Turns out I really like math...

June 2, 2016 12:56 AM

How can I continue to study it?

I'm a junior-and-a-half in college, earning a concurrent B.A. and M.A. in Computer Science. I started in physics at a different school, then transferred to my current school, and picked up the CS major while I was here. (As a transfer, I had to stick around for an extra year to fulfill all my prereqs anyway, and got enough financial aid/scholarships to take all the classes I needed.)

Something I didn't realize at my first school or until now (as I get close to graduation) is that I REALLY like math. Not the applied math that I mostly did at my very practical, untheoretical first school as a physics student, but the more abstract, proof-based math that I do at my new school. (New school is a top 5 school where everything is very theoretical.) I really really have fun in my math classes, and my only regret is that I didn't realize how much I liked it until now, because if I could go back 2-3 years, I would have majored in math here. I'm actually getting kind of depressed to wind down to graduation, because I want to take more math!

I especially liked my theoretical CS courses involving math-- advanced algorithms in particular was my favorite class. (So, discrete math.)

I know doing a PhD in math would be a totally different ballgame, and I have no idea if that's something I'd like to do. But I'd like to... find out? Is there a way to keep studying math? Should I try to get another bachelor's degree? (I'm thinking no but if it were free, I totally would.) Should I keep graduate school for math/computer science in the back of my mind? Would I do much math as a CS PhD?

My GPA is not incredible but pretty good (4.0 at first school, 3.5 average at first in second school due to poor study skills that I pulled up to a 3.7-3.8). I test well, so I think I could do well on the GRE. Don't have any research, but I have one year left to look for a project or a professor to work with. (I spent most of my time hunting down internships and "professionalizing" my resume which has made me appreciate academia more.) I wouldn't say I'm a math prodigy by any means-- I actually didn't think I was a math/science person until college, after a very bad public education-- but I feel pretty at home at the moment.

I do have a major fear of participating in class (though this has gotten better this year) and talking face-to-face with professors, which has always made me feel like I would really suck at graduate school. I guess it's something I'd like to overcome, but if my success depends on it, that's a bit scary for me.

I do well in my current math classes. I've been top of the class a few times, more frequently somewhere between the top and the upper quartile now that I'm around very talented people.

posted by anonymous to Education (9 answers total)

I'm only in a CS-adjacent field, so my advice is mostly meta-advice about academia. But I can tell you that I at least knew CS PhD students whose work seemed to involve a lot of proving stuff. If you can make yourself do the cold-call, I might e-mail some profs of classes you've done well in and enjoyed. They may be able to give you some really specific advice on whether or not you'd find doing a CS theory PhD satisfying, based on your interests and strengths.

There's also master's programs in math or in theoretical computer science; master's programs typically cost money, and a lot of it. But even if the programs themselves typically aren't funded, given your good GPA at a top-tier school in a (usually) tough department, there may be some fellowships you could apply for that could allow you to go for free or a reduced cost. Your CS department may have some relevant info, and additionally, there's probably an office that centralizes info about funding opportunities for undergrads. (Especially check this out if you happen to be female and/or a minority who is underrepresented in STEM.)

(I do think you want to at least try actual research first to make sure that you could see yourself doing it for 5-7 years, but my gut reading this says you should keep a PhD on the table: you mention that your brushes with industry had you appreciating academia more, and honestly, to me, being able to rise to a challenge and develop new study skills like you did after switching schools speaks way more highly of your ability to succeed in a PhD than just being a "prodigy" would have. Social anxiety around your peers/boss is something you'll face inside or outside academia so I wouldn't sweat that too hard either.)
posted by en forme de poire at 2:20 AM on June 2, 2016 [2 favorites]

Go talk with one of your current math professors. They have office hours; use them (even if you don't need them for help with the class). Perhaps you might be a candidate for a math masters program?

On the other hand if you really like the CS math, perhaps talk to one of the professors for those courses, and ask what your options might be.

Your professors can be your best resource here (downside: occasionally there are some serious dinosaurs who may discourage you for reasons that have nothing to do with your mathematical capacity, e.g. race/gender/etc. If that happens, ask someone else.)

I understand that you're pretty worried about talking to them- but given that you're managing to do better with participation in class, you seem able to overcome the fear. This is a nudge to do so.

If you *can't*, or if you want another option, can you find a graduate student or two to talk with? They can tell you about their own search for programs and what they're doing.

And the disclaimer-- getting an eventual job in academia is a total crapshoot even if you are brilliant and have a perfect resume. There's oversupply of people willing to do PhDs and put up with moving all the time and poor pay and etc. This doesn't mean you shouldn't do it, not at all -- but it does mean you should have a plan about how things will work if you don't end up staying in academia. And it does mean you should find out a way to not take on debt for it -- PhD programs should be funded, and even masters may have funding options. (Math has *lots* of non-academic career paths, even after graduate level study; find out about those too!)
posted by nat at 2:28 AM on June 2, 2016

As somebody who did a CS / math double major in undergrad, to me it sounds like you might be happier in theoretical CS rather than math. Talking to professors for the courses you have really enjoyed is an excellent way to find out which discipline is more likely to engage with the topics you would enjoy.

Now, if you are interested in going to graduate school in either topic, you will have to overcome your fear of talking face-to-face with professors. To be accepted into good graduate programs with funding, you will need strong letters of recommendation from your professors. It will be hard for a professor to agree to write you a good letter of recommendation if you've never even been to their office hours once. Professors will also be a good information source to find out which graduate programs you should consider applying to, or which professors at which school are doing research on theoretical topic X. Professors will likely also have opinions as to whether Dr. Z at Y University is a good Ph.D. supervisor, or their students have all fled in horror without finishing their degrees.

By the way, graduate school funding packages often involve being a graduate teaching assistant, or sometimes there is a requirement from the department that you teach at least one semester during the course of your Ph.D. Would you feel comfortable standing in front of a class and leading discussion sessions? I am not trying to discourage you from pursuing graduate studies - I just think it would be great if you could work on the issues you have mentioned while you are still an undergraduate student.
posted by needled at 3:25 AM on June 2, 2016

Start spending time with the "real" math folks. Get to the talks by visiting post docs. and if you're in a university dense town get to talks at other campuses.

Also ask the same question over on /r/math I've seen good responses about the same general issues.
posted by sammyo at 3:26 AM on June 2, 2016

There are a handful of funded math masters degrees, mostly at places without PhD programs. (I randomly remember the University of Nevada Reno has one and apparently the University of Vermont funds masters students, but doesn't look like they guarantee funding. Same for Loyola University Chicago--some funding exists, but who knows how common it is. There are more than that though.)

What math classes have you taken? Having had a real analysis or abstract algebra class would go a long way towards figuring out if you're interested in math or the math-ier bits of theoretical computer science. That's something of a false distinction (except that sometimes people are talking about the same thing and not talking to each other because they're publishing in different journals and going to different conferences), but I think some discrete math people are going to be happier getting there from CS and some are going to be happier getting there from math. And, well, if you hate both undergraduate abstract algebra and real analysis, you're not going to want to go to math grad school.

I test well, so I think I could do well on the GRE.

As a heads up, the general GRE is pretty useless when it comes to applying to math programs, to the point that the received wisdom in my undergraduate department was not to study. (Everyone applying to math programs does stupidly well on the math section. They've re-normed the test since I took it, so it might be a bit better, but a perfect score was only like the 95th percentile.) The math GRE is mostly calculus and most people have to study for it to do reasonably well (unless you're a physics major or a TA).

By the way, graduate school funding packages often involve being a graduate teaching assistant, or sometimes there is a requirement from the department that you have taught at least one semester during the course of your Ph.D. Would you feel comfortable standing in front of a class and leading discussion sessions?

Unless the thought actually gives you a panic attack, you're not going to be any less comfortable than the average person. No one is comfortable when they start--we had, I think, two days of TA training.
posted by hoyland at 4:15 AM on June 2, 2016 [1 favorite]

Should I keep graduate school for math/computer science in the back of my mind? Would I do much math as a CS PhD?

So, I am a mathematician, and I have several collaborators who are effectively mathematicians, but who teach in computer science programs, and publish in a mixture of pure math and CS journals. So absolutely, there can be a lot of overlap between CS and mathematics. (My friends publish in, among other things, graph theory and discrete geometry.)

I absolutely encourage you to talk to your professors.

If you think you might be interested in a math masters program (which, incidentally, my school has one with funding) you should try to take real analysis and abstract algebra at a minimum, and topology and/or complex analysis would be nice to throw into the mix. (And combinatorics and/or graph theory, if you've not had it and are interested in theoretical CS).
posted by leahwrenn at 4:29 AM on June 2, 2016 [2 favorites]

I do have a major fear of participating in class (though this has gotten better this year) and talking face-to-face with professors

Graduate school classes are small and intimate. You need to like to hang out with mathematicians and others like yourself. You're allowed to be shy, though.

Theoretical computer science is really a branch of math. You prove theorems. In my grad school, masters programs were generally paid for by people's employers while PhD programs were paid for by the school often with teaching fellowships.
posted by Obscure Reference at 5:40 AM on June 2, 2016

My husband was a math major in undergrad who ended up doing a lot of random programming in his real world job. We moved, and he got another real world job doing statistical analysis on some stuff for a university. It is much lower paid that his previous job but the benefits are amazing and include free tuition at said university. So he is getting a masters degree now. First it was going to be in CS but then he switched back to some kind of statistical math. So, that's one way to do it.
posted by dpx.mfx at 7:19 AM on June 2, 2016

Echoing what other people are saying here, the theoretical edge of computer science and the applied edge of discrete mathematics are basically the same field. If you pursue a combinatorial specialty within math, you're well prepared to enhance future studies in either CS or mathematics.
posted by jackbishop at 12:09 PM on June 4, 2016