The sum­mer pro­gram at Prince­ton funds eight weeks of on-campus math­e­mat­i­cal research and/or guided inde­pen­dent study. Any eight weeks dur­ing the sum­mer will do, pro­vided you can make arrange­ments to work with your adviser dur­ing that period; they do not even have to be con­tigu­ous, so you could for instance, work for four weeks in June, then leave for a cou­ple of weeks and return to fin­ish the pro­gram in mid-July. Over the past two years, the pro­gram has pro­vided $4000 stipends to approx­i­mately 10 math majors; ris­ing juniors and seniors are given pref­er­ence, but ris­ing sopho­mores are often accepted. The pro­gram is only open to Prince­ton stu­dents. Par­tic­i­pants are expected to sub­mit a writ­ten report or paper in early September.

How to Apply [Show]How to Apply [Hide]
To apply, first find an adviser. Note that your adviser does not have to be in the depart­ment, pro­vided your project involves sig­nif­i­cant math­e­mat­i­cal con­tent. After you have a fac­ulty mem­ber will­ing to super­vise a project, work with him or her to pre­pare a one to two page project pro­posal. The pro­posal should cover your plan of study, whether it is research or guided read­ing. The dead­line is typ­i­cally in April, and responses come out late in the month. If you need to hear back earlier—which will often be the case, since the sum­mer hous­ing dead­line is ear­lier than the program’s response date—talk to the pro­gram coor­di­na­tors: Pro­fes­sors Man­jul Bhar­gava, Christo­pher Skin­ner, and Robert Gunning.

An Exam­ple Project [Show]An Exam­ple Project [Hide]
Shotaro Mak­isumi. I par­tic­i­pated in this pro­gram in sum­mer 2011. My advi­sor was Tasho Kaletha, a post doc with a joint appoint­ment at Prince­ton and the Insti­tute for Advanced Study. We put together a plan of study cov­er­ing sev­eral top­ics, includ­ing the struc­ture the­ory of reduc­tive groups, Bruhat-Tits build­ings, and Galois coho­mol­ogy. I read text­books and papers he rec­om­mended, met with him reg­u­larly to ask ques­tions, and wrote an expo­si­tion on the struc­ture the­ory of reduc­tive groups.

How Is It Dif­fer­ent from an REU? [Show]How Is It Dif­fer­ent from an REU? [Hide]
The Prince­ton pro­gram dif­fers from REUs in sev­eral respects. Pri­mar­ily, it offers sig­nif­i­cant scope for choice: you can choose to work on what­ever kind of project inter­ests you, pro­vided you can find a super­vi­sor. This means you can work on a project that would sim­ply not be offered at an REU. More­over, while this is not always the case, par­tic­u­larly if you par­tic­i­pate in one of the top REUs, REUs gen­er­ally focus on areas slightly out­side the main­stream and prob­lems that require rel­a­tively lit­tle spe­cial­ized knowl­edge. The result is that an REU expe­ri­ence, par­tic­u­larly early in your under­grad­u­ate career, will likely be more of an oppor­tu­nity to focus on a sin­gle, spe­cific prob­lem than a way to learn math­e­mat­ics that you’re likely to use in the future. In con­trast, the Prince­ton pro­grams rep­re­sents a chance to build sig­nif­i­cant foun­da­tional knowl­edge in a spe­cific area, which is par­tic­u­larly use­ful if you wish to pur­sue research in it. Indeed, in many parts of math­e­mat­ics, such knowl­edge is absolutely cru­cial. Also impor­tant is the program’s flex­i­bil­ity: the time spent on the project can be bud­geted how­ever the stu­dent and adviser choose, and the project can be purely read­ing, purely research, or a com­bi­na­tion of the two.
We def­i­nitely rec­om­mend doing one REU for the research expe­ri­ence and pos­si­bly a sec­ond top REU. We do, how­ever, highly rec­om­mend the Prince­ton pro­gram as a way to learn a lot of math or, depend­ing on your inter­ests and prepa­ra­tion, work on a research project of your choosing.

Hous­ing [Show]Hous­ing [Hide]
There are two options: (1) cam­pus sum­mer hous­ing and (2) off-campus hous­ing. Room draw for sum­mer hous­ing is typ­i­cally in late April or early May, and you have to request a spot in the draw by early April. (Check the Hous­ing Office’s web­site for the details: the dead­lines are very strict.) Typ­i­cally, a very lim­ited num­ber of sum­mer rooms are air-conditioned (usu­ally in Bloomberg or Scully); if you’re not lucky enough to get one, you’ll have to put up with Princeton’s sum­mer heat. Many stu­dents do so, usu­ally with the help of fans and open win­dows. Pric­ing is approx­i­mately $1800 for the full sum­mer hous­ing con­tract from mid-June to mid-August. Shorter con­tracts are avail­able; again, con­sult the Hous­ing Office’s web­site for details. One poten­tial prob­lem with on-campus hous­ing is that all con­tracts end in the first weeks of August (check the hous­ing web­site for an exact date). If your intern­ship extends past this time, then you will need to look into off-campus hous­ing.
Prince­ton does not directly pro­vide off-campus hous­ing, so this is some­thing you must do your­self. There are two places to look for list­ings of avail­able rooms to rent. The first is Princeton’s off-campus hous­ing web­site. There, the best option is “fur­nished rooms to rent”. The other place to look is the Tiger Trade web­site, under the “Hous­ing and Apart­ments” sec­tion. Search­ing for off-campus hous­ing is not as easy as one might think. Here are some tips:
The main con­sid­er­a­tions when choos­ing off-campus hous­ing are price, prox­im­ity to cam­pus, and, if you don’t have a car, prox­im­ity to bus stops. The last one is cru­cial; going back and forth between your hous­ing and Prince­ton might be very incon­ve­nient if you don’t take that aspect into con­sid­er­a­tion.
Go through all the list­ings and con­tact many of the land­lords. Most likely at least half of them will already have a ten­ant, will not accept a con­tract that short, sim­ply will not respond to your emails, and so on. Thus, con­tact­ing them one at a time is a bad idea.
If you have found a place that works and the land­lord has agreed to take you, do not waste too much time before accept­ing the offer. While you are con­sid­er­ing mul­ti­ple places to stay, the land­lords might also be con­sid­er­ing mul­ti­ple ten­ants. Thus, even after you have made con­tact with the land­lord, he or she might let you know that there is another ten­ant who has already taken the room.
Even if you do not have time to visit any rooms, be sure to ask the land­lords lots of ques­tions: prox­im­ity to bus stops, avail­abil­ity of kitchen, AC, inter­net, laun­dry, and so on. Google Tran­sit is also use­ful for look­ing up prox­im­ity to bus stops on your own.
Given the dif­fi­cult nature of search­ing for off-campus hous­ing, be sure to start early.

Inter­na­tional Stu­dents [Show]Inter­na­tional Stu­dents [Hide]
Since the depart­ment pays, no OPT (Optional Prac­ti­cal Train­ing) is needed. The pro­gram is con­sid­ered on-campus employ­ment. Pay­roll will con­tact you about work autho­riza­tion. You will apply for a social secu­rity card in Tren­ton if you don’t already have one. Side ben­e­fit: with an SSN you can rea­son­ably apply for a credit card (you also can with a TIN, but credit infor­ma­tion is asso­ci­ated with either TIN or SSN, so you would lose any credit rat­ing once you get a SSN).

Acknowl­edge­ments: Many thanks to Shotaro Mak­isumi ’12 for con­tribut­ing this article.

Con­tacts: Shotaro “Macky” Mak­isumi ’12
smakisumi[at]gmail[dot]com