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I am a freshman at a top-20 university majoring in math. My dream is to be a college professor.

I am currently taking a combined multivariable calc/linear algebra class restricted to freshmen. It is very proof intensive and is supposedly considered one of the harder classes in the major. I expect to make an A- for this semester of the class... An A would come as the result of a a curve or me getting nothing wrong for the rest of the semester (a miracle).

I am still determined to take either number theory or differential equations next semester. I want to apply to some REU's this summer, so I feel like taking number theory might be more advantageous than DE, but I'd like second opinions on this. Would I even have a shot at getting into REU's as a freshman? I know I can get good recs, but I know I'd have to pick less competitive programs. Does ethnicity really comes into play in admissions? (I have heard differing things on this.)

Is it still possible to get into a top graduate program with a <4.0 math GPA? By top, I mean generally #40 and above on USNWR. (Admittedly, I don't have a good perception of all of this...)

Sorry for all of this. Admittedly, I'm not used to getting less than A's in math in high school and realizing that it's mathematically improbable for me to make an A this semester...

Thanks so much.

Jimbo James
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    I am sorry, I can't give you any advice about REU's, but I feel like I need to say something: keep studying hard, learn a lot but most of all... don't stress too much about grades! –  Oct 23 '13 at 05:29
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    Of course people get into these programs with non-4.0 GPAs. – tfw cant into math Oct 23 '13 at 05:32
  • Top applicants are often taking advanced courses at the graduate level and juggling several other responsibilities (research, extracurriculars, etc.) - it shouldn't be at all unusual for a large portion of them to have lost the 4.0 GPA somewhere. – Gyu Eun Lee Oct 24 '13 at 03:59

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To me, grades aren't the whole story. Some profs have individualistic grading ideas and may be particularly hard on the one thing you are worst at -- even if it isn't such an important thing. Or maybe the course was a stretch for you and an A- shows significant progress. Who knows?

What is much more important is to learn the material. Now by "learn" I don't mean get an A. I mean having a deep understanding of the subject. You could test this for yourself in a variety of ways. First, given a problem similar to one you've seen, can you do it? Can you do it easily? Next, given a problem in the subject that you haven't seen, but appears to be in the topic area, how much progress can you make on it? I wouldn't say, can you solve all of them -- your first try could well be one of those that look simple and are terrifically difficult. But can you get anywhere? And can you solve a good percentage of them?

How many questions do you have about the course material? If you think you understand absolutely everything, then you probably haven't learned enough. If you've got areas that seem fuzzy, or questions you hope no one ever asks you; or if you have dreams that you are failing a similar course -- you have questions. Drag them out into the open and get some light on them.

In general if you want to do very, very well at math, you need to work a lot of problems. Theory is all very nice, but there is nothing like trying to work a problem to demonstrate that you really didn't understand it. The more problems you work, the more you will know. If you get stuck, you can ask -- one of your profs, or post it here. There are bunches of eager, knowledgeable people here who enjoy helping out.

Re graduate school, quite a few will take you with less than a perfect average, particularly if you demonstrate a lot of knowledge. Some schools have a "come if you wish, stay if you can" philosophy, and basically let anyone in (no matter what the catalog says). Some of the anyone's are certainly not able to stay, but the philosophy is that if someone wants to learn they should be given a chance.

Re number theory vs diff eq, there are those who are impressed with one and those who are impressed with the other. I personally prefer the applied areas, but that is not a majority opinion. As to whether one is more helpful than the other in getting an REU, I suspect it would depend on who was reviewing your application and what his/her prejudices are. Take both, eventually.

REU's are very competitive, and I don't know how many go to freshman. You have 2 choices: you can apply and maybe you will get one, maybe not. Or you can decide not to apply and guarantee you won't get one. I say if you have nothing to lose, go for it.

Betty Mock
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  • I would like to add: some REUs favor sophomore and junior applicants, because (so the reasoning goes) freshmen have another year and hence another opportunity to apply to an REU. – Gyu Eun Lee Oct 24 '13 at 04:06
  • @kigen -- Also they think that with another year or two of experience the juniors and seniors know more. This is false reasoning. The students who know the most are those who have talent and work hard. But the system is that flawed humans made the decisions. – Betty Mock Oct 26 '13 at 03:53
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    I think that this system is not as flawed as you seem to suggest. It makes sense for REUs to prioritize older students over freshmen for the sake of equity. I'd rather give an older student who shows promise an opportunity to make something of himself than give that opportunity to a phenomenally brilliant freshman. We should capture mathematical talent whenever possible. And from the REU's perspective, since the funding comes from the NSF you'd naturally want some measure of confidence that the student will make significant progress, which does favor students with more background. – Gyu Eun Lee Oct 26 '13 at 04:42