Currently facing a decision between these 3 schools. I intend to major in math or applied math, but I might also have an interest in engineering. I did not receive financial aid from any of the schools, and I’m from Wisconsin, which is why Madison is in the running. If I do major in pure math, I might want to continue my education and earn a PhD, and with the cost of tuition from ND and WashU, I’m wondering if it’s truly worth going to one of these schools over my state school.
OOS UW parent here – stay in state, and enjoy the extraordinary opportunity that is UW. Plenty of room, and opportunity, for the serious student at UW. I’m sure there are lots of opinions, but if UW were our instate flagship, I could not see how other WUSTL or ND would be worth private tuition.
Save the money for Grad School.
It’s not worth it to go OOS when you received no FA, especially when you’re half unsure, half contemplating grad school. Go to Wisconsin.
UW has an outstanding math department, and historically so. In truth, it may be better than either ND or Wash U (in mathematics faculty, research, and prominence). ND and Wash U are excellent schools in their own right – but not necessarily as strong in your proposed major. Engineering is strong at UW, as it is strong at ND. Probably Wash U. as well, but I’m not familiar with their engineering.
But I’d certainly favor UW in your case and save money for grad school, etc. Also consider that with the stronger math department and faculty resources, your placement for grad school may actually favor the UW undergrad, if you are self-motivated and put in the requisite effort.
I always recommend taking these rankings with a grain of salt, but: UW graduate math currently ranked at 18 according to US News. The next school on your list in the math rankings would be Wash U., ranked at 39 for graduate math. And my experience is that the advanced classes and faculty access will be much smaller and feasible at a large research institution like UW.
My mistake: for graduate math, UW currently ranked at 14. Wash U. 39; ND 41.
Thank you for all of your replies! I just found out that I was accepted into Notre Dame’s Honor Program, would that change anything at all?
Go to Wisconsin and save money for grad school!
The only perk that would change anything tangibly would be if ND offered you some money to attend.
I just want to clear up a misconception about grad programs that is on this thread:
Good phd programs in math are free. In fact, the school pays you a stipend to TA classes. If a student is unable to be accepted into a funded (free + stipend) program, he or she should seriously consider whether math is the field to pursue.
While I concur with the point that students should not accept a PhD program offer in mathematics – or most other humanities and natural sciences – without requisite funding, said student ought not to be in debt from undergrad, or financially anemic when choosing to pursue an analytical discipline such as math for a career. The chances of success are by no means guaranteed, and I would aver that any cushion or financial certainty during the path to a potential academic or research career will be greatly appreciated. And the ranking of the graduate department in such a competitive discipline is not to be dismissed, either.
Yes, if you are gifted in math, you can get into a funded PhD program and that is the only type you should go to. If you don’t want to do a PhD, you may still want to do some other type of MS, though and that may be self pay.
I would also not really pay too much attention to the grad school rankings of the math depths at these schools. You would be an undergrad and they will all give you enough challenge and preparation.
How much does the money matter to your family? Undergrad work with profs are usually closer at the privates, but if you are an upper div student in math you may get plenty of attention at UW.
I am a current math major in UW Madison so here I think I can give some great insights 
TL;DR at the very bottom if you are too lazy to read.
- Math in UW Madison is hard. Really hard and can be challenging for even the brightest groups. In fact, I know ACT should be taken with a grain of salt but when I asked my peers how well they did on the ACT, most consistently reported around 33-35 (in fact, I am proud (?) to say I am a 35er too).
- UW Madison has variety of classes on a subject depending on how much rigor you want. For instance, for Calculus I,
- Math 171 for those who struggle with math
- Math 211 who aren't completely confident with their mathematical ability
- Math 213 (pretty much similar standards to Math 211)
- Math 217 for those who are almost confident with Pre-Calc but still need review
- Math 221 for most aspiring engineers (and ideally for any math major)
- Math 275 for those who are completely confident with their mathematical abilities. Note that for this course, personally, I do not support it as if you are smart enough for this course, you should have already gotten a '5' on your Calc BC exam. I personally think it's better to "jump" right into Math 234 directly than waste a whole year relearning the same thing. That being said, this class uses Apostol's book for Calculus I. The same book that CalTech uses and is known to be one of the most "rigorous" undergraduate first semester calculus textbooks. Also, do not be surprised if some of your classmates in this class are Olympiad contestants. That being said, it's very do-able to get an A if you put a decent effort as the more talented freshmen group tend to start from Math 234 or Math 521 honors instead. That being said, in Math 275, despite it being "Calculus I" do expect that all the students in class got '5's on their AP Calc BC. I just personally don't think it's worth it to relearn the same contents when you will be taking Analysis classes later on in your junior year.
Anyways, that being said, I have as you might have guessed skipped a couple math courses as an incoming freshman last year. Next semester, I am planning to take either the Analysis honors sequence or the Modern Algebra honors sequence (most likely the Analysis Honors though)
As for the actual rigor of the classes: Math classes in this school take a huge leap right after Calculus III. I will add that Calc I, II, III are not only poorly taught but very easy to get an A as a math major. In fact, it is pretty much a guarantee that math majors get A in those subjects due to the fact that engineers and pre-med majors take it ^^
Now, once you start taking more proof oriented classes like Math 341, I can practically guarantee you that in your first 2-3 weeks of class, you will be struggling to sleep 2-3 hours a day in the weekdays just to manage a mere 55/100 on the homework (even with all the Googling for answers and such).
However, don’t be intimidated! Just attend office hours at least once a week outside class and I can warrant you after the first month, you will be getting more than enough sleep as usual! Still, it is something to note as of the rigor of UW Madison.
As of Notre Dame, I believe for undergrad they have a very strong pure math program.
In fact, I believe they are very proud of their undergraduate placement which can be found here:
http://sumr.nd.edu/sumrgrads.pdf
Considering pure math is one of the most selective fields for graduate study, the school does place extra-ordinarily well. However, I might add that this is when you take the “honors” version and that the “honors” version at UW-Madison are just as hard if not harder (in fact, UW-Madison uses the same books for “honors” version and also encourages taking much more pure math courses undergrad for those planning on graduate studies)
And as of WUSTL, like all top privates, it too has a strong undergraduate program. However, I will like to note, there has been complaints the math departments are a “joke” because the exams are "multiple choice’ during the Calculus sequence. Personally, I think this makes no difference if your multiple choice is from A to M. In fact, I will place the rigor of WUSTL for undergraduate math a bit lower than Madison if not the same, and I am sure graduate schools will place no differentiation from those who came from WUSTL to those from Madison.
I do say however, go to the most affordable one of the three. You might be surprised but I did once upon a time get rejected to Notre Dame, waitlisted to Madison (and then accepted), and accepted to WUSTL.
Ended up chosing Madison OOS because it was cheaper.
At this level of college, for undergraduate math, you will all have identical advantages to graduate placement. Why waste more when you get same outcome?
And a small note: If you are choosing to be a math major, please do yourself a favor like me and have a double major in something practical. Getting accepted to graduate school in pure math is extremely hard and proof classes tend to be very abstract and useless (though so beautiful and fun!).
I am currently double majoring in Computer Science and I think this is a very good choice. Pure math majors right out of college are rather very unemployable and it hurts me how one of the most rigorous degrees in undergraduate studies (significantly harder hour wise than engineering) gets paid almost the same as other liberal art majors. Computer science in the other hand have a starting salary of twice what pure math majors start often and have for any decent mathematically oriented students, a guarantee job right out of college.
TL;DR. Go the cheapest option. Each of the three are very respected among the academia folks and you can always challenge yourself in any university. The student niches in pure math tend to be some of the brightest students anywhere
btw. If I placed any horrors of Madison to you, just saying that Madison is very fun! Just make sure you aren’t taking 18 credits of pure advanced weeder math/science courses and a part time job like me if you want more than 4-5 hours of sleep daily) In general, getting a 4.0 in Madison is extremely doable and in fact, with some effort, 4.0 really is … “easy”.
^^ Go Badgers! Oh and btw, from proof sequence, your classes get extremely small. I know this semester for Intro to Topology, there was only 3 students in the whole lecture -.-
The ratio at higher math is the same everywhere in the US cause not many students like math in the first place and those who do study engineering …
and if applied math, go take a look at AMEP major at madison. Although a small warning: This major is EXTREMELY hard. I am living evidence of how hard AMEP is with more pure math oriented classes. Expect to sleep 2 hours frequently to get a 4.0 each semester with 18 credits. I personally rather advise you to enjoy your college years and do CS + Math but then, I am very biased. Computer Science is the way I see it… a branch of mathematics, since what utilizes more rigorous logical reasoning than coding? 
If you can afford it, definitely pick ND or WashU over a state school.
Go the most affordable one
Math majors almost anywhere in the top 50 univesity is tough
In fact, for some reason math seems to attract usually the brightest groups
Anywhere you go
You will be competing against students who got 800s on SAT Math section or a 36 on Math
and out of those students, you will need to be in the t op 15% in each class to get an A
That being said, for math, all of them send students to top grad schools
I might add though, MIT seems to prefer pure math majors from Madison while Cambridge seems to prefer Notre Dame. Just saying ^^
However, I will note
Outside comp sci, math, chem engineering, and a few other areas, UWMadison rigor feels very very uhmm
what should I say, “normal”? xD
Like only a select few really feel top notch thanks to its influence on grad rankings but the liberal arts… feel more like the average student body
OFC since math majors or aspiring math majors usually aren’t really what you consider “normal”, this shuldnt be a problem for you UNLESS you plan on changing your major to a more liberal artsy field
On the UW board, another parent posted about the downside of instate students who see UW as ho-hum, because is their flagship and they may not appreciate what a truly world class education students get there. UW is not just a state school, it is a top institution.
I am biased, with an OOS kid there now, who is being taught by incredible profs, who are at the top of their fields. His double major departments are both in the top 15 in the country, and he couldn’t have asked for a better experience. Throw in the city of Madison, State St., Lake Mendota, UW football and basketball, and for kids who are comfortable in a university setting (like someone choosing among ND, WUSTL and UW), it is a bargain for instate students.
Not sure what #14 meant about “normal” – if that is a good or bad thing. UW is a work hard play hard place, and some kids err too much on the play hard side of the equation and it shows. But for students willing to put in the work, it is a wonderful education at a bargain price for an instate student.
Congrats on your choices, and good luck to you
And all those private propaganda of individual attention
This is in general true and almost ALWAYS true
HOWEVER
math classes in UW seem to be an exception starting from proof honors sequence
Expect from linear algebra honors proof to up to have from 3 to 20 students in the WHOLE lecture
Note though, this seems very specific to math from my experience, but privates really dont have a leg up from Math 341 to upwards
Individual attention? You will get more at Madison. But only upon entering higher math
If you are starting from Calc 1, … expect a huge lecture hall all the way to Math 319
Agree with Midwestmom. “Normal” is a poor descriptor, for a very large student body with a great range of skill levels and rigor, whether humanities, sciences or engineering – as is true of most top state flagships. I think “normal” is intended as a pejorative with the virtual wink. A simple refutation would be sociology, where UW ranks first in the country – occasionally tied with Berkeley – and above all ivies. Does this make UW a better institution for humanities undergrads overall? No, that would be untenable. Is it one of many examples that could complicate a blanket assessment about rigor? Probably.
I should add, with due respect to AccCreate, that the argument you mount for rating humanities students is a common one for many universities. There is a current thread going on cc about the status of humanities students vis a vis STEM students at Stanford. One could probably substitute chosen lines from the respective threads and retain their overall meanings.
Oh, and a quick note
If you plan on attending UW Madison, please do yourself a favor if you are considering grad school for pure math that you really challenge yourself all four years.
Ideally, you should have done AP Calc BC with a 5 and if not, please take a placement test to test out of Calculus I and Calclus II. Nowadays, this is almost a necessity as the honors course would then move faster than you (and the result is you won’t have the same advantage applying to grad schools)
You should spend this summer reviewing all the topics in Calculus II and Calculus III of Madison and ALL the questions
(https://www.math.wisc.edu/undergraduate/calculus-students-page)
Why? Because otherwise you will be missing too much. My high school never taught me how to integrate some of the problems and this can cause you problems later on (especially Math 319).
First year:
First semester (saying you start from Calc III):
Math 234: Calculus III
And if possible, add Math 240: Intro to Discrete Mathematics
Second semester:
Math 341: Linear Algebra
And Math 319 if you have not done so
(Try CS 302 during this semester. It’s better to double major in something practical like CS with pure math because of the high risk of getting denied to grad school. Also note that minors/certificates are virtually useless and a waste of time. Actually, even a double major really isn’t really worth it but in this economy, you should always consider a back up with such an impractical degree)
Second year:
<please spend=“” all=“” your=“” summer=“” self=“” studying=“” real=“” analysis=“” honors=“” and=“” if=“” cs,=“” ideally=“” of=“” intro=“” data=“” structures=“” most=“” computer=“” languages.=“” note=“” that=“” top=“” math=“” students=“” take=“” 421=“” before=“” going=“” to=“” 521.=“” in=“” fact,=“” universities=“” the=“” us=“” don’t=“” allow=“” you=“” jump=“” straight=“” 521=“” a=“” “proof”=“” class=“” like=“” 421.=“” madison=“” is=“” very=“” special=“” light=“” they=“” do=“” let=“” try=“” after=“” 341=“” truly=“” believe=“” are=“” confident=“” enough=“”>
First semester:
Math 521 Honors: Real Analysis Honors
or
Math 541 Honors: Modern Algebra Honors
I know this sounds very rigorous and over the top but if you are serious about considering math grad, you should note that if you want to go to top math grad, you will need to always be 1 step further than everyone else (think how many universities there are in the world)
Notre Dame sends its top math students to top grads BECAUSE they force the students to start Honors Algebra I from sophomore year (although this is equivalent to Math 341 in UW-Madison)
You really want to always be a step further than even the “very best” to be safe. In fact, to this day, I secretly regret not having started Linear Algebra Honors or Real Analysis Honors since freshman year.