Liberal arts college vs University for mathematics?

College Majors Math/Computer Science Majors
1

I’m pretty sure this topic probably came up some time in this forum, probably in other sections in CC, but I couldn’t really find a comprehensive answer that answered a lot of my questions. It’d be great if anyone could redirect me to a post or directly comment their experiences/advice!

So I’m currently a junior who is taking Calculus BC and planning to take math courses at a state college next year. I want to potentially attend graduate school and obtain a PhD in mathematics so that I could teach undergrad/do research. I was thinking about going to a liberal arts college because I highly value close teacher-student interactions and lack of graduate students to compete for research. However, top tier graduate schools for mathematics now look for graduate courses taken as an undergrad, which liberal arts colleges don’t offer, and liberal arts colleges in general don’t offer the same breadth of classes that are available at universities (except for maybe Williams, but I dislike the athletic emphasis and its rural campus). The LAC that I really liked was Swarthmore because the student body fit my personality, its proximity to Philly, its challenging yet rewarding coursework, etc. but even the math department there recognizes that they are no longer sending as many students to top 5 grad schools as they had years prior.

So, my question is should I attend an LAC or a University for an undergraduate math major to go to a good grad school? Thank you!

2

Take a look at St. Olaf.

Last I knew, LAC grads from good math debts were still doing well in PHD placement. LACs can offer tutorial type studies with their professors.

Check out this thread, especially post #110 from a math prof at a small LAC (as well as his later posts). Might be worth reaching out to him with questions.

http://talk.collegeconfidential.com/parents-forum/1912521-can-son-get-interesting-math-program-in-small-school-p8.html

3

http://www.swarthmore.edu/Documents/academics/math/grad_GRE/MathGradSchool.pdf

If your goal is a ‘top 5’ math grad school, then attending a university over a liberal art college is probably a better idea.
You will probably be taking courses in university for math during your liberal art college IF you are a fast learner in mathematics.
For instance, I would have done Real Analysis and Modern Algebra by second year. By those standards, I would have been completely ‘done’ with all the math courses available at Swathmore. Hence, from my third year, I would have had to do independent study or study in some university to do the upper level math courses (and I’m not a math major).

Since you are planning to do college courses from high school, I honestly recommend as someone who has took quite a bit of math courses (and being surrounded by math majors) that you attend a university.
You will be better served.
Let’s say you finished Calc BC with a 5 in junior year. Then in summer, you would probably take Calc 3 + Linear Algebra or Calc 3 + Differential Equation.
By your senior year, you might then take Differential Equation or Linear Algebra or a proof course (or maybe a higher upper level course).
Then in summer of your senior year, even if you DON’T take college classes, you will be starting your first year with Real Analysis or Modern Algebra. (I and II)
Then by your second year at most, you would be done with more or less all the math courses in Swathmore.
http://www.swarthmore.edu/mathematics-statistics/courses

That concludes most if not all of the undergrad courses in Swathmore (and classes such as Complex Analysis, etc. can be taken during your other math courses as college students take like 4~6 college courses a semester.)
At this point, you would probably run out of math courses in Swathmore except independent study or seminars. Hence, I personally recommend a university setting for people like you.

Other than that, Swathmore is a phenomenal place to study. Just note that at your pace, you can theoretically finish all of the undergrad math by end of first year (if you really decide to go heavy with college courses in your 2 summers and senior year).

Don’t fret too much. Anyways, don’t fret too much on this as ‘top 5’ math grad school is extremely difficult for anyone to get in regardless of coursework and that things are a bit more lax once you aim for the ‘top 5~20’ math grad schools.
But still, with your math pacing, I really don’t recommend LAC. I just can’t see how you wouldn’t finish all of Modern Algebra and Real Analysis by second year if you are also taking courses in high school. I didn’t do that and I finished those two by my second year.

Just do note that (although I am an abnormal case) if a non-math major like me is able to complete the undergrad math curriculum by second year, then it isn’t impossible for math majors to run out of courses during their years in liberal art colleges.
Some of my math friends were doing graduate level courseworks during their end of first or start of second year. So… if you are planning on being like them (do note I do attend a ‘top 5’ USNews school so the experience I have is not the norm by any measures), then do note universities would better serve you.
Plus, if you get lucky with university courses, you would once in a while find middle school or high schoolers taking graduate courses with you :slight_smile:

4

You might be better off at a medium sized research Uni such as MIT, Yale, Brown, Chicago, Northwestern or Duke.

5

Given how advanced you are, a university with a math PhD program is likely a better fit for you. You will likely skip most of the large frosh/soph level courses and go straight into the small junior/senior level courses anyway, meaning that you will not gain the main advantage of a LAC (small frosh/soph level courses) in math.

6

You are advanced and will bypass many of the lower-level/entry math classes. Upper level classes at a university will be much smaller. Graduate students (the younger ones) will be your peers once you get to the upper classes. Interacting with them and working them will be a big positive and the lack of them is one of the negatives of a school without a grad program—for someone who will come in with first year done. As a generalization, graduate students = more research overall = more research opportunities overall. I wouldn’t think of them as competition.

There are many, many reasons to study math at a LAC. Just the ones you mentioned wouldn’t be the ones I’d put above studying math at a university.

I have 2 advanced math kids. D is math major at a LAC and came in with 2 -yrs of Calc (so less than you). Wanted to double major in a performing arts and specifically wanted small liberal arts school experience. Very happy at her small LAC.

S is one yr younger than you. Will finish Calc BC & 2nd yr Statistics next year (as junior) and take multivariate or Lin Alg at nearby college senior year. Some of the schools I’m looking into for a summer tour + suggestions from others are here in case that is a part of the country you are looking at:
http://talk.collegeconfidential.com/college-search-selection/1927453-college-tour-ideas-for-great-lakes-area-math-engineering-p1.html

7

@AccCreate Thank you so much for the comprehensive answer. My goal isn’t really to get into a “top 5” graduate program rather than to study math, but I do recognize the value in attending good graduate schools. Would you consider liberal arts colleges that are notorious for their math, like Harvey Mudd, Reed, or Williams?

Everyone else: thank you!

8

Harvey Mudd, Reed, or Williams would be great schools for a Math major.

9

I don’t know much about Harvey Mudd, Reed, or Williams other than knowing that they have great academics overall.

Anyways, I looked at the courses at these schools:

Williams
https://math.williams.edu/courses/
It seems it has more than enough math courses to keep taking math courses freely for four years. It feels the math catalog is more analogous to a university math courselist than a liberal art college math courselist (in the number of courses available).
I can see why this school is well respected. A good way to figure out is to see the amount of courses after Real Analysis or Abstract Algebra.
Williams math courses basically has graduate math courses too so in terms of amount of math courses, you should not run out of it. In fact, I am quite amazed by how many courses are available for a ‘liberal art college’. Many universities don’t even have this much undergrad math available to students.
Basically, you can go hard-core math nerd in this school and still have many options available for your four years.

Harvey Mudd
I know this place is phenomenal for STEM fields overall. I mean it’s like the MIT of cs for the liberal art colleges. (at least that’s what I hear overall)
However, I have looked at the courses at Harvey Mudd.
https://www.math.hmc.edu/program/majors/mathematics/
Your fourth year courses might require you to take courses at a university (Claremont Graduate University).
If you love pure math, I will admit I think a university will be better suited for you overall than Harvey Mudd after looking at the course catalog.
If you love the more applied math (especially related to CS), then I think Harvey Mudd would be a phenomenal place to study for undergrad.
If you have no idea what math you like (like me when I was in high school), then I think applying to top universities aren’t a bad idea. After all, if you are academically qualified for Williams and Harvey Mudd, then you probably have a really good shot at getting into MIT, Harvard, Columbia, CalTech, Princeton, etc.

Reed
http://www.reed.edu/math/courses.html
Ok, I will get quite a chunk of hate but the one phrase I can think of this school for math is, “goodbye pure math, hello computer science math”.
What I mean by this is that if you are interested in pure math or other branches of applied math (outside CS), then you will probably be largely dissatisfied with this school.
I honestly can’t recommend this school for you. You will quickly run out of courses to take and because of this, you will be taking probably lots of unrelated “math” courses that quite frankly look more like CS courses than “math” courses.
Just look:
Mathematics 113 - Discrete Structures (CS)
Mathematics 121 - Computer Science Fundamentals I (CS)
Mathematics 221 - Computer Science Fundamentals II (CS)
Mathematics 241 - Case Studies in Statistical Analysis (CS -intro to machine learning (?)-)
Mathematics 243 - Statistical Learning (CS -more like intro to machine learning-)
Mathematics 374 - Divisor Theory of Graphs (CS)
Mathematics 382 - Algorithms and Data Structures (CS)
Mathematics 384 - Programming Language Design and Implementation (CS -compilers (?) is a math course (?)-)
Mathematics 385 - Computer Graphics (CS -it even states it’s ‘computers’-)
Mathematics 387 - Computability and Complexity (CS -algorithms(?)-)
Mathematics 388 - Cryptography (CS -or applied math-)
Mathematics 389 - Computer Systems (CS)
Mathematics 441 - Topics in Computer Science Theory (CS)
Mathematics 442 - Topics in Computer Science Systems (CS)
So basically, the ‘math’ courses in Reed are basically CS courses and good CS universities will have far more choices for CS courses.
I just can’t recommend this school at all for you. Reed is a phenomenal place to study but I just can’t see how it would be a match for you. All I can see is you regretting in this choice. And in case you are confused by the ‘math’ courses of Reed, do note I took extensive number of math courses AND computer science courses. I can tell you right here that those ‘math’ courses in Reed aren’t ‘math’ courses. It’s CS courses in which universities solid in CS would be a better choice then (simple since the courses in Reed ‘math’ courses seem a very specialized field in certain subfields for undergrad meaning you will miss out on the other subfields in CS)

If you are serious about a more liberal art college setting for math, why not also consider schools like Princeton Univ? It’s like the ‘holy grail’ for math majors. Terrance Tao got his graduate degree from here. The ‘Beautiful Mind’ John Nash graduated from here. I know it’s probably also a crapshot but just do note top universities are also phenomenal places to study mathematics overall.
Anyways, don’t pidgeon-hole yourself to just liberal art colleges. Most liberal art colleges with your math skills will require you to take courses outside your own school (no idea how this works). If you are academically qualified for schools like Harvey Mudd or Wiliams, then you probably have a good shot at top universities.
That stated, Williams seem to be a great place to study math out of the liberal art colleges you listed. Harvey Mudd if you enjoy the more applied computer science oriented math. As for Reed, I don’t think it’s a good fit for you. If you are the type to enjoy Reed math courses, then just apply for schools with good CS.

10

Don’t forget that Williams specifically as well as other LACs allow for tutorials so you aren’t necessarily limited by the posted course offers.

Maybe we can get @mathprofdad to chime in with his thoughts.

11

@AccCreate The reason why I’m not considering Princeton is that I wouldn’t get in lol. I could maybe get into Cornell if I applied early decision next year, but the only thing holding me back is the lower professor-student interaction compared to liberal arts colleges. Of course, with higher level classes I doubt this would be an issue. The supposed cut throat environment and the grading curve have been scaring me a bit too, although the former is often negated by many Cornell students. Besides Cornell, I’ve also looked at UChicago, which again, I probably wouldn’t get into, but I would probably like it more than Cornell because of its “nerdiness”. It’d probably be my first choice, but it’s so difficult to get in.

12

I’m also a pretty “learn for the sake of learning” type person, which I’ve also heard is a common LAC trait, although I do understand that universities could satisfy me in that regard too.

13

There is a tool called webcaspar that shows where PhDs did their undergraduate work. I filtered on PhDs in math and statistics.

Some that jumped out at me as “do able” for someone who can’t get into Princeton:

Arizona State
Brigham Young
NC State
UW Madison
OH State
St Olaf

But you can play with the data and find more. Remember to factor by graduating class size. Six phds from Olaf is really impressive for the size of the school, compared to seven from UIUC.

https://ncsesdata.nsf.gov/webcaspar/index.jsp?subHeader=WebCASPARHome

14

TL;DR Read the last paragraph if you are lazy. Sums it up more or less.

Most if not all the top universities in the US has this type of thinking.
It is not limited to LACs. Once you enter the ‘top’ undergrad USNews universities, because the academic body is high, you will get the constant aura of ‘learning for the sake of learning’.
And top schools of any sorts tend to have the trait of ‘nerdiness’.
Remember, the universities that are peers to the liberal art colleges you listed are not your everyday-run-on-the-mill universities. They are universities catered primarily to nerds from all over the world.

After taking some math courses myself, I will note in universities, up UNTIL Real Analysis I, you will see lots of students. Like hundreds per class.
Why?
Real Analysis I is a requisite for most phd or master’s in the more applied math (econ, stats, computer science, etc.)
However, AFTER Real Analysis I, you will note even in university settings a HUGE drop in the number of students in the upper math courses.

And by your pace, you should be able to go for Real Analysis I by first year (if you really want to) or at most by second year first semester.
After that, you really should not have issues with large student to professor ratio.

Anyways, the student-to-professor ratio is very misleading (at least from my experience). The numbers you see in the USNews is more in tune with the humanities courses. In the more STEM (science, technology, engineering, math) fields or econ, class size is going to be far larger than the numbers you see on the USNews.
For instance,
https://www.usnews.com/best-colleges/columbia-university-2707
Columbia Univ has a 6 to 1 ratio. But in reality, I have never had a “6-to-1” ratio class in my years and neither has my friends (well maybe except one but that was a rare morning friday recitation with only 3 students (including me) overall).
Most of my classes have honestly been rather medium large lectures and this includes the upper level courses too. In fact, even the ‘upper’ level courses, it was not unusual to have like 150 students with almost 200 students in the waitlist at the beginning of the semester.
And THIS is a 6-to-1 ratio.
Now in the humanities, most of the courses were of course <20 students.
And even on the courses with very little students, the professor seemed to teach in the exact same method as have it been a large lecture. Why? There are just too many chapters to cover in a semester to get ‘personalized’ in the sciences.

And considering Williams
https://www.usnews.com/best-colleges/williams-college-2229
has a school ratio of 7-to-1 ratio, I highly doubt it begs to differ considering Columbia has far more classes with <20 students.
Don’t over fret with the “personalized” raito as much. Unfortunately in many of the STEM fields (and econ), you won’t be experiencing this in your major courses. You would experience this in the courses outside your major but at least for your major, math, I highly doubt that is the case.

Maybe I am wrong. But at least for university settings, don’t trust the ratio as much in the math fields. I have also checked with my friends in Cornell, CMU, Stanford, Brown, UCBerkeley, UCLA. The situation is very similar.

Just take this into note when you apply to colleges (LAC or universities). For the more mathy fields, most students don’t experience the ‘student ratio’ that the USNews likes to claim.
Don’t be upset though. About third of your courses is going to be humanities so you can still get that ‘student ratio’ in your other courses, just don’t expect as much in math.
Of course, once you pass Real Analysis I, then the student ratio really shouldn’t matter in either LAC or university. And since you can finish Real Analysis I by end of your first year or by beginning of second year, I wouldn’t worry as much.

Ahh. The classic ‘cut throat environment’ every high schooler fears.
Na. It’s just as ‘cut throat’ as your high school. Students don’t turn into demons the moment they get accepted to a certain school. And I do know friends in Cornell (or were) too so I don’t think my beliefs are largely unfounded.
But ya, I will not disagree with the fact that it is harder to get higher GPAs in the same courses in the math and sciences in top schools. This is because many of the math and science courses tend to be graded on a curve aka your grade is decided upon how much higher you scored on exams relative to your peers. Hence, if all the peers in your lecture are all ‘A’ material, even getting the average will require substantial amount of work (and even that doesn’t guarantee an ‘A’).

However, don’t confuse this with ‘cut throat environment’. Students aren’t trying to kill each other by any measures.
Maybe the professors (and I honestly think so) with some rare courses requiring 30 to 80 hours a week (Operating System in Columbia Univ.) but I don’t think math courses are like this in general. The time consuming ones in my experience were the ones that requiring coding, not proofs.
Math is more of a subject that doesn’t take as much time but requires far more abstraction. The benefit of abstraction is that you can do your homework lazily and just gloss over the questions in the day you get it and during your weekends while walking outside, you might figure out a problem or two of the homework.

Anyways, don’t be afraid of the ‘large lecture halls’ or ‘cut throat environment’.

  1. If you are a math major, classes tend to be large in general until Real Analysis I. After that, your choice of LAC or university should not matter much.
  2. Large and small classes in the sciences tend to in my experience feel the same. Maybe things operate differently in LAC but at least in the university I am, the only time I feel the difference of small classes is the humanities because we can voice our own opinions constantly during class (and highly encouraged to do so).
  3. ‘Cut throat environment’. Haven’t really felt it and so claims my friends who were from Cornell.
  4. Large lecture halls aren’t that bad. Most of the learning you do anyways is outside class anyways. I haven’t really ever learnt much in lectures. Most of it was figuring it myself with my friends (and/or TA) in college. And (rather unfortunately) majority of my peers seem to agree with the fact that except for very few courses, the classes did not seem to help much at all with their learning.
    Oh and many math professors tend to go over derivations of the theorems during class which is really (un)helpful in helping one gain intuition of the chapter. It’s basically, the ‘learning’ is off by yourself at the end of the day.
    Maybe things are different in a LAC (since university is about research first) but do note that. It might be like that in a LAC too. Who knows. And it doesn’t really help that many STEM professors are great at research but downright terrible in teaching. Eh.
15

" If you are a math major, classes tend to be large in general until Real Analysis I"

Not at most LACs. Plus more personalized attention from profs to undergrads. LACs also choose profs based on teaching ability.

16

Definitely look into St. Olaf - they are always very high o the list of liberal arts colleges that generate the most students who go on to doctoral degrees. Last time I looked they were 3rd in the nation in mathematics. And the place is always top ten on “best teaching” lists.

Whether at Olaf or someplace similar, these high end small colleges will focus on you, and not their graduate students. Check out Grinnell, too, they send a huge number of students on to top graduate schools.

Hope this helps. Pay most attention to where you feel like you fit. That is the most important thing.

17

If you are wondering how university sizes work out in math courses:
http://bulletin.columbia.edu/columbia-college/departments-instruction/mathematics/#coursestext
This is my school.
Note from “MATH GU4032 Fourier Analysis. 3 points.”, the enrollment is only 7.
Sure Modern Algebra I or Analysis I might still have like ~50 students but right after that, there is basically a huge drop in the number of students in upper level math courses.

Basically, after your first or second year, it is not abnormal to have a class with like 5~9 students even in universities. Heck, in some years there were only like 2 in a class.
I honestly doubt even LACs can beat out this.
Just do note that unfortunately until around partial diff eq, you get classes with 60s to maybe ~100.

Now, this isn’t the case for all upper level fields. In hyped fields like CS, there’s quite a chunk of students even in the upper level courses. But since you haven’t expressed in that field specifically, it should not be of concern for you.

Anyways, I will state this.
I have taken classes at large state schools. Some of the humanities courses there are 6 students, 16 students.
So, even universities DO offer low student to professor ratio classes. And the difference between 6-1 and 16-1 is more or less the same in my dictionary.

18

“I honestly doubt even LACs can beat out this.”
Well, Williams is known for its tutorials which are exactly 2 students and 1 professor.

19

I have deep respect for Williams.
I am not sure though if most LACs are like Williams though.

However, ya, Williams is a damn fine LAC to study math.
I quite envy the teaching method there looking at the course list. Seems a phenomenal place to study math.

But are most LACs like Williams?
As I don’t think it’s quite the case (maybe it is, I don’t know much about LACs) and most LACs just don’t have enough courses for students like him for four years, outside a very few LACs, I think a university would cater better for him.

That stated, I think the education one receives in Williams is arguably the best in the country for undergrad.
I have always thought so and see it as an equivalent of Harvard for undergrad.
However, outside Williams, what LAC would suit a student like him? I don’t know much about LACs but out of the ones he listed, the rest just doesn’t seem to have the ability to challenge him as much as he could be during his four years.

Anyways, for the OP, Williams is arguably some of the best schools in the country (if not the world) to study math in undergrad.
And considering Williams has a special relationship with Oxford University (http://exeter.williams.edu/), it just shows how much of respect it retains for its focus in undergrad studies.
And Williams does well with its graduate placements so don’t fret much there in the math fields. It regularly places at least one of its students in the “top 1~3 grad math USNews ranking” schools something even top universities have difficulty doing.

Do also note that the difference in a class with 2~13 students are trivial.
Really really trivial in the learning. Difference between 2 students in a class and 4 students in a class isn’t much in the learning the contents itself so also don’t fret with little differences in the size of the class when classes are around <13 students although Williams has a very different approach to teaching so that might change the ‘experience’ of learning -though this is unique to I believe Williams and is not the norm for most schools-.

Williams is the best math education in the East.
Harvey Mudd College is the best math education in the West (but the math slants more towards computer science bias).
Outside those two, I don’t really know much of other LACs for students like the OP.

20

Don’t know the OP’s stats (might be a good idea to share them so posters could pinpoint school’s that would be good fits in terms of matches, reaches, safeties) but in addition to Williams as a reach (as it is for all), St. Olaf as previously mentioned would be a good option.

Here’s a quote from mathprofdad in the link I referenced back in post #1 in reference to another poster’s request for math/music schools. OP should look closely at the schools mentioned to see if they might be a good fit:

"I am a bit late to this discussion, but thought folks might want to hear from a faculty member at a small school. I am a tenured professor at a top tier liberal arts college. I started visiting CC recently, and find it (mostly this particular forum) interesting and informative, but don’t have time to post regularly. However, I can stick around for a few days if anyone would like to discuss this topic further.

Just a word on the choice of schools, copied from above.

St. Olaf, Oberlin, Kenyon, Amherst, Grinnell, Davidson, Furman, Vanderbilt, William and Mary

All are excellent choices – I know people at all of them except (I think) Furman, and all those I know are excellent mathematicians. In some departments (certainly St. Olaf, Davidson, Vanderbilt, and W&M) you’ll find some at the world-class level, but that doesn’t matter much. You should at this point be focused primarily on teaching quality, and the student’s learning experience. Given the interest in music, I think this makes St. Olaf an excellent choice.

I haven’t reviewed all of the posts on this thread, but looking at the original post:

I think your son would be in a good position to start a math major at my institution, or any of its peers. He would start in multivariable calculus in his first semester, as do the vast majority of our majors. He certainly wouldn’t lack a peer group who are very excited about mathematics, and wouldn’t run out of courses to take.

Our program (like that of many of our peers) is designed around learning experiences, rather than courses, that can be tailored to what an individual wants out of the major (folks at St. Olaf, for example, will tell you they are a “big tent” department, and take this point very seriously). We have students who go on to graduate school and get PhDs; others who work on wall street, as actuaries, as consultants; other students go to law or medical school, or into K-12 education.

On this point, I think an advantage in undergraduate education that a small college may have over a larger university is its flexibility. Since students are our primary focus, and we are encouraged to engage them in all sorts of learning experiences, it is easier for a strong student to get involved in close work with faculty than it may be at a large research institution. Students can sit in on graduate courses at a state flagship, but they can learn the same material from us one-on-one (or in small groups of a few students) if they are so inclined. We routinely offer these sorts of experiences, and have time for them built into our workload.

We are also able to use mathematics to help students develop their basic skills like writing and public speaking (my colleagues and I are discouraged by the fact that, notwithstanding their top test scores, many of our students do not begin with these basic skills). These are important skills even for a research mathematician like myself.

Before concluding, I should mention that the division between liberal arts colleges and universities is somewhat arbitrary from an undergrad’s point of view. I think the advantages that a small college has can also be found to some degree at a smaller university (e.g. Vanderbilt, Yale, Rice, Dartmouth) where undergraduate teaching is valued. I suspect that my department and peers would see more commonalities than differences with those departments in terms of the student experience.

Sorry for the lengthy post (I didn’t have time to compose a shorter one!), but I hope some of that was helpful. Congratulations on making excellent choices for your son, and I wish you both the best of luck!"