First, a little note about myself. I am in the third year of the B.Sc. (Hons) Mathematics and Computer Science course at Chennai Mathematical Institute. I am keen on doing further research in mathematics, though I am open to the possibility of switching to computer science. After completing my degree at CMI, I plan to join for an Integrated Ph.D. programme at a place that offers great resources and guidance. Hence, this year, I am applying to places. Given the current distribution of good research universities, most of the places I am keen on are in the United States, but there are a few in India.
Currently, I don’t have a very narrow area of interest/focus, and I enjoy a lot of the mathematics (as well as some complexity theory from computer science) that I have been exposed to. However, one area that has particularly caught my attention is group theory, and finite group theory in particular.
Universities that I am considering right now: University of Chicago, MIT, Princeton, Harvard , Caltech, University of Pennsylvania, and Wisconsin. Others such as Michigan, UIUC and Berkeley seem ruled out due to a four-year rule (they require four years of post-secondary college education). I’m not completely sure, though — I hope to confirm things further before ruling them out fully.
In my attempt to narrow down and decide which universities to apply to, I talked to Professor Ramanan, who works both at CMI and at the Institute of Mathematical Sciences. Professor Ramanan gave me the following pieces of advice:
- On places to work in: There are two aspects. First, the place should accept me (be willing to take me in). Second, I should find an environment and faculty there to help me pursue my area of interst.
- On how to look for an advisor: Professor Ramanan suggested I look for an advisor who has done a lot of good work, and is middle-aged (in mathematics, middle-aged means around fifty). Somebody too old may not be interested in taking new students and pushing them, and somebody too young may not have that much experience behind him/her.
- On what the places look for while admitting students: The Graduate Schools are experienced — they look precisely for the qualities that make for a good researcher. These are the twins of focus and flexibility. Focus means the ability to zoom in on a specific topic and give one’s whole heart to it. Flexibility translates to the ability to change gears, change one’s area of focus, allow oneself to get interested in a new topic based on attending a seminar. Great mathematicians have done great work in one subject, then migrated to another subject based on a sudden fascination, and done great work in that subject.
Recently, I was reading the book How you can get richer.. quicker by M.R.Kopmeyer. He gives a very important piece of advice, that makes a lot of sesne for graduate school applications. Here’s the advice:
- Figure out what they want, and give them more of it.
- Figure out what they don’t want, and give them less of it.
To figure out what a Graduate School wants, it is enough to look at what they ask for. Below, I review the typical components of a graduate school application, and give my own opinions on what the School wants in each component.
Components that involve scores/grades/marks, where the direction of improvement is clear:
- GRE general scores: These are important to the Graduate School as they indicate basic verbal and quantitative abilities. The Graduate School wants students with a reasonable vocabulary (Verbal), reasonable passage comprehension skills (Reading Comprehension part of the Verbal), good quantitative skills (Quantitative), and the ability to analyze and express thoughts (Analytical Writing). It is also obvious why they want these skills — they are necessary for practically all academic work and social living. I believe that a score of 700+ (out of 800) in verbal, 800 (out of 800) in quantitative, and 4.5-5.5 (out of 6) in the essay/argument is good enough to give them what they want.
- GRE subject test scores: I haven’t investigated the Subject Test much, but its basic utility, so far as I can figure out, lies in its being the only objective way of evaluating the student’s aptitude in the subject. Its again not a big puzzle what the Graduate Schools want: people who are better at the subject. From what I’ve heard, I believe a percentile of 90+ is good enough to giev the graduate school what it wants.
- TOEFL scores: Listening, speaking, reading and writing are the four ways we send and receive information, and these are precisely what the new Internet-based TOEFL tests. While TOEFL scores in general are not so important, a good TOEFL score could be a plus point while applying for teaching assistantships. Basically, the Graduate Schools are looking for people who can handle the medium of instruction — English, with ease. Because the TOEFL pattern has changed, I’m pretty unclear of how much the Graduate School really wants.
- Grade point average: Performance in the undergraduate academic institution counts for a lot, particularly in the subjects that I intend to pursue for further study (in my case, Mathematics) and in secondary subjects related to it (in my case, Computer Science). Apart from using these to judge the student’s academic ability, the Graduate School also wants to learn, from the grades received by the student, his/her ability to survive in and cope with an academic evaluation system. Universities in the United States give GPA out of 4.0, and they expect the GPA to be around 3.7 or more, so that translates to above 9 on the 10 GPA scale used in CMI. You can check out my own academic record here.
In the coming points, we start moving away from what the Graduate School wants in terms of ability to what the Graduate School wants in terms of personality. Here are components that depend on past academic choices and skills demonstrated:
- Courses taken: The choice of courses that the student takes reflects the student’s interest and willingness to take up challenges. A senior told me that taking up a worthy course and getting a somewhat poorer grade counts for more than taking an easy course and sailing through with a good grade. Another senior told me that the entire pattern of courses a student takes determines the picture the student conveys to the Graduate School.
Prima facie, it is unclear what kind of picture the Graduate School wants, or does not want. Whereas in the earlier four requirements (GRE general, GRE subject, TOEFL, grade point average), the direction of improvement was clear, here it is not. In fact, I don’t think there is any ideal pattern of courses for each student to take. Rather, the pattern of courses should fit in with other components of the student’s application, such as summer projects, extra achievements, and Statements of Purpose.
- Summer projects and summer schools: How the student spends his summer indicates not just the student’s talents but also his/her choices, priorities, and goals. A research life is a lot about choosing one’s topic and devoting time to it.
Also, a student can, in the summer, hope to put in a much more focussed effort towards learning a topic, mastering a paper, or attempting an unsolved problem, that would not have been possible during term time. My seniors have told me that a person whose summer programmes are synchronized towards a clear and focussed goal stands a better chance of admission to any graduate school. The reason: graduate schools seek students with the ability to focus, and the best indicator of such ability is a past record of such focus.
- Extra achievements: While graduate schools do look for focus, they also look for a personality with wide-ranging interests. This means that extra achievements, extra activities will be viewed favourably by graduate schools if they indicate commitment to a cause, the ability to work hard, and the skills needed to succeed at arduous tasks.
What graduate schols do not want is a string of impressive-sounding achievements in what they consider to be inconcsequential settings. Interestingly, the same achievement can be cast in terms that provoke very different reactions from the graduate school. The student needs to highlight what he/she put in and what he/she learned or gained. The graduate school seeks a person with certain qualities, and achievements are important only insofar as they highlight the necessary qualities.
Personal statements of the student and of others who know the student:
- Statement of purpose: Summer camps, extra prizes and honours, extracurricular activities, courses, course grades, are all just facts. The real personality comes through in the Statement of Purpose. This is not some test that the Graduate School subjects the student to in order to test his/her essay writing skills. Rather, it forces the student to clarify what he/she wants from the Graduate School and is willing to give the Graduate School. As I read in a book Wanna Study in the U.S., the Statement of Purpose should show the student’s life as a painting in the making, with the next stroke on the canvas being the student’s admission to and entry into the Graduate School.
- Letters of recommendation: This is an aspect of the application over which the student, apparently, has least control. Some recommenders prefer not to let the student see their recommendations, leaving the student in the dark as to how he/she is placed with respect to the possibility of admission. Like the Statement of Purpose, this component could make or break an application. I think what the Graduate School seeks from recommenders is confirmation of the student’s ability to fit in the bill for research life.
Here’s my overall feel: graduate schools are looking for people who are willing and capable to do research. Tests go only so far as to show ability, while personal choices show both willingness and ability. And the statements of the student and recommenders go further into showing both the willingness and the ability.