FAQ about gradschool applications

Before COVID 19, American schools asked for the GRE (general) and the TOEFL/IELTS. Some schools asked for the GRE subject as well.

GRE (general and subject) was not required by most universities when I applied, due to COVID. TOEFL/IELTS/Duolingo score was still needed as a proof of English. Some schools were happy to substitute these English tests with a proof that your college instruction was in English. Also please find out which of these scores your university accepts.

Please find out if your universities of interest ask for the above exams, because there was already some discussion in many university to simply not have the applicants take the GRE.

Check the ETS website for more details. Here are the links for finding more about GRE (general) and the TOEFL.

It also costs $27 to send the GRE (general) score and $20 to send the TOEFL score to each university.

Here is a list of steps with the general guidelines. Point (1) in the answer does not apply to BSc students applying for a PhD.

US PhDs generally require candidates to have a 4-year (undergrad) degree before applying. Of course Masters students can apply (because they'll have completed 5 years of education). However, there are exceptions to this 4-year rule. If your undergraduate degree is strong enough, you can apply to almost every university (modulo some constraints). These exceptions always include the Chennai Mathematical Institute and the Indian Statistical Institute.

Some universities might ask for a proof of equivalency of your 3-year degree with their 4-year degree. In such cases, you might have to avail services from agencies like the WES or Scholaro. There are many more websites which provide similar services are are equally good (however your university might recognize some but not others). They will most often charge some fees (I had to pay $100 in one such case).

It is always better to directly email the graduate director (or secretary) of your department of interest to ask if such a certification is required. The information you find on the application websites (of the universities) are often outdated. Or it is also possible that someone from your institution had already submitted such an evaluation, in which case your institution is recognized to give a degree equivalent to theirs.

Always start early. These are my suggestions assuming that the earliest deadline is December 01 of the year before you'll be starting your graduate studies.

• Summer: Ideally you should do away with all your tests during the summer, so that you can concentrate more on the other parts of the application. But it's possible to do the tests later too.
• July: Start looking for universities. Go to different websites and get a list of 200-300 universities and departments. Start looking for their degree and testing requirements. Organize in an excel sheet.
• August: Finalize the names of your recommenders and contact them. Refine the above list of universities - based on the faculty present there, your 'research' interests and other requirements. (Advice: Make sure you apply to all "tiers" of places - for example, don't apply to just MIT, Harvard, Princeton and Stanford). Start writing your Statement of Purpose (SoP).
• October: Refine your list more. Add/subtract universities, if needed, based on your budget and the number of recommendations you are getting. For example, a couple of my recommenders asked me to limit to 12-14 places for them. Assign recommenders to universities. Most US universities ask for 3 letters. Edit your SoP and make a CV.
• November: Finalize your SoP and CV. Send to your recommenders a final list of places you want them to write letters to (containing university name, subject, course, deadline).
• December to February: Submit applications to universities. Edit your SoP and CV if needed.

• Apply to Europe (to masters if you're in your bachelors, or to PhD if you're in your masters) - these universities mostly have zero application fees and also dont ask for official TOEFL/IELTS and GRE scores.
• Try to find if any university in your list accepts an alternate proof of English - for example, a certification that your undergrad/master was entirely taught in English. You can save $20 per such university for the TOEFL/IELTS scores.
• Try to avoid sending your GRE scores unless it is mandatory or it enhances your profile. You'll save $27 per university.
• Email the graduate director and ask if you can apply now (with unofficial test scores - no cost) and send the official scores after you've been admitted.
• Email the graduate director and ask if there are any application fee waivers or reductions. Rarely, this might be mentioned on the application website. Also ask if it is ok to submit your application for now and pay the fees once you've been admitted.
• Finally if you're desperate to reduce the total cost, simply apply to fewer universities.

I applied to departments outside math as well.

For fun, I applied to the Applied Math programs at Princeton, Harvard, Stanford, Yale, Brown, Columbia, Cornell. All of them rejected me. I paid for only three of them.

For the same reason, I applied to the Computer Science programs at TTIC and CMU. Both rejected me (TTIC called me for an interview, though). I paid for none of them.

I applied for the math programs at 17 places. 4 of them were in Europe, the rest in the US. I paid for thirteen of them.
Accepted by Rutgers, Oregon, MSU, NCSU, BMS, ALGANT.
Waitlisted by Notre Dame.
Rejected by Toronto, Michigan, Rice, Purdue, IST, Virginia, Brandeis, Oxford.
I had withdrawn from Northeastern, Boston University.

(suggested by Amik Raj Behera)

• A collection of advice from CS professors.
• A detailed report.
• A talk for gradschool suggestions.
• How to write an SOP. Link 1. Link .
• Asking for a letter of recommendation.

• Have a personal webpage with some writeups, lecture notes, presentations of your own and put this link in your CV. (helps in computer science).
• Talk to a lot of seniors about your application, places to apply and their personal suggestions. None of the personal suggestions is set on stone because there is no definite way a graduate hiring committee (in math) works. It is upto you to do what you think is best.
• Find abuot the research of your prospective advisors. Most math profs have outdated webpages, look for alternate ways to find about their current research. You can look up arXiv, Google Scholar and similar websites. Or simply email them.
• Talk to recent passouts/current graduate students of the department to know more about the current research directions of the department and the professors there. This is a good alternate to know about the research of the professors.
• It seemed to me like US universities like to see some `published' work - something which has been checked by some mathematician. This is just to see how developed your mathematical writing is and judge your research experience. I'm not saying it's a definite game-changer, but just an observation I made.

Note that stipends are taxable.
The stipends below are approximate.

Department (Mathematics)	Stipend (in 1000$)	Payment duration (in months)	Per month average ($)
Princeton University	40	9	4450
MIT	36	9	4000
University of Washington	33.6	11	3050
Northwestern University	36	12	3000
Rutgers University	30	10	3000
Washington University St. Louis	29	11	2640
University of Utah	23	9	2550
University of California San Diego	30	12	2500
University of Minnesota	22	9	2450
University of Oregon	20	9	2220
North Carolina State University	20	9	2220
Michigan State University	20	9	2220
University of Texas at Dallas	18	9	2000