The most basic requirements I need to write a letter for you are (1) that I know who you are, (2) an explanation of why a letter from me is relevant to your goals and (3) I need to have a good impression of your abilities.
Requirement (1) is pretty self-explanatory. If you are a student, please tell me the course(s) you had with me (title(s), semester(s), course grade(s)) and what your experience was like. If you know me from outside a graded course, remind me about the context and what you remember about it. Either way, with your request please include a copy of your latest CV or resume. It should include your relevant experience and awards (if any).
For students pursuing programs or jobs in mathematics, requirement (2) doesn't need a lot of work, although if you're going to law school I'd need some convincing.
Concerning (3), if you are an undergraduate asking me for a letter because you were in a class of mine, then except in unusual circumstances I can write a strong letter only if you got an A- or higher.
Students who received a grade of B or B+ will need to make a compelling argument for why I should write a letter. Anyone with a grade below B in my class should seek another letter writer if your performance in my class should have any bearing on the reason you want a letter.
If I feel I need to know more about your background, I will ask to meet with you before agreeing to write a letter, in which case you should bring your application materials to my office and be prepared to talk about your plans at a time convenient for both of us. Asking to meet with you does not mean I will necessarily agree to write a letter.
If I agree to write a letter, you need to give me a copy of your application documentation at least 3 weeks in advance of my deadline for writing the letter. The following conversation really has taken place, with me as the second speaker: “Can you write me a grad school letter?” “Yes, when it is due?” “Tomorrow.” “Oh, um, ah,...” Something else to keep in mind is that faculty (as well as students) are often extremely busy near the end of the fall semester, so it is best to approach us early in the fall semester about anything due early in the spring semester, so we can spread out our tasks. In particular, students thinking about graduate school in the US or Canada should seek out letter writers before the end of October, not during fall final exams.
Feel free to send me an email reminder a week before my letter is due (or even earlier) if I haven't told you I wrote the letter yet.
Here is the documentation I want from you before the 3-week period preceding my submission deadline:
General Things to Provide
A copy of everything you will submitting: completed REU application, statement of purpose for graduate programs, research or teaching statement for jobs,...
I would prefer that any electronic documents you send me are .pdf files. If you don't know how to convert your documents to .pdf format,
go here and convert them. You are of course welcome to give me hard copies of all your application materials.
A list of all the other letter writers (confirmed or planned), and any particular aspects you think I could, or should, write more about concerning your qualifications than
the other writers.
College or Graduate School Applications, Summer or Study Abroad Programs, Scholarships
A typed list of where you are applying, each one on a separate line. Indicate on each line
when my deadline is (note: some graduate school fellowships have different deadlines for applicants and for letter writers) and whether my letter should be submitted online or by mail. Make this typed list easy to read.
For anything except a college or graduate school application, give me the address of a webpage about the program or scholarship.
Latest unofficial transcript (if you are a UConn student, you can generate a concise one using the Course History
option in Peoplesoft).
For applicants to math graduate programs: all your GRE scores, both general test and math subject test. (If you are taking the test late in the fall, tell me your scores when you receive them.)
For each paper application, fill out your part and my data part (obviously leave the area for my signature and the date empty),
place the application in the envelope you want me to mail it in, and address and stamp the envelope yourself. Remember that the return address information should refer to me, not you (yes, someone once messed that up) and
check your postage. One U.S. Forever stamp, for example, is not sufficient postage for a large manila envelope. (I learned that with an NSF fellowship application.)
WAIVE your right to see my letter if there is a place to do so in the application. (For undergraduate and graduate programs, this option is always there and I will look for it.)
This is very important. If you screw this up in a paper application by
checking the wrong box and not waiving your right, you can fill out another application. But if you
check the wrong box in an online application and then submit it, often it is not possible to repair the mistake (or it is possible only by a really awkward method; paper applications are better than online ones for something!), and in
that case I won't submit a letter to the program.
Jobs at Colleges or Universities
Tell me which kind of letter you want me to write: research letter or teaching letter (or if it is something else).
If it is a research letter, provide me electronic copies of some of your papers or a thesis draft. (Your work has to be in number theory or a closely related field if you want me to say anything substantial.)
For a teaching letter, provide me with some xerox copies of past student evaluations (statistical summaries as well as written comments from which I can select suitable quotes). Keep your originals, since you will want them a couple of years from now for your next
job application. Note: Unless you were my TA or I had some particular discussions with you about teaching before, don't expect me to be the right person to write a teaching letter (I'd need some convincing).
I haven't written a whole lot of non-academic job recommendations recently. In my latest experience, I needed to provide the employer not a letter but only contact information to set up a discussion by phone or in person. If I get more requests in this direction, which gives me something definite to say about letters for non-academic jobs, I will put something more focused here. For now, at least follow the guidelines above under General Things to Provide. Don't ask me for a copy of my letter for your records. I would only send it to the employer directly.