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I am currently a first year graduate student in a pure math PhD program in a top-100 university studying topology. I declined offers from top 20 schools to attend this school because I liked the professors at this university and the location of the school was good.

After going to a couple of conferences and talking to some post-docs/grad students from other universities, I found out that the career prospects for someone like me look quite terrible (if I wanted to stay in academia). Even grad students from Stanford/Berkeley (i.e. top schools) were having a bit of trouble finding a spot in academia. Given that I'm really far down the "food chain" and I want to stay in academia, it looks very unrealistic for me. Also, the math is really hard :)

I realize that I should go to a top-20ish school to have access to enough resources to make myself a competitive applicant in the future (I realize that I should focus on my work, but it's hard to grow a lot at my current university given the lack of learning seminars/seminars in general).

That said, I've been going to conferences and giving talks and "doing the right things." However, I am finding that the current research I am doing is quite abstract and I don't have people I can regularly talk to about it. I've recently discovered the subfields of topological data analysis and DNA topology and I'm finding those subjects really appealing in that I can actually see how my work might impact people and I can actually understand the material that is covered in seminars (the topics are very approachable).

From what the grad chair told me, I'm one of the strongest students that has entered this school's PhD program so I'm suspecting that, if I want to transfer, my letters of recommendation would be fairly strong.

However, the main issue for me is that I still do want to stay in academia. I know that I don't need to go to a top 20 school to do "good" work but I don't see myself finishing my PhD at a school that isn't in the top 20.

So, that's the background.

I really want to transfer to a top (whatever that might mean) applied math program from my current institution. I have only taken pure math classes. I don't know how to nicely approach my professors and say "I don't want to stay here. Please write me a letter of recommendation so I can get out." My current plan is to say something like "I've developed some interest in applied math and we don't do that here. I'm seeing myself doing research in applied math. Will you write me a letter (etc)?"

  1. How realistic is it for me to transfer to a (top) applied math program? My GPA is currently a 4.0 and my undergrad was completed at a top 5 university (with a 3.8).

  2. If it is realistic, how do I maximize my chance of being admitted into a (top) applied math program?

  3. If it is realistic, what are some better ways to approach professors at my current university about this?

If it isn't realistic, I might just finish a PhD here. I know that I can get more specialized attention at my university, but I thought I'd do a preliminary pass here to get a sanity check before I ask people in my department. I am not familiar with people transferring from pure math to applied math programs.

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    Have you raised this with your Department's graduate student advisor or the graduate studies faculty officer? It seems to me that you're desire to remain in your institution gives you access to resources that will be specific to your situation and which we will be unable to provide given that our responses will be rather generic in comparison. – user65587 Dec 18 '16 at 2:06
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    I really want to transfer to a top (whatever that might mean) applied math program --- No, you don't. You want to apply to a department in which people actively work on topological data analysis and/or DNA topology. That might be math; it might be applied math; it might be statistics; it might be biology; it might even be computer science. TDAists are a pretty interdisciplinary bunch. – JeffE Dec 21 '16 at 4:18
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    You might find appliedtopology.org helpful/interesting. – JeffE Dec 21 '16 at 4:21
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  1. Get your feet wet in applied math to make sure you'll like it. Apparently there is no applied math program where you are now, but you can still do this, through a combination of self study and courses offered in your own and in other departments. Look at some applied math programs at other universities to get a flavor for the variety involved, and to give you some ideas of what sorts of courses to look for. Programming skills are not required for all areas of applied math but can really come in handy for some.

  2. When you're ready to ask for recommendations, be honest, just say that you are hopeful an applied math degree will make you more employable.

  3. I assume you'll want to pursue this process with some transition time, during which you'll continue working to some extent with your current program including your research project.... If so, please find some people to interact with remotely, in your area.

  • There is an applied math program here, but it does not focus on the type of applied math I'm looking at. For instance, if I mention the phrases "sheaf cohomology" or "K(G,n)," I get redirected to the math department (instead of people who are interested in data analysis). I am planning on applying next December, which gives me a year to fiddle around with these applied concepts. I'll definitely follow along courses of departments that do do these things (eg. Columbia/Stanford). Thanks for the tips! – Bob Dec 18 '16 at 8:45
  • @Bob - Have you looked at your university's course offerings for spring semester, and the corresponding course descriptions? What exactly is the type of applied math you're "looking at" (please include at least one link)? What do you mean, "mention," "get redirected"? Have you taken a look at the web pages of the applied math faculty at your institution? Have you spoken/emailed with anyone at that department? I'm not against your plan to transfer, but I would hope that department can at least help you build a bridge to another school. (You might even be able to do something ... – aparente001 Dec 18 '16 at 20:22
  • ... interdisciplinary at your present institution. (I'm not saying you can, or that it's likely that you'll be able to, just that at this point it might be too soon to rule it out.) // Do you have an advisor? Is s/he helpful at all in connection with this wondering you're doing? // Have you found some papers in the area that interests you? – aparente001 Dec 18 '16 at 20:23
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You've made it clear from your question that you're very interested in the area of topological data analysis. This is a current "hot topic", and there is considerable interest in that topic, but relatively few people are actively involved at this stage. Most applied mathematics programs won't have any faculty working in this specific area, so simply transferring to an applied math program isn't going to be sufficient. Furthermore, this is a topic very far from the main stream in applied mathematics departments, so you might find that the applied math programs you consider either won't offer the right coursework or will require you to spend too much time on other topics.

What you really need to do is to find a program with a faculty advisor that you want to work with (and who wants to work with you) and degree requirements that will allow you to pick coursework in support of a dissertation in this area. This might end up being in an applied math department, or a pure math department, or perhaps in an interdisciplinary program that specializes in machine learning or data analysis.

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Your two options are either finishing the PhD where you stared or transferring in the process. (Oh, and also: giving up entirely.) As a first-year it might be Ok just to switch. It might be easier and better for you just to pull the PhD through and to transition afterwards. You will have to anyway if you aim for the academic career. And if you don't: your struggle finishes anyway with the PhD.

Can you gain something from your current school, so the first year is not lost? A research paper publish? A Master's? (Though in some places (cough, US, cough) Masters's might be frown upon as their are sort of "unsuccessful PhDs, so check this for your local culture.)

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