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I'm an international student who finished my undergraduate degree at a top-20 US university last December (double-majoring in math and comparative literature) and currently staying in my home country. The math that I studied as an undergraduate was pure math exclusively. In particular, I loved algebra, and my plan was to pursue a PhD in algebraic geometry. For example, I took courses in commutative algebra and 1st-year algebraic geometry, but never took a single course on any topic like ODEs, probability, statistics, programming, etc. My undergraduate GPA is 4.0/4.0.

However, my PhD application results were very disappointing. I was rejected by every program among the 15 or so PhD programs that I applied for. This might be due to that most of these are top US programs and hence way too selective. Due to short-sightedness in planning, I didn't apply for enough back-up programs.

The only two offers that I got were for the math MS programs at NYU and at the University of Bonn, respectively. The former has a tuition fee that I can't afford, and for personal reasons I'm also not a big fan of living and studying in Germany (especially in a small city like Bonn) - though I initially accepted Bonn's offer. On the other hand, my French is fluent, and Paris is a very ideal place for me to continue my studies. However, I didn't apply for any French universities this year, so if I want to go to France for my master's I'll need to do a gap year before applying again.

Moreover, in the last few months, due to changes in family situation, I became more and more aware that a career in pure math is way too competitive and financially unreliable. I decided that pure math is too risky a path to pursue, and that I would instead like to transition to applied math (most likely to operations research, modeling, or simulation) for my future studies.

Therefore, my current plan is to gap for a year, and then apply for M1 master programs in applied math at Paris universities like Paris-Saclay, Sorbonne, Ecole Polytechnique, and PSL. However, I'm worried that the lack of applied math courses on my undergrad transcript might have a negative effect on my chance of being accepted to these programs. I'm also worried that a gap year with no math experience might give grad school admissions people the idea that I'm not staying mathematically sharp enough.

My question is: given my pure math background, is there any activity I can do (preferably math-related, but not necessarily so) during my gap year that can prepare myself better for next year's master applications and also for my future studies of applied math?

A few options that I can think of (but not sure how to proceed with) include:

(1) Take some courses on topics like ODEs, numerical algorithms, optimization, etc. This sounds very good, but the biggest problem is I don't know where to take these courses. Are there any study abroad programs (maybe similar to the Budapest Semester in Mathematics program) that accept students in my situation? In fact, I'm also very happy to self-study these subjects, but I'm afraid that without official academic records, such self-study experience might not be well regarded by grad schools.

(2) Find an internship, whether in my home country or abroad. The main problem with this is, currently having few professional skills, I'm not sure what kind of internship can (a) agree to take me, and (b) have a positive effect on my future masters applications. I'm under the impression that most internship positions in my home country that are feasible for me (i.e. do not require a high level of professional skills) involve doing a large assortment of miscellaneous daily tasks that have very little to do with mathematics.

(P.S. I am aware that this question might depend too much on individual factors, but if that is the case, I am very much willing to edit it and make it more answerable. Thanks!)

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    "in Germany (especially in a small city like Bonn)" The following won't help much if you decided against the programme itself. But it might be worthwhile to mention that it takes only 30 minutes to go from Bonn to Cologne via train. Commented May 22 at 10:25
  • And what is your home country, as a matter of interest ?
    – Trunk
    Commented May 22 at 10:43
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    Bonn has 300,000+ residents and is tied in to the excellent train network. Why did you apply if you were going to reject it for such a trivial reason? Would you reject an offer from Princeton since it has a population 10 times smaller?
    – Jon Custer
    Commented May 22 at 14:24
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    Look up “graduate non-degree studies” - in the US I was admitted in this scheme and took higher-level math courses with permission of the instructor during a gap year. You pay per course.
    – Dawn
    Commented May 22 at 17:50
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    Frankly, rejecting Bonn was stupid. Thinking that applied math is less competitive may also not be very smart.
    – Dirk
    Commented May 22 at 20:35

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You have been - and remain being, it seems - far too casual about planning and executing your career.

Getting a good GPA and double majoring with comparative literature will not per se open a range of alluring career vistas for you. You have to hustle for the next step just like everyone else. No one wants a "Casual Dan" working in the organization. While your past university may be top 20 in the US, its math department may not be anywhere near top 20 in the US - that is a different thing entirely.

Even at this stage it might be helpful to you if you were to seek feedback from the top math graduate schools that rejected you. My impression is that your curriculum may have been more limited than you appreciate. The second major that you chose might also be a factor indicating a more limited focus. It is important that you make clear in applications that your professional focus is now entirely on math - literature will just be a pastime for you.

Another thing you should do is engage with your undergraduate university's careers office to see what possibilities may be there for you. If you enjoy friendly relations with any of the professors of math at your old department, you might seek some advice off them too.

I think that your rejection of an acceptance at Bonn was foolish: the more so on the specious grounds that you offer for rejecting it. Please do not ever reject another offer of a place without consulting some competent academic on the matter. I can't speak for everyone but most people I know (myself not least w.r.t. a Max Planck Institute) who rejected a proposition from a respectable institution soon bitterly regretted it.

Ideally, if you want to do postgraduate studies in France, it would be best to go and work in some capacity near Paris so you get up to speed with the very fast speech of Parisiennes prior to starting the MS.

But failing that try to get an internship/research assistantship that encourages you to pursue any missing math courses during the evenings over the gap year. Look through academic job listings, send out CVs to government research bureaux, job agencies, newspapers, etc.

Hup to it.

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  • Thank you so much. Will follow your advice of asking for feedback from schools that rejected me, contacting former professors, and doing a thorough search for internship opportunities. I admit that my CompLit major as well as my sudden shift from pure to applied math may seem rather casual. However I have a few points to clarify: (1) my undergrad school is UMich, whose math dept ranks #11 in the US. (2) I only spent one year - my junior year - studying literature exclusively (in fact I didn't pick up that major until then), while all other semesters are principally devoted to math courses. Commented May 24 at 13:37
  • In any case, while my transcript might not be that "limited" from a pure math perspective, it is certainly very limited from an applied math / practical perspective — which makes it quite hard for me to find suitable internships. I do have previous research experience, but all strictly in pure math. I am now considering finding a university (US or French) that offers the opportunity to do non-degree studies and take some math courses. But if you know there's any particular kind of internship that might accept students of my background, that would also be very, very helpful for me. Commented May 24 at 13:57
  • I also think I made it quite clear in my application essays that "literature will just be a pastime for me" from now on. However I'll see what feedback I can get from those schools on this point. I do agree that I didn't make future plans carefully enough as an undergraduate, and also treated my applications somewhat imprudently, but in any case I won't be posting my question here if the thought of going to Bonn isn't something that really distresses me every day (I explained the reasons a little more in my comments above). Commented May 24 at 13:58
  • @violetiris Please refer to my comments under your original question. I mean this sincerely, for your own personal welfare even more than for your career. Everyone here wants you to derive fulfilment from your life as well as from your talents.
    – Trunk
    Commented May 24 at 14:44

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