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  1.  
    I don't really know whether the following question is acceptable for MO.

    I've been wondering exactly how faculty members write letters of recommendation. So I am in a couple of interesting classes right now with very good professors who, if they wrote decent recommendations for me, could probably be helpful for the REUs/other summer programs I will likely be applying to in a few months. On the other hand, they don't grade the problem sets, and I don't see how they can get any impression of the students. Thus their only impression of a student will be proportional to the number of reasonable questions she asks in lecture; some lecturing styles, however, don't lend themselves to asking questions in the middle (except to point out mistakes).

    Basically, I'd like to know what I should do between now and the end of the semester so I don't have to walk up to them in February and say "Hi! You probably don't recognize my face from your ---- class and/or office hours, but could I have a letter of recommendation?" It would be helpful to know how this letter-writing business actually happens.

    I do know other faculty members from earlier much better, but I think I have already bothered them for recs too much, and anyway presumably recs for an undergraduate should be from faculty who have taught them courses at university.

    I don't know if this counts as MO-level since the situation likely doesn't apply to graduate students, who work directly one-on-one with their advisors. On the other hand, there are many more mathematicians here than on math.SE. Also, while I myself can only speculate here, perhaps some mathematicians at the start of their careers might themselves be interested in how letter-writing works.
  2.  
    I don't think it's a great question for MO because it's too subjective and too specific to one's specific situation. But on the other hand I'm tempted to answer it, so I'd expect you'd get several answers if you did post it.

    If someone has already written you a letter of recommendation then I wouldn't worry too much about bothering them again, they'll just send out the old letter with minor modifications. It's more of a hassle for someone new to write you a rec. Also, I think you're wrong about thinking you should have recs from profs at your school to the exclusion of other people who know you better. In your case in particular, a letter from your Intel project research advisor really should get you into any REU. No one is ever going to think "Oh, hrm, well-known mathematician, advised him on a very successful and difficult research project... But he was only in highschool then? Bah, I'll just ignore it since it's not from one of his undergrad class teachers." Finally, are you in 55 now? If so that's a good second person to ask, even if they don't interact with you one-on-one much they can say "one of x best students in 55" which is good enough even without much detail.

    For the more general point, I think it's a good idea to try to talk to your professors about something interesting in their office hours at some point during the semester. When you have an interesting question go ask them and have a conversation. It's good mathematically because you'll learn a lot from talking with a great mathematician about a problem, the prof. will probably be happy to talk about something interesting during office hours (rather than just the homework), and as an added bonus they'll be more likely to remember you when you ask for a rec. But also keep in mind that people don't necessarily expect an undergrad to have had that close of contact with very many faculty. Your senior thesis advisor will be able to say something detailed, if you have an REU advisor or take a small class with a paper project that's another person who knows you well, but if the other people just say "he did very well in [difficult class]" you're going to be fine.
    • CommentAuthorEmerton
    • CommentTimeSep 16th 2010 edited
     

    Dear Akhil,

    The generic answer to your question is as follows:

    When writing a letter for an undergrad (who is not a senior thesis advisee or in some similarly close relationship), I (and I suspect most people) take into account the following: the performance of the student in the very classes they have taken with me, including their grade, their ranking in the class, and the overall difficulty of the class, together with whatever sparkle they have given off in discussions during class or office hours. (As Noah suggests, office hours are typically better for this than class, since there is more time to discuss and interact, and one can do so on topics other than those directly relevant to the class.)

    I suspect that in your case, the generic answer is fairly irrelevant, though. Noah has given you some advice that is more tailored to your particular situation, and it sounds good to me. Just to reiterate his advice: given all the math you have been teaching yourself, surely you must have some questions. Instead of just asking them on MO, discuss them with your instructors. (Don't worry about whether they have any connection with what you are studying in your course.) Most professors enjoy discussing mathematics with bright students; indeed, this is typically the biggest reward of teaching.

    By the way, the exhortation to discuss mathematics with the people around you (including other undergrads, grad students, post-docs, professors) extends beyond the issue of just getting letters of recommendation. It's a great way to learn things and to improve your understanding, and some of the people that you meet will become life-long friends and colleagues.

  3.  
    Profs. Snyder and Emerton,

    Thanks very much for your thoughtful comments and advice! I appreciate it, and there is no further need for me to ask the question on MO, where I now agree that it would be at best a borderline question.

    I'm not taking 55 (it conflicts with a classical algebraic geometry class that I'm enrolled in), but probably the same comments apply to my other classes, which also have substantial problem sets. And I won't be shy about approaching past mentors for recommendations in the future, since your point about re-using old recommendations versus writing fresh ones makes sense. Hopefully I'll take a reading course sometime, in which case the person will know me somewhat better anyway.

    I only recently started trying to drop in on professors' office hours, but I learned quite a bit from doing so earlier today, and I'll keep doing that in the future. It was actually surprising how friendly and open the professor was, since I was asking about completely irrelevant material to the class (on commutative algebra). I also see that it will help them in writing a recommendation.