Advice on Letters of Recommendation

Question

I'm currently applying to the masters program at my undergraduate institution for a degree in mathematics. Due to my rather ambitious nature and biting off much, much more than I could chew at times (sitting in on multiple graduate courses and doing the coursework for them as an undergraduate for example), my GPA is not ideal for applying to graduate school (3.13) with my in-major GPA being even lower (just below a 3.0 I believe).

That said, I have heard of people getting into graduate school here with less than a 3.0 and I believe I have a decent opportunity of getting in, but I'm struggling to decide who should write my letters of recommendation.

In high school my GPA was much, much higher, so I got good letters of recommendation from both my teachers as well as people who knew me in other areas of my life. Of course now, I'm guessing that graduate schools are completely uninterested in letters of recommendation from anyone that isn't a professional in your field. Because I haven't had any internships or done any summer programs or anything, this pretty much just leaves my undergraduate professors to write letters of recommendation for me.

Given how small my school's pure math dept is and that we are required to have 3 letters of recommendation this is very limiting. There are very, very few professors I've had more than once, and those I have had I haven't necessarily done well in thier classes. So I've given the question of who should write my letters of recommendation a lot of thought and see the following 3 options and am wondering what might be viewed as the best option:

1. 3 letters of recommendation from professors of mathematics in the pure math dept of my university. This would certainly conform to standards but they would not likely be glowing letters of recommendation due to my less than stellar undergraduate performance (the highest grade I would have gotten in any of these individuals classes is an A-...less in others)

2. Given that you ideally have letters of recommendation from professors whose courses you did very well in, I could get letters of recommendation from math professors whose classes I've gotten A's in. The problem with this is that these classes are few in number and the professor's that taught them were in either applied mathematics or mathematics education (the 3 classes I got an A in were one in pure math taught by an applied mathematician, one in applied math taught by an applied mathematician, and one in math history taught by the dept head who's in math education). I also do not know most of these professors very well at all.

3. 3 letters of recommendation, from a more diverse pool of people, but would be closer to what you'd consider a "glowing letter of recommendation". I'd of course have 1 from a math professor that knows me well, but then two others perhaps from a professor of physics (I'm very interested in mathematical physics, but I'm applying to the pure math program not the applied math program and this physics professor's research is in physics education), and then one from either an acquantince who knows me well who is in the graduate program now, or a lifelong mentor of sorts who can speak to my work ethic and who I am as a person, but is not at all in the field.

Sorry for such a long post, I don't often use the academia site, but I'd really like to know what my best option is. Thank you!

Answer 1

Since this is an "internal" application, the recommendation letters are really a formality. The department wants to know whether you're likely to succeed in their program. Since they already know you, they have a good idea what sort of student you are.

In my opinion, your real problem is that they know that you're that type of student who bites off more than he can chew. That sort of student is not likely to be successful. (I don't know why, but that sort of student annoys me deeply. It pushes some button deep in my psyche.) You expend lots of effort but you don't master anything. All these graduate profs have had you sitting in their classes, thereby soaking up some of their effort and for no results. Meanwhile you dogged your undergrad classes, and wasted the efforts of those professors.

My advice, if you want to get into their program, is to go on a mission to convince the faculty that you've learned your lesson, that you know you need to focus and master today's learning today. That you won't, in the future, be distracted by every shiny object that arises. Yes, lots of different bits of mathematics are interesting to the point of being seductive, but you can't learn them all at once. The moral of the story is that joke about the old bull and the young bull looking down the hill at a herd of cows.

Answer 2

GPA is a function of how well you follow orders. Far far more important is the relationships you built with your professors, by talking with them before and after class, while in classes with small class sizes. That is to say, how well they remember you, and that the remember your positively.

Didn't do that? Then you are deep doo-doo.

Answer 3

You sat in on graduate courses and did the course work. Do the professors who taught those courses know about the quality of your work; did they grade your papers along with those of the officially enrolled students? If so, then could they write recommendations for you?