Applying to grad school may seem like a long and complicated process, but we will attempt to present a clearer approach here.
It is evident that in order to achieve the best possible result from grad school applications, you should first rank graduate programs in order of personal preference, and then do everything possible to be accepted into those that you listed highest. In this guide it is assumed that you already have your personal preferences sorted out, and that it only remains to increase your chances of acceptance.
Your one take-away from this guide should be that graduate programs look for these categories, in order of importance: (1) Recommendation letters, (2) GPA, (3) GRE test scores, (4) Personal statement, (5) Extras (to be described below).
These components will be addressed in order in the sections below.
Contents
Recommendation letters
A good recommendation letter is determined by (a) how well the professor can attest to your academic strength in a research context, (b) the renown of the professor, and (c) how good the professor’s opinion of you is. Obvious steps that can be taken to improve these characteristics are taking lots of their classes (if you are a sophomore/junior) and asking them to chat over a meal, and of course asking them to be a research advisor! Applications require 3 recommendation letters, and students typically ask (a) their senior thesis advisor, (b) an REU/summer research advisor, and (c) their junior paper advisor or another professor from classes to write their letters, though this is not a hard-and-fast rule.
In terms of logistics, it is good practice to ask your letter writers 3 times: once in person end of junior year (for politeness), once more by email near September (to remind them), and lastly right before you send them all the links (to give them deadline information). It is good practice to give your writers a full month’s notice to write their letters.
GPA
There’s not much to be said here, other than the fact that grad programs probably don’t look at your non-math GPA very heavily. You should also give as much information as possible on the application forms, if there is room to describe your courses – many Princeton 300+ level courses are common graduate courses elsewhere, so it’s worth mentioning the textbook you use. Specifically, nearly all 400 level courses are graduate courses at almost all other colleges, including other top schools such as Columbia and Brown.
In terms of logistics, most grad programs WILL accept the unofficial version TigerHub. For those that require a mail version, this can also be requested on TigerHub.
GRE test scores
See the page that’s entirely devoted to the GRE.
Personal statement
This doesn’t need to be a spectacularly fancy piece of writing. It should show that you can write in English with decent grammar and vocabulary. The format can be varied but I found a letter format was easiest.
You should cover (a) what you thought about your math courses, while also explaining any holes or strengths in your transcript; (b) your research experiences; (c) your expected field of interest (naming a specific field is preferable to saying “undecided”); (d) how this particular graduate program appeals to you. If you so desire, feel free to (e) describe what you think your research strengths are; (f) sparsely mention professor names at Princeton and at the target school; (g) (La)TeX it.
To explain (d) it helps to ask around other schools for what the “feel” of their program is like. To give some brief examples, Stanford is particularly strong in geometric analysis and algebraic NT; Princeton is particularly strong in harmonic analysis, analytic NT, and probability; MIT is particularly strong in combinatorics; NYU Courant is particularly strong in PDEs; Columbia is particularly strong in geometric analysis.
In terms of logistics, once you write up your first one, you can resort to changing (d) and (f) while leaving the rest the same. Thus, a worst-case procrastination schedule is: ~2 weeks before your first deadline, write up a version and ask a friend to suggest some edits; correct and re-edit over 10 days; write up the (d) & (f) changes ~2 days before each deadline.
Deadlines start in late November/early December. The start of winter break / end of the Fall semester is usually when seniors submit a majority of their applications. And as always, START EARLY!!! :)
Make sure to contact the departmental senior advisor (currently John Pardon) if you have questions regarding graduate school applications and associated fellowship apps.
Extras
“Extras” to your application include Putnam and IMO performance and published or submitted papers. These do add to your application, and can be listed in a brief resume (there’s usually a spot on the application form for one).
We hope this helps clear up some confusion, and good luck!
(This page was originally written by Bowei Liu ’13, with minor additions by Sumanth Maddirala ’22.)