Taking a Year Off Before Graduate School (Math)

[klackity]

I'm currently a sophomore at NYU. This semester I've been taking some pretty hard classes (Functional Analysis being the hardest). I'm probably not going to do so well grade-wise - probably a few B's.

Basically, I want to understand as much mathematics as I can before I start graduate school. Currently, I know more Analysis than anything else. I've only taken a single course in Algebra. I haven't taken a course specifically in topology, but I know the basics.

Here are the courses I will have taken after this semester:
Calc III (in high school)
Linear Algebra (in high school)
Real Analysis I/II
Algebra I
Vector Analysis
Differential Geometry I/II
Real Variables (mostly measure theory)
Probability
Complex Analysis I/II
Functional Analysis

To try to get myself together more, next semester, I'll be doing the MASS program at Penn State. This will be 3 courses, and I'll get a chance to really focus on understanding and living mathematics.

I expect to graduate with around a 3.85 GPA (in math, and overall) at NYU, if I don't mess up.

But here's the thing. I've talked to a few other NYU students, and the people who get into the top phd programs (like NYU, Columbia, etc.) tend to have really perfect GPA's. I'm talking like 3.99 - all A's and a single A-. I know already that I can't get that. But I've also started taking advanced courses earlier than they did.

Here's the dilemma. On the one hand, I know I will be appealing to top graduate schools because of having prepared very well, and studied a lot of mathematics as an undergraduate. But I will not be so appealing, because I will have a few B's, while the students who didn't try to take difficult graduate courses so early will have straight A's.

If I get lower than an A, it's really because I do not know the material as well as I should. So what I would like to do is take a year off after undergraduate and just spend my time studying over all the material I have learned, until I know it like the back of my hand. I've already become mostly proficient at reading mathematics books independently. I would also maybe travel at the same time, and enjoy my youth, you know?

But I worry that taking a year off to do this will put me at a disadvantage when applying to the top graduate schools. It would be hard to explain, exactly, that I really was using the year to advance myself.

I *could* maybe do a program like Cambridge Part III, or the masters program at NYU. The problem is that this is A LOT of money, which my family doesn't really have. Moreover, from what I've heard, the grades from Part III aren't released until very late, meaning doing well in Part III wouldn't really be so much of an advantage for graduate school.

So here's my question. Is it possible to take a year off from graduate school and improve my chances at getting into a top graduate school? Or am I better off just applying to and going to graduate school right after undergraduate?

Here's another thing too, though. What if I were to somehow get a professor to vouch for me that I did in fact use that time to study? My father is a math professor at University of Warwick (one of the top, top mathematics programs in the UK). I could maybe spend a year in the UK living with him and studying math, and doing a bit of traveling, and perhaps I could informally sit for some exams to show my competence in certain areas. Perhaps get short letters from a few faculty members that I know what I'm doing, and haven't been screwing around for a year.

Perhaps I could get an NYU professor also to vouch for my improved competence in various areas after the gap year.

The thing is... this kind of stuff is not usually done. I feel like most students in my position would just suck it up and go to graduate school straight away. Do you think my plan is possible, or do you think it's hopelessly deluded?

 

[QuarkCharmer]

Why don't you take a research position somewhere during that time and continue working as you please in parallel. That way, you can explain the gap, and you also garner valuable research experience that would benefit you in being accepted to a top-tier grad program despite a few B's?

 

[klackity]

QuarkCharmer: I've never heard of such a thing. Research programs for undergraduates/recent graduates usually run in the summer, or under the advisement of a faculty member while enrolled in an institution during the academic year.

I'm trying to avoid doing something that looks hokey.

Ideally there would be some good institutional options (that wouldn't cost a ridiculous amount of money), but this seems not to be the case.

 

[Ryker]

I'm trying to avoid doing something that looks hokey.

I don't think that would look hokey. In fact, in my opinion it would look less hokey than getting professors to somehow vouch for what you did when in fact there's no way of telling what you were in fact doing. I'm not saying that you're going to be goofing off and have hoax professors into vouching for you, but if I imagine myself on an admissions comittee, I'd be more suspicious and see less relevance in that than what QuarkCharmer suggested. Maybe try and mix the two by working with someone at Warwick, although here again the connection with your father might add an element of hokeyness.

In all honesty, though, I think it is hard to "prove" that you've been advancing your knowledge in your off year, because isn't that what formal education is for? I don't know how they look upon gap years, and I'm guessing it also differs from one committee to another, but, again, maybe try and put yourself in their position and think of what you as an admissions officer would like to see from people taking gap years that would put them in a better position not only compared to their own without a gap year, but also in comparison with others. I'm pretty sure it's not easy, and this is something you'll need to deal with.

Again, can't really offer any expert advice, but I'd say don't do a little bit of this and a little bit of that. Either try and think of something really good that would improve your chances or travel like you said you want to. In the first case and if you're successful, you'll get better odds of getting into the program you wish, and in the second one, you'll have the experience of a lifetime. But if you half-*** both of them, you'll probably get neither.

But seeing as you're only a sophomore, you still have some time on your hands to think about this, right? Maybe keep it in the back of your mind, but just go with the flow and see where your interests in the next couple of years take you.