Sciences and math at a liberal arts college

[R.P.F.]

Warning: This is more of an expression of my frustration than a question looking for an answer.

I'm a junior math major in a small elite liberal arts college. Just recently, I became very repelled by the idea of studying sciences or math at a liberal arts institution. There are simply not enough resources. The research opportunities are scare: almost no professors take on students during the year and maybe one or two take on students during the summer. There are no possibilities of taking graduate level classes. If you don't get along with someone, then you are screwed because the department is so small that you see everyone every single day.

Now I just think it is totally not worth the tuition I'm paying. When I go to grad school(if I get into one), I'm already left behind by my peers from research universities.

If you went/are going to a liberal arts college, what do you think of it? Maybe you could make me feel better.

 

[micromass]

I'm already left behind by my peers from research universities.

Not necessarily true. A lot of people in grad school don't have research experience or have done grad classes. I didn't.

A small university is actually quite fun: you get to know the professors personally and they will be more open to questions.
In a huge university, you hardly know your professors, you can't speak with them.

Just make sure your courses are decent (and if not: self-study).

If I had the choice, I would go to a small university instead of a huge research college.

 

[R.P.F.]

Not necessarily true. A lot of people in grad school don't have research experience or have done grad classes. I didn't.

A small university is actually quite fun: you get to know the professors personally and they will be more open to questions.
In a huge university, you hardly know your professors, you can't speak with them.

Just make sure your courses are decent (and if not: self-study).

If I had the choice, I would go to a small university instead of a huge research college.

May I ask when did you go to grad school? I just get the feeling that everything in academia is getting insanely competitive these days, starting from REUs and grad schools. I'm also not working 80+ hours a week to get into a top 50 program. I'm shooting at top 15. I have a profile that is as strong as I can make it. So at the moment I'm just not sure what to do. Clearly, I'm not good enough(Just got turned down by my first-choice summer position).

You are right about the student-professor relation part though. I got to know my professors really well. But I also had really great experience with one professor from a research university.

 

[Mépris]

Micromass is in Europe, so the situation is somewhat different there. One has to do a Master's degree first and then move on to a PhD. To the best of my knowledge, grades are what get you into grad school. I'm not certain about the transition from MSc to PhD but from BSc to MSc, it's definitely grades! Much simpler, if you ask me...(not saying it's necessarily better or anything, mind!)

 

[mal4mac]

You don't necessarily need an MSc to do a PhD in the UK. The most important thing is to get a good honours BSc degree (probably a 1 or 2(i)).

A typical requirement (copied form jobs.ac.uk) is "A good degree (1st class preferred) in Physics, Materials Science or Electronic Engineering..."

It is debatable what a "good degree" is. A "Desmond" (i.e. a 2(ii)) may be thought good if you have some redeeming qualities (e.g. an MSc or work experience or good attitude or a good excuse...) With a "third" I'd think about re-doing your BSc :)

 

[eri]

I started at a small liberal arts college, went on to earn a masters and PhD, and now I'm teaching at a small liberal arts college. I loved the small college environment - I got to know my professors, professors taught all of my classes and labs, I got to work with them one-on-one in research projects, I had full access to the equipment the school had (and since it was a very good liberal arts college, we had plenty of stuff to work with) and I got into many good REU programs while in college. It's what you make of it, and it's where you go. My college had about 8 faculty members in physics for about 10 majors a year. Other colleges have only 1 or 2 for 10 majors. It's a huge difference.

 

[eri]

I should mention that students from my college also got into top graduate programs for physics, math, and engineering - Harvard, Stanford, Georgia Tech, Cornell, Columbia, and U Michigan just to name a few people I know in particular. Starting at a liberal arts college certainly doesn't hold you back.

 

[R.P.F.]

I should mention that students from my college also got into top graduate programs for physics, math, and engineering - Harvard, Stanford, Georgia Tech, Cornell, Columbia, and U Michigan just to name a few people I know in particular. Starting at a liberal arts college certainly doesn't hold you back.

At colleges like Harvey Mudd, Williams and Swarthmore, there are a few students going to top math PhD programs every year. But if you look at the big picture, students from liberal arts colleges are certainly disadvantaged. MIT's math PhD program did not accept students from liberal arts colleges for several years because the last one they had really struggled.

 

[R.P.F.]

I started at a small liberal arts college, went on to earn a masters and PhD, and now I'm teaching at a small liberal arts college. I loved the small college environment - I got to know my professors, professors taught all of my classes and labs, I got to work with them one-on-one in research projects, I had full access to the equipment the school had (and since it was a very good liberal arts college, we had plenty of stuff to work with) and I got into many good REU programs while in college.

I'm glad it worked out for you. I liked it the first two years and now it's becoming too much for me. I get the feeling that at a liberal arts college you can only go so far. I have a perfect major GPA, very good recommendations and one publication. But this is as far as I can go. I cannot take graduate level classes or anything. And yet I'm still having trouble get into some REUs. I'm just clueless on what I could do to improve my chances.

Thanks for sharing your experience. It's always nice to hear from someone who made it through.

 

[cdotter]

I'm a senior applied math major at a small liberal arts school. For the reasons you listed (poor course offerings, no research opportunities, etc.), go to a bigger school. I wish I had.

 

[eri]

You can't expect to get into all the REUs you apply for, no matter how good your application is. Some of them are getting more than 500 applications. There are plenty of students applying with perfect GPAs and publications. It's certainly true they don't offer graduate courses, but you could do an independent study with a professor on a more advanced topic. That's pretty common at liberal arts colleges.

There's a wide range of liberal arts colleges. Top colleges have good researchers who can offer a range of coursework and a lot of research opportunities. Lower ranked ones can't. The same applies to universities.

 

[Vanadium 50]

MIT's math PhD program did not accept students from liberal arts colleges for several years because the last one they had really struggled.

What's your evidence for this?

It is true that there are unofficially two kinds of math degrees. One goes into substantially more depth and into more topics, and is intended for those who want to go to graduate school. The other is not, and serves people who don't go to graduate school - people who go immediately into industry or secondary education. This is independent of the type of school: I went to MIT, and they would have been happy to give me a math degree (when I was there, physics majors usually fulfilled the minimal math degree requirements, but they did not permit double majors) but I was not and am not qualified to study mathematics at the graduate level.

 

[lisab]

Warning: This is more of an expression of my frustration than a question looking for an answer.

I'm a junior math major in a small elite liberal arts college. Just recently, I became very repelled by the idea of studying sciences or math at a liberal arts institution. There are simply not enough resources. The research opportunities are scare: almost no professors take on students during the year and maybe one or two take on students during the summer. There are no possibilities of taking graduate level classes. If you don't get along with someone, then you are screwed because the department is so small that you see everyone every single day.

Now I just think it is totally not worth the tuition I'm paying. When I go to grad school(if I get into one), I'm already left behind by my peers from research universities.

If you went/are going to a liberal arts college, what do you think of it? Maybe you could make me feel better.

I can't answer that question, since I was a physics major at a large research school (University of Washington). Let me give you a bit of perspective.

I have a vivid memory of finishing the last final of my bachelor's. It wasn't in the physics building, so I walked over there, feeling...mixed emotions. Mostly I like, I'm done, like really done! Can't believe it, I actually finished! Stuff like that.

So I walked through the physics building. From the ground floor to the top floor, up and down the halls, looking at all the people. I recognized a couple profs I had taken classes from, but they didn't acknowledge me (not unusual...that was not the culture of the department, I guess?). The prof I did research for wasn't around - he rarely was. In fact I hadn't seen him in a long time.

No one knew me. I mean, *no one*. I think that's not unusual for undergrads at a big research schools.

 

[R.P.F.]

What's your evidence for this?

I heard this from a student who went to the MIT open house last year. I suppose he didn't just make it up.

I think a good way to distinguish the two kinds of degrees you mentioned is to have a separate honors degree for more serious majors. Sadly, my college does not have that.

 

[R.P.F.]

No one knew me. I mean, *no one*. I think that's not unusual for undergrads at a big research schools.

That sounds really sad. But I guess at the moment I'm just more focused on my future than getting attention from professors. Of course it is possible that I'm only saying this because I already have plenty of attention from professors of the department. Actually, I occasionally want *less* attention because this is a small department and I want to have my privacy. But I definitely appreciate the openness that my professors showed. I agree that the possibility of having more intimate relations with the faculty members is *the* pro of going to a liberal arts college.

 

[R.P.F.]

I'm a senior applied math major at a small liberal arts school. For the reasons you listed (poor course offerings, no research opportunities, etc.), go to a bigger school. I wish I had.

I know what you are talking about. But hey, on the brighter side, you are almost done! So stick it through for the last few months.

It's certainly true they don't offer graduate courses, but you could do an independent study with a professor on a more advanced topic. That's pretty common at liberal arts colleges.

I actually really regret not doing independent studies this semester. I didn't think about this till two weeks after the semester started and then it struck me. I'm still taking the more challenging classes the department offers. But due to limited choices I decided to take classes that don't interest me particularly. That was not a wise decision. Really should have replaced it with an independent study.

 

[bpatrick]

I went to a small, private university (~5k undergrad) that awards PhDs in science / has professional schools / etc... I found that balance to be wonderful. I was in the honors college (about the top 10% of my class based on SATs/high school grades) where we took separate gen-eds from the rest of the university. So for all my intro stuff, I had a 1:3 prof to student ratio and then when I got to upper level classes, there were only those in the major to take those, so class size went up to about 1:10.

The good part about being at a university with a graduate school is that I had loads of opportunities to take grad classes as a senior undergrad (I took 2 graduate level math classes, a graduate level geophysics course, 2 grad level musicology courses, and a graduate seminar in proteins at the medical school).

The bad part (I guess if you want to look at it like that) is that since it was small, there were no REUs available since any RA/TA positions went to grad students. Another bad part was that the tuition was right up there with the ivy leagues and good liberal arts colleges.

My fiancee is in her last semester at a small liberal arts college (ranked top 5 in the U.S. for overall rigor ... whatever that means). I audited Topology and an econ course in time series here. Both of those are things only offered once every 2 years as upperclassmen electives. When I look through their courses, it's pretty standard and every math major pretty much takes the same things with maybe 1-2 courses being different from somebody graduating the year before/after them. Sure, they'll all get three semesters of calc, two of linear algebra, a semester of algebra, semester of analysis, two semesters of number theory, and one course in differential equations ... which should give you a decent preparation for grad school. There is usually room for taking one of those special electives that are offered every 4 semesters. These seem to be: topology, Fourier analysis, numerical analysis, and differential geometry ... where any given student will most likely only take 2 of those depending on if they're graduating an even or an odd year.

I could see how this is a bit distressing if you already had an area of mathematics that you were interested in. My undergraduate institution had 5 different tracks that you could take to earn your B.S. in math: pure, applied, computational, actuarial, education. They all had the core: 3 calcs, 1 diff equ, 1 linear algebra, 1st semester of graduate algebra, 1st semester of graduate analysis.

The pure track was finishing the 2nd semester of graduate algebra, 2nd semester of graduate analysis, first semester of graduate topology, and first semester of graduate differential geometry (or 2nd semester of topology). In theory, this pure track gave you the tools to go right into grad school being able to pass quals in analysis, algebra, and topology if you really had your **** together ... I only knew one guy who was in this program and he was pretty hard-core ... not sure where he is now though.

Applied was finishing the 2nd semester of graduate analysis, doing the 1st semester of graduate complex analysis, and then taking a year of either PDEs or dynamics / bifurcation theory.

The computational was taking 1 semester of stats (or discrete math), 1 semester of number theory, and a full year of numerical analysis.

The actuarial was pretty much just taking 2 stats courses, an econ, and a finance course after the core math stuff.

Education was finishing the 2nd semester of graduate algebra, taking a year of "history of mathematics", and then another course in math pedagogy.

So each track had an additional 4 courses you had to take after the "core". I definitely like that whole system a lot more than what is at my fiancee's liberal arts college where every single math major of the same year took the same classes, and if you were not lucky enough to have gotten through the required prerequisites in time to take one of those 4 courses as a junior, you'll never get exposure to it unless you self-study. So part of the problem there is that if you don't already know what you want to study in grad school, all you have to go on in your cookie cutter liberal arts math degree, so all the "applied" math you might be exposed to is an intro to ODEs and maybe a numerical analysis class ... assuming you managed to take linear algebra (pre for ODE), ODEs, algebra (pre for number theory), and number theory before the 1 in 4 semester rolls around that they offer numerical analysis or Fourier series.

Looking at a negative aspect of this system: if you were at my undergrad institution, had AP credits for calc 1&2, and didn't know exactly what you wanted to do, you might have had until 2nd semester sophomore year before you started taking courses in areas that didn't overlap. Assuming you took linear algebra, multivariable calc, and diff equ all your freshman year, then started 1st semester algebra your sophomore year, you might not have had enough exposure yet to know if you wanted to do pure math and continue taking the 2nd semester of algebra, or if you should be taking a stats class, complex analysis, discrete math, etc... not that it would be a sin to take extra math courses beyond the requirement, but for accelerated individuals, that program does have you branching into your "specialty" during your sophomore year rather than your junior/senior year.

Back , to the liberal arts school stuff: given the fact that I audited two courses here, the level of rigor is nowhere near what you are exposed to if you are at a university where you must take a couple graduate level courses (with grad students in them) as an undergrad. My exposure to Topology was more a review of some analysis/set theory, then gently baptize you in the soothing waters that are topology so you're not lost when you get into it your first year of grad school. You can't really get away with that in the university setting where you're in the same class as the crazy first year grad students from China coming over to get their PhD in math. It's sink or swim right off the bat.

So not that I was in your position, but I do sympathize and maybe even empathize a little with your situation. I don't think you're going to be unprepared for grad school, but you can never expect to be up to the level of the foreigners who have MSci degrees already when they come here for the PhD ... if a school accepts you as a grad student, they think you've got the stuff to make it through their program and are willing to invest their time and money in you, regardless if you have a B.A. from a liberal arts college, a B.S. in a slightly more specialized math focus from a university, or have a MSci. from the State University of the Republic of XYZ.

 

[R.P.F.]

Hey bpatrick,

Thanks for you input. In fact, based on your description of your undergrad institution, it sounds a lot like Notre Dame. But whether it is ND or not, I do think that an elite moderate sized private university is the second best choice for undergrad education if a person cannot get into an Ivy. After that, it's good liberal arts college and then state universities.
I can see where your feelings about courses at your fiancee's college come from. Some professors at my college also try to make things easy for the students because they try to be 'nice'. Luckily I haven been picking challenging professors on purpose. The topology class I had was actually very intense. It was like 25 hours of work every week.
I hope when I apply to grad school this year things could turn brighter. My college don't have good luck in terms of getting students to grad school. Because professors don't care that much together with the fact that students here don't have credentials as strong as students from Ivies or elite private universities. Hopefully I could be one of the few exceptions.

 

[deRham]

I cannot take graduate level classes or anything. And yet I'm still having trouble get into some REUs. I'm just clueless on what I could do to improve my chances.

There are definitely some options. You could take the chance and do a master's degree. If you think about it, that's the whole idea behind a liberal arts college education - it's somewhat less with the intent of getting super-specialized.

Another option is, like people said, to sign up for independent study. Most of what you need to know to research is not in graduate courses either, and you have to learn it on your own depending on where your interests take you. My advice is to do whatever you do study in detail, because there's really an infinite amount of stuff out there.

A final option is to see if there are any research universities nearby and see if you can register during some terms for a graduate-level course here and there. Many universities have the option of registering for a fee. I do think it's generally somewhat unlikely that you'll get into a top PhD program with an intent of specializing in, say, PDEs, without having some graduate level functional analysis, measure theory, and other topics.

However, I am reasonably sure when I say that taking graduate courses beyond the fundamentals in a few of the things relevant to you doesn't help THAT much in getting accepted to great PhD programs, perhaps for similar reasons that any particular research project will not generally help you get accepted. Usually, evidence provided by qualified letter writers who give no-nonsense descriptions of your abilities much better serves your needs than loading up on projects or courses.

In fact, this is why beyond a few geniuses, it is actually somewhat difficult to predict, at the face of it, which students will make a ton of top programs and which students will not.

Finally, a slight bit of advice that is not strictly academic - do try to enjoy your liberal arts college education. Try doing some of the things I suggested, so that you feel you can both enjoy the benefits of the liberal arts college and not get your future messed up by your situation.

Your words about MIT's math PhD program are quite believable to me. People usually make a list of top math PhD programs looking something like "Harvard, MIT, Princeton, Stanford, Berkeley, Chicago, ..." which, of course, I think is a little misguided, but has some truth to it in a way. However, different top math programs are quite different in terms of the student who best fits them. I'd say the last 3 of those 6 are quite a lot more forgiving to students who aren't coming in very specialized (aka, with the equivalent of a master's degree). Whereas Princeton, Harvard and MIT are 4-5 year programs rather than 5+, and what's more, their program structure even shows it. Princeton doesn't really offer much in the way of introductory graduate coursework (though its undergrad courses cover many topics); Harvard's qualifying exam tests an extremely intense number of graduate level courses; MIT offers freedom to its students to take introductory courses, but requires no introductory work whatsoever, probably signifying that its students are supposed to be nearly past that stage.

However, there seem to be at least a reasonable number of students at programs like Stanford, Chicago, Berkeley, (maybe MIT), various Ivy Leagues, etc who are admitted before they are very close to ready to begin specialized work. Look into those. A lot of them have great programs.

 

[eri]

I do think that an elite moderate sized private university is the second best choice for undergrad education if a person cannot get into an Ivy. After that, it's good liberal arts college and then state universities.

So, you think that going to WPI would be better than going to Berkeley, or Michigan, or UT Austin? You'd be making a big mistake. You simply can't make sweeping statements like that.

 

[20Tauri]

I'm a senior at a liberal arts college. My experience in the math department has been wonderful. You can get a lot of individual attention and help from professors, and because the department is so small you really get to know people. It's true that we don't have the same opportunities you do at a research university, but professors are definitely willing to take on capable students, and if you need more of a challenge, they will find a way to give it to you. One of my friends has done a ton of independent studies, helped with research over the summer, and got to do a summer REU at another school. He's doing an honors project now, which is basically graduate level work.

As for getting into grad school, we had a math/CS double major last year who is now doing a PhD in computer science at MIT. I'm not a proper math major (I came over late from another department), but I've been accepted to a couple mathematics master's programs for next year. You can do more than you think with a liberal arts background.

 

[alan2]

Do what you love, love what you do, and good things happen. Young people worry too much about where and what. If you are good it will happen. You might be surprised to hear that Kalamazoo College is always ranked in the top twenty of all undergrad schools in the percentage of grads who earn Ph.D.s. They have all of 1,000 students on a good day and offer nothing beyond the standard undergrad curriculum.