difficulty math courses knowing that it would not help my gpa (only increase the chance to reduce it) I understand there are probably many students that are at least similar to me in these qualities, but I have immense confidence in myself.
Feedback is appreciated.
I think the issue heâs pointing out is that a 770 on the Math 2 subject test (which is curved heavily â so it may indicate weaknesses in your foundational knowledge) and lack of Olympiad level competition suggests that you should be cautious about applying to/surviving in the super-high-end math programs (Harvard, Princeton, MIT, possibly Chicago). These schools are very brutal for math. Your confidence and will power will help you, but it will be very difficult to catch up to their level of preparation while also taking super-rigorous courses that demand this preparation. These schools are also very sink-or-swim, at least as far as math is concerned. University-level math is very different from high school math, and your high school grades probably do not indicate well whether you will succeed or not. You were the valedictorian of your high school, but I suspect the rigor of your school and possibly peer competition were lacking. Lots of successful math students at Harvard, Princeton and MIT particularly have qualified for AIME or USAMO and/or seen less rigorous versions of linear algebra and differential equations either though a rigorous magnet high school (e.g., TJ, Montgomery Blair) or a local college.
I personally got 800s on Math II, and 770+ on all other tests and qualified for AIME. My grades and high school motivation were not as strong as yours (and I also didnât get an 800 on the SAT I). I didnât get into an Ivy and certainly would not survive at Princeton as a math major.
So if you like math, it might be better to go to a school where your preparation is more in line with other students. This includes great schools such as Rice, the Ivies (except maybe Princeton, Harvard, Caltech, and maybe Chicago), Harvey Mudd, UIUC, Waterloo, and Toronto, and top liberal arts schools. Iâm not discouraging you from applying, but you should be aware of this. You will have great peers and will be able to prepare you for a top graduate school if you demonstrate that youâre capable.
I like your list. I like @frontpageâs suggestions. I like them a lot.
A few more that you might not know about. Ohio State has a terrific honors program and a serious honors calculus class (Spivak) for people who get 5âs on BC Calc. Wisconsin also has an honors math program. Ohio State has many honors scholarships and should make that affordable, perhaps even lower than UIUC instate which has all kinds of budget issues. Wisconsin has less scholarships but is less expensive than Michigan and of equal quality. Not too many other schools have these type of entry honors math courses. These are both trivial applications and are almost an automatic admit for you.
Also you might consider Reed. Not sure if you consider Portland 4 seasons compared to IL, but it isnât southern California.
frontpage is right on in their assessment.
I would agree that 30 points on the Math II will probably not by itself prevent admission, but it will raise a red flag. It is usually possible to get an 800 on Math II even with a number of errors, so a 770 suggests many errors. I suspect (donât know for sure) that the vast majority of math majors at schools like MIT and Princeton had 800âs on their Math II. Iâm sure that a 770 would be fine if you had some other strong evidence of your math ability like invitations to write the AIME for 4 successive years with good scores on the AIME and invitations to write the USAMO a couple of times with decent scores on it. Excellent marks in university math courses especially at the graduate level would also make the 770 irrelevant.
A 770 on Math II for a potential math major is quite different from a 770 on the math component of the regular SAT. Because an 800 on the math component usually requires either a perfect or near-perfect score, a tiny slip or two can result in a 770 and such slips can be corrected by retaking the test. On the subject test (i.e. the Math II), a 770 is the result of many slips, or of several gaps in knowledge, or of weak reasoning ability.
Which math courses have you taken outside your schoolâs curriculum? If just AP Calc BC, then that will make little difference. Both of the students that I mentioned earlier who switched out of their math major at an Ivy had self-studied Calc BC and got strong 5âs in it (I base the strength of their 5 on the practice test they did for me). Both of these students had incredible will-power also, but that was insufficient for surviving as math majors at the top level found in the schools that are strong in math like Princeton, MIT etcâŠ
Hereâs a quick easy way to assess your math strength: find an old AIME, take it under timed conditions, and score yourself. As well, you may want to look at some old USAMO questions and see not only if you can answer them, but also if the type of thinking required appeals to you. As frontpage indicates, university math is very different from high school math. [I am not suggesting that the AIME or USAMO are university-level math, but facility with them would indicate an aptitude for rigorous higher-level study of math.]
I second the suggestion of Ohio State.
I second St Olaf: it has everything you want, the math major is very strong (you background would be pretty average for their majors), music is extremely strong, they offer merit as well as need-based aid, they have 4 seasons, the right number of studentsâŠ
What about Hamilton? I think Iâve heard they have a strong Math department. I like Colby and Haverford too, but have no idea how strong their Math departments are.
I as well like Hamilton and Haverford for you, @ManaManaWegi, even though they are somewhat beyond your preferred geographical area. Cornell should be considered also.
Have you run the net price calculators for all of the schools on your list? A good number of them are need-only and unless there are extenuating circumstances donât expect to get much more than the NCPs indicate. If you donât âneedâ aid on paper, you may not come up to the level that you really need.
I would concur that Williams fulfills just about everything on your wish list and would not that it offers many music performance opportunities for non-majors. I would suggest you submit a performance supplement, even if you do not intend to major in music.
Williams would be a reach, but I believe your demographic (middle-eastern, first generation) will give you a boost as will your extensive music involvement, moreso than at the other reaches on your list. Since you seem to prefer small and medium sized schools, you should continue to research safeties that fall into that category.
MIT actually does publish statistics about SAT Subject Test score ranges for admissions. See http://mitadmissions.org/apply/process/stats
The middle 50% score range of admitted students (25th and 75th percentiles) in 2016 was:
SAT Subject Test - Math [780, 800]
SAT Subject Test - Science [740, 800]
Caltech, which the OP didnât mention but others have, has a middle 50% of [790, 800] on Math Level 2.
https://www.admissions.caltech.edu/content/class-profile
@merc91 @WalknOnEggShells Should I be concerned with only having liberal arts options in the match section of my list and only university options in the reach section?
Should i have another safety?