Letter of Recommendation from Professor whose class I didn't do that well in

[Robbentheking]

Hey guys,

I'm really worried about my third letter of reccomendation. I'm a math student applying for stats grad programs, but I also study German and haven't taken a math class in a year, so I'm sort of short on potential letter writers who can speak to my ability to comprehend higher level material. I'm considering asking my grad-level Topology professor from last fall, but I'm really nervous about this. I got an A- in the course, which really isn't that good as grad courses tend be graded easier. Most worryingly, I had my worst ever exam result in this course. On the second midterm I did really badly. It was a take home exam and while I can't remember exactly what I got, it was easily below average, tending towards the bottom of our 20 person class. I did however do well on the first exam, score respectably on the final, which was also a take home exam, and go to office hours a decent amount, so he knows me and my work ethic.

Basically, my only other option is my complex analysis professor from last fall who essentially doesn't know me, but who I got a solid A from. 

 

Any thoughts?

[avflinsch]

I see that your location is Germany, if you are applying to US (or non German) schools, then I would go for a LOR from one of your German professors (assuming that the other 2 were from the math department), Doing it this way, you show yourself to be proficient in multiple areas, and that you are more than just a math geek.

if you are staying in Germany, then the A- from the topology professor might be a better option, the professor knows you, and would be able to write a better letter on your behalf.

BTW - where in Germany? My daughter was taking political science classes in Kassel over the summer, and is considering going back to Germany for her PhD.

[Robbentheking]

1 hour ago, avflinsch said:

I see that your location is Germany, if you are applying to US (or non German) schools, then I would go for a LOR from one of your German professors (assuming that the other 2 were from the math department), Doing it this way, you show yourself to be proficient in multiple areas, and that you are more than just a math geek.

if you are staying in Germany, then the A- from the topology professor might be a better option, the professor knows you, and would be able to write a better letter on your behalf.

BTW - where in Germany? My daughter was taking political science classes in Kassel over the summer, and is considering going back to Germany for her PhD.

I'm a US international, went to school in the US and will be applying to US schools; I'm just working in Germany currently. I actually intend to ask the head of the German department back home to write a rec for me, but I was thinking of making this a fourth rec. It should actually be a very good rec because she really likes me and has openly pushed for me to get somewhat undeserved department awards in the past, but because I'm applying to a quanitative field, I want to make sure I fill my required recs with people that actually have an understanding of what it takes to do grad level work in a quanitative field.

I'm in Berlin. I would consider staying here, but to be honest I sort of miss the US and speaking English all the time. It's just a bit easier haha

[TakeruK]

The point of reference letters is not to demonstrate that you have high level understanding of the material. There are many other ways that the admissions committee will get this information, such as your transcripts. Getting a letter from someone that taught you a course isn't very helpful. So, on the flip side, if you didn't do amazing in it (A- is still a good grade), it won't hurt you either.

Ideally, you want professors who can write you letters attesting to your ability to do good work as a researcher in graduate school. The best letter writers are those who have supervised your research in the past. I am assuming you might already have this lined up for your first two letters, and you don't have a third supervisor so that's why you are seeking a third letter?

If so, then my advice is to get in touch with the grad level topology professor from last fall. Do more than just ask for a letter---also reconnect and renew your previous relationship with him. A good way to do this is to let him know that you are applying to grad schools and that you would like to pick his brain for his thoughts and then also ask him to write you a letter. Do this fairly soon since deadlines are only 2 months away. You will get a much better letter from him if he knows more about your motivations and your grad school plans. Through discussions with him, he will gain insight into you as a new researcher and this information can be conveyed into his letter. This will make it a good letter, instead of a bland "this student did well in my class and understands the material", which isn't a very useful letter. The other advantage is that you took a graduate level course from this professor so he can discuss your preparedness for graduate work more directly.

I would advise against asking for a letter from the head of your German department. If you did do research in German then maybe your research advisor would write a good letter. If it's a letter about your research ability, then the actual field of research doesn't matter (although the closer it is to your planned PhD field, the better). I agree with @avflinsch that having diversity and breadth is very good and very important, but the LORs is not the right place to show that. The committee will be impressed by your breadth through transcripts and probably a notation on your degree that indicates you have studied German. And you would presumably write about your experience in Germany in your SOP as well. 

I would also caution against getting a 4th letter of reference. In many programs where they specifically ask for three, they only want to see three. Even if there is an option to upload a 4th letter, I would advise against it because your 4th letter from the German department isn't going to be as strong as the other three letters. The admissions committee is going to only want to read three letters, and sometimes, when students submit more than 3, they might just read the first three in the pile. In addition, they are going to form an opinion about your application's LORs after reading all 3 (or 4) letters and coming to some impression. This impression will be averaged out over all the letters, so you would be better off if they read 3 strong letters than if they read 3 strong letters plus 1 okay one.

[Robbentheking]

@TakeruK

First off, thank you for taking the time to write this long and clearly well thought out post.

While I'm aware of the fact that getting a recommendation from someone who only a taught me in a course is not ideal, I would like to say that especially in math, and to a lesser in statistics, this is not totally uncommon. Certainly in math, no one outside of the true rising stars knows anywhere near enough as an undergraduate participate in meaningful research. In this sense, one of the better measures that grad schools have of future research potential is simply to try and make sure a student is not close to reaching his or her mathematical 'ceiling'. In this sense, professors one has had a course with are really not the worst evaluators. Certainly research need not be meaningful to give an indication about research potential, but I clearly recall going to a prospective math major QandA session when I was a sophomore whereby someone asked about how to get involved in undergrad research. One of the professors on the panel, one who was subsequently fired for his lack of teaching ability but almost immediately picked up by UChicago becasue he was a brilliant researcher, gave the following answer: 'Don't waste your time with research as an undergrad. You just don't know enough. The best thing you can do to prepare for grad school is pick up a text book during the summer and try to do all the problems'. This answer struck me as ridiculous at the time, but other, more level headed professors I've asked about this answer have pretty much agreed. Coming from a math background, my interests in stats are almost totally theoretical and intersect heavily with pure math. I do not have any research experience in this field and while it'd be nice to have some, I'm not killing myself over this, especially because half of me really thinks a masters program would be best for me right now anyway for a bunch of reasons only partially intersecting with research. I've done what can easily be spun as descriptive statistics research in the bit of professional experience I have, but haven't gotten a recommendation from a previous employer because I just don't think that would at all be helpful in evaluating my research potential in the topics I'm interested in.

The reason for my concern about asking the topology professor follows largely from my comment about 'mathematical ceiling.' I think the way in which a letter from a professor can be helpful is by giving a vote of approval that the ceiling isn't in sight and that the student has an inquisitive mind and a love for mathematics that takes his or her study to a somewhat extra curricular level, and I'm really not sure doing mediocrely in a class really encourages the professor to give his seal of approval that I will be able to tackle anything thrown at me in the future. You can't push the mathematics further if you don't have a full grasp of the existing knowledge.

As for German, I did write a pretty significant senior thesis and could get a recommendation from my advisor. Mostly, I just wanted to include a letter from someone who knows me well through the German department because it's something I spent if not half, a significant part of my time on in undergrad; it's a big part of who I am as a student and I just feel like even though it's totally irrelevant in the fields I'm interested in, I want to put my full self on my applications.

 

 

 

 

 

[TakeruK]

I didn't realise the mathematical sciences had very little research in undergrad (I guess my undergrad school was a little different, or maybe my friends in the math department had different subfields). I still think it would be a good idea to develop a deeper relationship with your topology professor. Especially if you want the letter to show that you haven't reached your mathematical ceiling**, your conversations with him now can show that you are still actively thinking about mathematics and that you know the relevant literature etc. 

I think a letter from your German advisor is better than the German department head, however, I would be hesitant to put it as a 4th letter. I understand the appeal of putting everything about yourself in your application, but I caution against this approach in academia in general, especially for other applications later on in your career. As I wrote above, the more information you provide, the less each piece of information will be weighted, so it's better to say less and focus on the aspects that the committee will care about instead of just giving them every piece of information about yourself, regardless of relevance. The evaluators will read your application for just a tiny fraction of the time you put into preparing these applications. Again, I am not saying you should avoid discussing your German studies---this is a great thing to discuss in your SOP and it will show that you can think and excel in other fields/modes of analysis, but I wouldn't add it as a 4th letter. 

** With regards to the concept of the mathematical ceiling: I wonder if this is a concept shared by all mathematicians, or just the ones you have interacted with? I know that in academia, there is the "growth mindset" and the "fixed intelligence" mindset, and the whole idea of there existing a mathematical ceiling sounds very much like a "fixed intelligence" mindset. My impression of academia is that more and more people are moving towards the growth mindset model. I am obviously an outsider to your field, and maybe this doesn't apply here. But I wanted to point this out because as students (both undergraduate and graduate), we are just beginning to interact with the academics in our field and I have made the mistake before of assuming that an idea is common because everyone I talked to preferred that one. 

[Robbentheking]

@TakeruK

Well, I may be deemphaisizing research a bit on some subscious level just as an ego boost, but what I've written above is a pretty decent respresentation of what I've heard in my math department.

With regards to the mathematical ceiling, I think it can really have a more dynamic definition. Math can get really hard and no matter who you are, you are going to get to points where you just really need to like math enough to put in the time and grind through the rough patch. The degree to which you are willing to sacrifice for the subject is part of your ceiling I think, and I think most professors would agree to that. Mathematical ceiling is a phrase that is casually thrown around a lot that is actually pretty deep imo.

In general, I'm wary of people who fall cleanly on either  side of the fixed intelligence vs. growth mindset debate. I think experience shapes all of his greatly on everything from aparent ability to desire to learn something, but the idea that there aren't people with inherent advantages in certain areas doesn't make much sense to me. Forgive me if I sound really stupid because I'm reaching far out of my field, but I'm not sure I understand how humans fit into the evolutionary framework if intelligence is just something we all acquire during our lifetimes.

Edited October 7, 2016 by Robbentheking