What Is Research?

March 29, 2008

Frequently (?) asked questions

Filed under: Advice and information,Places and events — vipulnaik @ 2:37 pm

Yesterday, I went and attended a “panel” held at the Chemistry Department about science students who’ve gone on to unconventional careers related to science, outside both academia and industry. A few weeks ago, there was a panel discussion between us grad students at the math department and four post-doctoral students. And I’ve been watching some panel discussions on videos on the web. Based on this, I’ve started getting a feel of what the Frequently Asked Questions are in panel discussions. So I’m just imagining that I’ve been invited to a panel discussion, and the audience is now asking questions, and I’m trying to figure out what answers I’d probably give.

By the way, if any of the readers has a question that isn’t answered here, put a comment stating your question (or send it to me) and I’ll add my answer to that to this post.

How does life as a student in the United States, differ from life as a student in India?

I’d have to confess to very limited experience on both counts: I completed undergraduate studies at Chennai Mathematical Institute (CMI), and am currently doing graduate studies at the The University of Chicago. CMI isn’t the most typical undergraduate institution in India, and I haven’t been long enough at the University of Chicago to udnerstand exactly how the system works.

From what I’ve seen till now, one key difference is the emphasis on assignments and homework. In CMI, we didn’t have a whole lot of regular assignments. Most subjects had at most 3-4 assignments a semester, and there wasn’t a very strict rule about when to submit assignments. There certainly weren’t any graders and teaching assistants: all grading was done by the instructor herself or himself, so the motivation to give assignments was less.

In the University of Chicago, there is a lot of emphasis on regular assignments and regular testing. Apart from the teaching sessions, there are also separate sessions where the teaching assistant helps sharpen the students’ problem-solving skills. In short, there’s more activity. Most of the assignments (as far as I can see) aren’t deep or creativity-inspiring. They’re largely mundane, with a few gems. The goal, from what I can make out, is to give students a lot of practice and a lot of experience in writing solutions.

Moreover, all assignments are graded by the teaching assistant, rather than the instructor. So there is a full-time involvement of two people in teaching a course, rather than of one person. Both teaching and learning is a more hectic and intense activity.

Another difference between life in CMI and life in the University of Chicago is the size and diversity of the place. CMI was largely an “only-math” institute. There were only three subjects of study: mathematics, physics and computer science. Even within these subjects, the number of people doing research and the amount of active research was fairly low. In the University of Chicago, on the other hand, there are researchers of all stripes. There are a whole lot of Ph.D. students. And there are also researchers in other disciplines, and there are a whole lot of facilities apart from those geared at research (including an athletics center, a bookstore, some huge libraries, an office of international affairs, and many others). There are more festivities and occasions and activities outside academics (just as there’s more activity within academics).

How does graduate life differ from undergraduate life?

Again, I have limited experience in this area. Broadly, I’d say that in undergraduate life, the focus is on learning a lot of different things, on scoring well, on getting a good idea of mathematics, and on developing credentials that’ll impress graduate schools. There’s also a strong element of competition with others in the same year, because there are far more undergraduates than the number of openings at graduate schools. In other words, just as much as it matters how good you are on absolute terms, it also matters (at least, to some extent) how you compare with your immediate peers.

In graduate school, this element of competition is probably less. Of course, the number of post-doctoral openings is significantly less than the number of people who do a Ph.D., so there is still strong competition. However, the competition now is not so much against your immediate peers in your specific institution. Applications beyond graduate studies are fairly specialized, so people with different mathematical interests are likely to be seeking different jobs at different places under different scholarship schemes. Thus, the element of cooperation is probably more.

Graduate school also brings with it a host of teaching responsibilities. Undergraduates are largely responsible or answerable only to themselves. Graduates, who are also involved in teaching duties, have to balance their research with their teaching requirements.

Finally, graduate studies, at the end of the day ,requires a Ph.D. You don’t get a Ph.D. for general knowledge in mathematics. Rather, a Ph.D. is contingent on solving one or two specific problems, usually problems that extend things that have already been studied by the research community or problems that would open the way for new ideas. So graduate studies isn’t just more of the same undergraduate studies. It requires going deep into some area and struggling hard to solve problems, often giving up and returning again.

In what ways did your undergraduate education prepare you for graduate school, and in what ways do you think you were underprepared?

As far as basic mathematical knowledge is concerned, I’d say that my undergraduate education at CMI, combined with whatever I had read on my own, prepared me fairly well for graduate studies at the University of Chicago. Of course, one can look back and say: I wish I had done a course in algebraic topology or if only I had taken a course in functional analysis. But many of my friends who are from leading American univerisities, also hadn’t taken such courses in their undergraduate years, so I do not think I was significantly disadvantaged in a uniform way, as far as coursework was concerned.

That said, I’d say that considering that the CMI course is three years long, while that in most American universities is four years long, there are elements of detail that aren’t covered in CMI courses. Secondly, because we didn’t have to do too many assignments, I didn’t brush up my calculus skills at the undergraduate level. Thirdly, my impression is that CMI’s focus on analysis is low, and this was one of the factors that made me find analysis disproportionately harder.

However, what I value most about my undergraduate life is that it gave me the freedom to explore in mathematics and it was during those years that I started forming my interests. It is possible that if I were subject to a hectic system of assignments, I would not have been able to explore so much and develop the specific interests and viewpoints within mathematics, that I did. On the other hand, it is also possible that a more hectic and challenging course structure could have brought out more from inside me. I don’t know.

Undergraduate program(me)s in the United States are four years long, while the typical duration for a B.Sc. in India is three years. Is this a disadvantage?

It really depends on the specific nature of the undergraduate course. An honors course that covers most of the prerequisites needed for graduate school, is good enough to satisfy most US graduate schools, though some of them have a strict four-year requirement.

However, it is true that B.Sc. courses offered at most institutes in this country do not cover enough material to start a Ph.D. with. In that case, doing a M.Sc. is advisable before applying for a Ph.D.

Why did you apply for graduate studies to the United States? How do options in the United States compare with those in India?

I was specifically interested in the University of Chicago, though I did apply to many other graduate schools in the United States (some of which turned me down as well). My interest in the University of Chicago arose because of two factors: the overall reputation of the University, and the presence of two group theorists: Professors Alperin and Glauberman. It didn’t hurt that some of my seniors and other acquaintances were already at the University and had given me positive reviews of the place.

On the whole, I’d say that if you can do it and are keen on pursuing doctoral studies, then universities in the United States are a good option. Being in the United States isn’t a magic cure. But there are certain factors about the United States universities that set them apart. First, a reasonably large university in the United States will have people doing research in diverse topics, so there is enough scope to interact with a lot of different styles of doing mathematics. Second, there is a culture of hardwork and commitment, and the opportunity to acquire skills in teaching, presentation, research, and forming mathematical communities. Third, there are also good opportunities to interact with other departments.

In India, Tata Institute of Fundamental Research is a place where high-quality research is done in mathematics and a number of other science subjects. It’s small compared to a place like the University of Chicago, but may be among the best choices in India. The Indian Institute of Science has a greater diversity of subjects, but its mathematics department is relatively smaller. From what I’ve heard, the mathematics department is expanding. The Institute of Mathematical Sciences is a good place to pursue doctoral studies in mathematics. The other subjects here include physics and computer science, and all three departments are fairly good.

Nonetheless, an opportunity to study in a top-range or mid-range US university for a Ph.D. can prepare one better for the challenges of research (in my opinion).

What are the pros and cons of pursuing undergraduate studies in the United States as against in India?

The pros:

  • Easier to get admission to top-quality graduate schools
  • More rigorous and challenging coursework
  • Greater interaction with other disciplines, the option of doing a double-major, the option of studying a lot of subjects on diverse areas
  • Greater opportunities for undergraduate research, and the opportunity to interact with cutting-edge researchers during day-to-day coursework


  • Making a move to a new country at a younger age could be harder. There is less interaction with the family, and it could be harder to make friends.
  • If you ultimately plan to return to India, it’s also important to understand the structure of research and education in India. My stint as a student in CMI gave me a fair idea of what goes on in India. So I’m better equipped to return to India at a later stage.
  • The coursework could get really hectic, and making a transition between the exam-based style of learning in India and the assignment-intensive style of learning in the United States could be hard.

None of the cons, however, is totally unavoidable. In other words, by being aware of the possible cons, one can plan to minimize their effect. Thus, if you plan to go abroad, start preparing for it psychologically, physically and mentally a year in advance. It’s not the quantity of preparation as much as the mental transition needed.

Similarly, if you want to go abroad for undergraduate studies, but want to stay in touch with the research opportunities in India, this too is not hard, if you’re aware of it.

The most important thing to remember is that just after high school, we could be pretty impressionable, and may get swept off by the assignment-intensive style of doing things, losing out some of our skills and approach. So it is important to keep in mind that there are a wide variety of different ways of learning and approaching a subject. While joining a University, one must abide by and work with the rules of the system. But that doesn’t necessarily mean that one needs to embrace that system in every way. One can try to keep the best from all the different systems of learning one has seen and learn in a way that is most suited to one’s personality.

Is the money you receive sufficient to meet your expenses in the United States?

The University of Chicago offers a fairly generous stipend, which is considerably more than enough to meet day-to-day expenses. Though stipends vary widely across Universities, mathematics departments by and large offer stipends that can cover living expenses reasonably well, and probably allow you to save money.

For undergraduate studies, the situation is somewhat different. Students from India usually get tuition waivers, but scholarships that more than cover the expenses are relatively rare. I don’t know much about this, though.

How does the United States compare with Europe?

Europe and the United States differ in various respects, but again I don’t have much firsthand experience of studying in a European institution. One difference is language. A second difference is probably culture. The core American system is based on hardwork and the testing pattern is usually assignment-based. Students are actively involved with teaching and learning. In Europe, the system of scholarships, stipends and other stuff works differently.

If there was one thing you wish you’d known before beginning graduate studies in the University of Chicago, what would it be?

It would probably be that even though the system of evaluation and the structure and setup is different here compared to what I’m used to, the fundamental values remain the same. These are the fundamental values of being sincere, hardworking, creative, and cooperating with others. The fundamental principle is to be honest to oneself, to have faith in one’s abilities, and to have fun and find one’s equilibrium in a new climate.

I cannot really say I suffered here; I did pretty well in the first two quarters. But during the first quarter, I was somewhat stressed because of the expectations of the new system with three assignments a week. It took me some time to come to terms with this and to find joy and fun in my day-to-day activities. I’d encourage everybody who goes to a new learning environment to not be blown over by the superficial differences and to know that in the end, it is good fundamental values that triumph.


  1. Was happy going through the blogs..I felt the question of comparison between US and Europe unnecessary.Well i would feel glad if you answer to this question..a more familiar one

    Can indian students applying for graduate course not so bright in Mathematics(but have interest..like me)..cope up with the environment there?

    Comment by Chandrasekhar — April 1, 2008 @ 6:36 am

  2. It usually depends from person to person. I don’t see anything very difficult to cope with in the US environment, but still, it is very far from India so some time is needed to adjust to the new place, the culture etc. Secondly, you may not have a support system of family and friends in the United States.

    In my experience, it is not the level of intelligence of a person that matters as much for research as it is the level of dedication and interest in mathematics, and the internal strength and energy they have to cope with new situations. Smart people who do not have the same love and dedication for the subject find it harder to cope with the challenges of a Ph.D. program than people who may have fewer problem-solving skills, but are keen to d otheir best for the subject.

    If you feel your B.Sc. course has not prepared you well to apply abroad, then stay in India for a Masters or apply for a Ph.D. program in India, and you can later decide whether to apply abroad.

    I’ll integrate some of these things into the post in due course.

    Comment by vipulnaik — April 1, 2008 @ 1:04 pm

  3. sibyl says : I absolutely agree with this !

    Comment by sibyl — May 28, 2008 @ 3:31 pm

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