Advice for a prospective math phd

[upsidedowntop]

Hi,

I'm looking for general advice on quite a few topics related to grad school. I'll give you some background information and then ask the questions which I've been having trouble reaching conclusions about.

I am a senior at MIT majoring in math with computer science. During Sophomore Summer, I did undergraduate research in bioinformatics. I spent Junior year at Cambridge studying math. Currently, I'm working an internship in algorithmic trading.

I really enjoy school. I enjoy taking courses in math, physics, and computer science; and I enjoy even more talking to people about these subjects. I would love to stay in school for years to come. But, I don't really like doing research, or at least that's the impression I have from my summer of bioinformatics research. I really like teaching and studying. I would love to be a TA, tutor, grader. I already grade some of MIT's lower level math courses, and I really enjoy it.

There is no particular area I'm interested in. There are subjects I like more than others, but I would much rather study something I have no exposure to than to learn more about one of the subjects I have already studied.

So, I want to go to grad school because I will be able to help teach undergraduates and take more courses. But I don't really want to do research in or focus on a particular subject.

There is another difficulty in that if I go to grad school, I would like to go somewhere good for math. I'm already living in Cambridge, and my girlfriend already got into a masters program at MIT, so MIT and Harvard would be my top choices. I have a perfect GPA at MIT and I think I can get good references and do well on standardized tests, so I should have a good chance of getting into one of them. But, saying that I'm not really interested in doing research doesn't make my case.

There are more choices to be made. I've finished almost all of a math major, so if I change majors to pure math, I'll get to take about whatever I want as a senior. So, if I decide to, I could take a bunch of grad level courses in some math subject, and I could pretend to want to do research in that subject. But that's not very appealing to me. I would much rather take the half dozen medium level computer science courses necessary for me to finish the "with computer science" part of my major.

I also talked to the administration about taking a year off from school. The idea is that if I have another year, I can probably find a subject I'm willing to do research in for a few years. MIT would probably let me grade and tutor their courses, which pays well enough to live on, and I could use the opportunity to more firmly establish my understanding of basic undergraduate level math (linear algebra, analysis, abstract algebra, topology, calculus, etc). But if I can get into a phd program this year, I could just take courses in all those subjects, which would be easier than going over them again myself. And there is a chance taking a year off school will just turn into a wasted year, so I hesitate to go through with it.

Sorry for the long explanations. Any academic guidance you can give would be appreciated.

 

[micromass]

If you do research then you must really put your heart into it for 100%. If you don't like research, then don't bother going to grad school. It sounds harsh, but it's the truth.

I understand that your passion lies in helping students instead of advancing your own skill set, and I respect that very much. Maybe there are jobs available that only want you to teach and not do research itself?? I found such a jobs and I considered going into them...

Anyway, I can probably also say that you don't know what research is about. You had some bad experiences with research, but that doesn't mean that you won't like research alltogether. You must find a field that you are incredibly passionate about and where you really want to know more. You must enjoy doing such a research. If you don't enjoy it, then I don't think you'll make it

PS I forgot to answer your question. Maybe taking the year off isn't such a bad plan. You can think about what you really want in life and whether research will be really for you. You can also look out to nice teaching jobs that you might like...

 

[TylerH]

Maybe you should get a Masters degree, which, in some cases, doesn't require research. You would be able to teach at community colleges with it and possibly lecture at universities.

 

[deRham]

What TylerH said is a good point - you can find several teaching opportunities with a Master's.

A PhD in mathematics will be frustrating to you, probably. There's a large part of me that can't imagine 5 years of your life being spent that way without tons of regret, based on your post.

Taking a year off is fine if you plan to do a lot of soul-searching, which I'm always in favor of. Maybe you can try tutoring or doing something or the other that helps you teach like you enjoy, and talk to people.

and my girlfriend already got into a masters program at MIT, so MIT and Harvard would be my top choices.

I'm confused what is meant by "grad school" - if it's in CS or mathematics, often there are no masters programs. I'm pretty sure MIT doesn't do them for those fields, except perhaps for CS, a 5 year program for its undergraduates only. But I'd look this up. If it is a PhD in mathematics, then you want to look at way more schools than that. Harvard and MIT get zillions of applicants, including exceptionally brilliant international students whose main passion is researching mathematics. They are likely to have topped their classes in academics and standardized test scores, and also have done other impressive things - simply because research is where they want to be.

It's important to apply to a wide range of schools for PhD, where you can find your interests met.
Research as an undergrad may lie to you about what research will be. The important thing is to care a lot about a subject enough to want to learn. As you go up, you'll see ideas interlink, and the way you learn is partially by synthesizing what you know using research problems as a focus point. Usually you'll think about a lot of things and do a lot of independent figuring before you actually write a paper or something, which is generally a compilation.

But still, even with this description, it doesn't seem to be what you want - i.e. cornering yourself into some very specialized way of thinking (note - your research will be specialized, but it can very well involve a DIVERSE mix of topics, as long as they mix together in a significant fashion).Another remark - I think a lot of professions have places for someone who is an expert, who helps with so and so. Maybe some aspects of consulting.

 

[TopCat]

Certainly either of those schools in your area has a Master's in Education program? That would appear to be interesting to you given your post above, and doesn't require you to do boring research.

 

[Bourbaki1123]

Carnegie mellon offers a doctor of arts: http://www.math.cmu.edu/graduate/PhDprogram.html"

No original research required, only an overview of some relevant discipline.


Also, you could technically always get accepted to a PhD program with funding and quit after the masters degree if you still feel the same way after a couple of years. They might not be happy about it, but you could do it.

 

[upsidedowntop]

Wow, Thanks everyone. There is a lot of good advice here. I'll respond to each of you, but will refrain from quoting people since that would make for a ridiculously long post.

Micromass,
I'll remember your comment when I make the decision whether or not to go to grade school. Research is what PhD students do; if you don't want to do research, it doesn't make sense to become a PhD student.

"I understand that your passion lies in helping students instead of advancing your own skill set"
This I do not really agree with. I am passionate about learning and teaching. Of course research is a type of learning. But when you're working at the edge existing knowledge on a subject, it takes so much effort to learn just a little more. The most interesting and rewarding aspects of a subject are the first which you pursue, so as you learn more, the new information becomes less rewarding per your efforts. In research, it's a struggle for every little bit of information, whereas in learning what someone else has already discovered, the information is spoon feed you by the author. With the pure goal of learning more, it seems strange to me not to take the low hanging fruit first, but that indicates broadening my knowledge, not deepening it. Research would much better fulfill a desire for the later.

"Anyway, I can probably also say that you don't know what research is about."
This I do agree with. I'm not really concerned with "making it." That is, if you mean graduating. I'm looking for something that I want to do after undergraduate, a lifestyle, not a path to somewhere.

Tyler H,
I've considered studying for a masters, in science xor education. But this seems too easy to me. None of the upper tier universities I've looked at (Harvard, MIT, Stanford) have masters programs in math for non-matriculated students. The programs I've looked at else where (actually, I've only looked at UofMin and SDSM) didn't seem challenging. For example including Real Analysis 1 in the advanced math track to a masters of statistics seems a bit fishy to me. Masters in math education is even more... non-mathematical. I just looked at the degree requirements at NYU (a respectable school I should add), the only math was linear algebra, discrete math, geometry, and number theory. There were 0 advanced courses.

I will only commit to a masters program if I feel that it will be challenging.

I'll reply to the next three in a subsequent post.

 

[TylerH]

I've considered studying for a masters, in science xor education. But this seems too easy to me. None of the upper tier universities I've looked at (Harvard, MIT, Stanford) have masters programs in math for non-matriculated students. The programs I've looked at else where (actually, I've only looked at UofMin and SDSM) didn't seem challenging. For example including Real Analysis 1 in the advanced math track to a masters of statistics seems a bit fishy to me. Masters in math education is even more... non-mathematical. I just looked at the degree requirements at NYU (a respectable school I should add), the only math was linear algebra, discrete math, geometry, and number theory. There were 0 advanced courses.

You can get a masters in pure math an still teach. Both my calc I and II instructors did that. One of them was at a CC and the other at a small university as a lecturer. But be aware that they won't let you anywhere near the fun stuff. You'd be teaching "college" algebra and calculus your entire career, unless you went back to get a PhD. From the older of the two instructors, I got the sense that it can be quite demeaning to teach those subjects. He would actually make snide remarks about how simple the other math classes he taught were compared to the calc class I was in. (The remarks were to us, the calc students. I don't think we was rude enough to talk to the students of those classes like that to their faces.))

 

[jbunniii]

I'm not really concerned with "making it." That is, if you mean graduating. I'm looking for something that I want to do after undergraduate, a lifestyle, not a path to somewhere.

You don't want the graduate admission committee to know that you are looking for a "lifestyle, not a path to somewhere." To be admitted, you have to persuade them that you are likely to complete their program successfully.

However:

There are people like you in Ph.D. programs all over the US. You can spend quite a few years in most programs without doing much/any research before they will get around to kicking you out.

You will have to pass your qualifying exams, but if you can get that far, you can probably get away with staying around for several years after that, perhaps with a change of advisers or two.

If your end goal isn't necessarily to obtain a degree but just to stay in school and learn a lot of math, this path might work perfectly well for you. Also, in most departments you will be able to leave with a master's degree as a "consolation prize" as long as you took a certain number of courses and passed a qualifying exam or two.

 

[upsidedowntop]

deRham,
It looks like we have a second vote for the opinion: "If you don't want to do research, don't pursue a PhD." Like I told Micromass, I'll keep your comment in mind while I make the decision.

"I'm confused what is meant by \"grad school\" - if it's in CS or mathematics, often there are no masters programs."
While what you say is true of masters in mathematics, I don't think it is true in CS. None of MIT, Harvard, or Stanford offer Masters in Math; but as far as I can tell, all three have masters in CS. My girlfriend is doing the 5 year masters as a continuing undergraduate, which is how she "already got in." You get admitted automatically, assuming your GPA is high enough at the end of Junior year.

"Harvard and MIT get zillions of applicants, including exceptionally brilliant international students whose main passion is researching mathematics."
I'm familiar with how competitive admission to those two schools is. I interact with their grad students quite regularly; they TA my courses. Harvard and MIT share an outdoors club and dance team (they only kind of share the dance team); I've meet grad students from both schools through those organizations. Yes, they're good at what they do, and they care about what they do. But they're by no means mind blowing. Harvard accepts 11% of their math PhD applications. I imagine MIT is similar. It's competitive... but not that competitive. I have a friend that got into MIT's math PhD without majoring in math or even taking any theoretical math courses (She did Aerospace Engineering).

"It's important to apply to a wide range of schools for PhD, where you can find your interests met."
While I see the benefit of researching a lot of schools to find one that fits my interests, I don't see how applying to numerous schools helps me find a better fit. Admittedly, with each additional school you apply to, you increase your chances of getting into one of them. But getting in isn't really my priority. I'm pretty confident that if I find a school and program and fit my interests, that I'm excited about attending, that I won't have trouble convincing them to let me attend. If I'm not excited about what I would be doing at a school, I'll have a hard time convincing them to let me attend. Either way, the number of schools I apply to doesn't factor into my utility much.

"I think a lot of professions have places for someone who is an expert, who helps with so and so. Maybe some aspects of consulting."
I'm currently interning as an algorithmic trader. They certainly prefer people with diverse skills to specialists. For different models they use differential geometry, stochastic processes, Bayesian and classical statistics.. It's important to solve the PDEs that result in a limited number of milliseconds, so numerical methods is important. Additionally, all the models have to be implemented with keen attention to processing time, which makes a good understanding of system architecture and algorithms important. If you want a team of a dozen people who together can work in all those areas and review each others work, you need at least some of them to be broadly knowledgeable.
However, most such positions are primarily open to PhDs and PhD dropouts. My impression is that the extra years of study and research do make a big difference in how capable one is.

TopCat,
If I wanted to teach pre-university math, I would do an MS in math. I would rather learn math than pedagogy.
I don't really think research would be "boring"... just hard and frustrating. I think it's a worthwhile and noble pursuit, but it's just so much effort to discover so little.

Bourbaki1123,
Regarding DofA in math, it's a wonderful suggestion! I didn't know such a degree existed. I am much more excited about compiling, structuring, and organizing other people's discoveries than I am of making my own.

The idea of starting a PhD and dropping out after the qualifying exams had occurred to me. One of the downsides to a masters is that you usually don't get to TA. The first 1-2 years of a PhD is essentially a masters + TAing, so it's tempting.
That feels a little dishonest to me though. It seems like I should be able to find a suitable plan that doesn't involve misrepresenting myself. Thanks for the suggestion anyway though.

Tyler H (round 2),
I could get a MS and still teach. But, it would still be hard to get a job lecturing university level math. Teaching calculus would be fun if I were allowed to use a liberal amount of epsilons and deltas. I'm pretty sure that most states disallow teachers from using of more than 3.2 epsilons per semester though. I think I'm out of luck.

You'll have to forgive the sarcasm.

 

[jbunniii]

I could get a MS and still teach. But, it would still be hard to get a job lecturing university level math. Teaching calculus would be fun if I were allowed to use a liberal amount of epsilons and deltas. I'm pretty sure that most states disallow teachers from using of more than 3.2 epsilons per semester though.

Not necessarily - I went to a private high school and took honors (not even AP) calculus. It was epsilon-delta rigorous from start to finish. Most public schools are probably a different story, but I'm sure there are some good math-oriented charter or magnet schools out there somewhere, e.g. Stuyvesant High in New York City:

http://stuy.enschool.org/apps/pages/index.jsp?uREC_ID=126659&type=d&termREC_ID=&pREC_ID=253269

 

[deRham]

It's competitive... but not that competitive. I have a friend that got into MIT's math PhD without majoring in math or even taking any theoretical math courses (She did Aerospace Engineering).

No, that's a mistake it's easy to make. Your friend is atypical. Further, MIT has plenty of people studying applied math - a third or so of their Mathematics PhD students are applied. Your mistake is that you took the exception. Is your friend studying pure mathematics?

For, I can also tell you of people who spent 4 years excelling in mathematics at top undergrad schools, with straight A's and exceptional standardized testing scores, along with solid efforts at work under professors, strong rapport with famous ones, who didn't get into MIT's math PhD. It is generally very hard to get in. But sometimes you hear about cases that make you pause.

Generally, people who apply successfully to competitive pure math PhD programs with a good chance are math majors with very strong background.

Harvard's math program is typically 10-12 students in size, from their website. Given the international competition, I can't see how this isn't very competitive.

While I see the benefit of researching a lot of schools to find one that fits my interests, I don't see how applying to numerous schools helps me find a better fit.

It's because if you do your homework, you'll find there are more places that meet your needs than you would initially suspect. I once thought as you did, and I'm pretty steadfast in what I want to do (making it less likely I'd be satisfied at any school good at math). Know the major professors who do work in your field of interest, and trace where they now are.

Yes, applying widely is to increase chances. But don't make the mistake of assuming applied widely means succumbing to a worse fit.

Why do people make that mistake? Because they assume that if they want to find a good fit, they should limit the number of schools they should consider. WRONG. You should limit the number of advisers you want to consider. And that often means including more schools, but realizing that only some of the professors at those schools meet your needs.Yes, you are right that I more or less vote for the opinion - if you don't want research, don't pursue a PhD. However, I'll slightly soften that statement. I'll say if you want to be TRAINED to be a researcher (for, as math professors often say, that, and not learning, is the goal of the PhD), then go for it. Perhaps some of the non-academia professions you mentioned would value that kind of training.