Math: Job prospects after a PhD in PDE research

[Hercuflea]

What would the career prospects be for someone who does a Ph. D. in Mathematics with a research focus in partial differential equations? Assuming you got some computer skills along the way like parallel computing, programming, etc? Sure, you could become a professor but most people don't make it that far.

 

[homeomorphic]

As long as you did numerical stuff and not existence of solutions in Sobolev space, it's probably somewhat okay. I don't know. I just know pure math sucks for getting non-academic jobs in this job market, unless you are a bit of a wiz at job-searching.

 

[StatGuy2000]

Well, I have a good friend who finished his PhD in applied math, specializing in applying graph theoretic methods to build a bridge between quantum information theory and classical statistical mechanics (I assume he has a strong background in PDEs and numerical methods), before doing a postdoc in bioinformatics, and he's now working as a bioinformatics researcher at a major research institute devoted to oncology in Ontario. And I've known others with similar backgrounds find lucrative positions.

So long as you have strong computing skills and take the effort to pursue internships while pursuing both undergraduate and graduate studies, I'm fairly confident that you will find your skills marketable.

 

[Hercuflea]

As long as you did numerical stuff and not existence of solutions in Sobolev space, it's probably somewhat okay. I don't know. I just know pure math sucks for getting non-academic jobs in this job market, unless you are a bit of a wiz at job-searching.

I actually was more interested in functional analytic techniques in finding solutions to PDEs, especially PDEs which arise from problems in kinetic theory/statistical mechanics and fluid dynamics from physics. I'm more interested in analytic techniques, but I'm not opposed to doing numerical simulations to check my theory.

Well, I have a good friend who finished his PhD in applied math, specializing in applying graph theoretic methods to build a bridge between quantum information theory and classical statistical mechanics (I assume he has a strong background in PDEs and numerical methods), before doing a postdoc in bioinformatics, and he's now working as a bioinformatics researcher at a major research institute devoted to oncology in Ontario. And I've known others with similar backgrounds find lucrative positions.

So long as you have strong computing skills and take the effort to pursue internships while pursuing both undergraduate and graduate studies, I'm fairly confident that you will find your skills marketable.

Cool...I really would like to end up as a researcher in a physics group at a national lab (i'm doing a master's in physics), but I find that physics courses and research don't go as deep into the theory and analytic techniques as I would like to go. They tend to sort of derive the equation and go straight into how to solve it approximately on a computer. Only thing is, I'm afraid employers will see a math degree on my CV and automatically dismiss me for physics/engineering jobs even though my research might have been directly related to the field.

 

[homeomorphic]

He may find a SUBSET of his skills marketable. However, the fact remains that outside academia, people tend not to give two hoots about the very theoretical side of PDE, so that PART of it is probably not very marketable. That might seem like a small issue until you take into consideration the amount of time and effort required to study the theories in question. Unless it can give you more insight into the more practical stuff, I don't know that it's worth it.

 

[homeomorphic]

Only thing is, I'm afraid employers will see a math degree on my CV and automatically dismiss me for physics/engineering jobs even though my research might have been directly related to the field.

There are a lot of positions that will say applied math or engineering or related quantitative discipline or something like that. I'm not sure the degree is such a big issue, although, personally, I would much rather have an engineering degree, if you ask me. What you should worry about is developing a skill set that they will want, even including non-technical skills. If you don't have the skill set, you could end up like me with my topology PhD, not knowing where you fit in. So, I'd start looking at applied math postings now to see what they want and by the time you get a PhD, you could make yourself very marketable.

I didn't really start this process until the end of my PhD, in addition to not getting internships, which wasn't a very marketable degree to begin with, so I'm now having to develop marketable skills under the pressure of being extremely underemployed and having to do a very difficult job search in the mean time, just in case someone out there is willing to hire me as is. The thing is, it's not just out of ignorance that I wasn't prepared. A big part of why I wasn't prepared is that the PhD was very difficult and took all my energy. Granted, if I had known I was headed out of academia, I would have had plenty of time to do things that industry would like, instead of all the things I was doing to prepare myself for academia.

 

[f95toli]

I actually was more interested in functional analytic techniques in finding solutions to PDEs, especially PDEs which arise from problems in kinetic theory/statistical mechanics and fluid dynamics from physics. I'm more interested in analytic techniques, but I'm not opposed to doing numerical simulations to check my theory.

Analytical techniques for PDEs are of very limited practical use so I don't this would be a very marketable skill in industry (or even anywhere outside the math community in academia). However, if you instead were to work numerical methods for solving PDEs (FEM etc) I am pretty sure you would find it much easier to find a job afterwards; for the obvious reason that there are a vast number of practical problems which require those types of skill to solve (fluid dynamics etc) .

 

[Hercuflea]

There are a lot of positions that will say applied math or engineering or related quantitative discipline or something like that. I'm not sure the degree is such a big issue, although, personally, I would much rather have an engineering degree, if you ask me. What you should worry about is developing a skill set that they will want, even including non-technical skills. If you don't have the skill set, you could end up like me with my topology PhD, not knowing where you fit in. So, I'd start looking at applied math postings now to see what they want and by the time you get a PhD, you could make yourself very marketable.

I didn't really start this process until the end of my PhD, in addition to not getting internships, which wasn't a very marketable degree to begin with, so I'm now having to develop marketable skills under the pressure of being extremely underemployed and having to do a very difficult job search in the mean time, just in case someone out there is willing to hire me as is. The thing is, it's not just out of ignorance that I wasn't prepared. A big part of why I wasn't prepared is that the PhD was very difficult and took all my energy. Granted, if I had known I was headed out of academia, I would have had plenty of time to do things that industry would like, instead of all the things I was doing to prepare myself for academia.

I'm more interested in getting a postdoc in a physics/engineering department at a university or national lab, however, I would like to have a more rigorous understanding of the sorts of equations you deal with than just running simulations on a computer, and that's why I'd like to get some background in PDE research and functional analysis. Why did you choose not to do academia?

Analytical techniques for PDEs are of very limited practical use so I don't this would be a very marketable skill in industry (or even anywhere outside the math community in academia). However, if you instead were to work numerical methods for solving PDEs (FEM etc) I am pretty sure you would find it much easier to find a job afterwards; for the obvious reason that there are a vast number of practical problems which require those types of skill to solve (fluid dynamics etc) .

Do you think, as long as I work on developing numerical computing skills (I already have to some extent), that I could do a theory PhD and still be marketable to physics/engin. postdocs and job postings?

 

[homeomorphic]

I'm more interested in getting a postdoc in a physics/engineering department at a university or national lab, however, I would like to have a more rigorous understanding of the sorts of equations you deal with than just running simulations on a computer, and that's why I'd like to get some background in PDE research and functional analysis.

Why did you choose not to do academia?

I'm not really a lecture person, and my research wasn't on the level that I could avoid that. Plus, I got sick of things being so far away from reality and applications (part of it was disappointment as well as getting sick of it because I thought that it would be possible to be closer to physics). It used to be cool when it wasn't as complicated, but the complication of all the theories disillusioned me and made me realize that I want to do something more practical, if I was going to have to work so hard for it. There are other things that exacerbate the problem, like the dysfunctional communication in the mathematical community, where papers are written and talks are given for too narrow of an audience, and some people even admit to purposely making their work harder to understand in order to make it seem like it's more substantial than it actually is (example: http://njwildberger.wordpress.com/2012/11/10/my-boring-seminar-talks/). I "chose" to leave, but the decision was mutual, I'm afraid because I'm pretty sure academia wouldn't take me, anyway, except as an adjunct, which is almost like slavery. Both my teaching and research were a disaster. Actually, I may be forced to become an adjunct next semester if no jobs are forthcoming. I am not a natural at teaching, and I don't enjoy the constant pressure of having to prepare for classes over and over and over again, 3-5 times per week with the whole class counting on me and ready to pounce on me if I don't satisfy them, but I can do it if I have to, with a monumental effort.

 

[Arsenic&Lace]

Hercuflea, if physicists in general do not bother to learn PDE theory, and it has been repeatedly mentioned that it is not relevant to industry, you may want to consider asking whether PDE theory is meaningful at all or if it's the pathological offspring of a bizarre, anachronistic philosophical view of what mathematics actually is.

 

[StatGuy2000]

Hercuflea, if physicists in general do not bother to learn PDE theory, and it has been repeatedly mentioned that it is not relevant to industry, you may want to consider asking whether PDE theory is meaningful at all or if it's the pathological offspring of a bizarre, anachronistic philosophical view of what mathematics actually is.

Correct me if I'm mistaken, but in order to effectively work on numerical methods for PDEs, wouldn't Hercuflea or others in his/her position (Hercuflea, I believe you are male, but correct me if I'm mistaken) need to have an advanced understanding of PDE theory, such as analytic techniques? So it's not as if in pursuing PDE theoretical research that numerical methods will somehow be neglected. And besides, so long as a solid understanding of PDEs are developed which can then be translated into actionable use for industry, I'm certain that Hercuflea can be very marketable.

 

[f95toli]

Correct me if I'm mistaken, but in order to effectively work on numerical methods for PDEs, wouldn't Hercuflea or others in his/her position (Hercuflea, I believe you are male, but correct me if I'm mistaken) need to have an advanced understanding of PDE theory, such as analytic techniques?

Of course, but there is a difference between having an understanding of the techniques and pursuing research on PDE theory. The analytical techniques you need to do research on numerical work are -as far as I understand- pretty much well understood and does not really include too much "exotic" math. Moreover, on a more practical note I believe you will find that PDE theory and numerical methods for solving PDEs (FEM etc) are quite distinct field of mathematics, at least to the extent that the research is done by different research groups at most universities. Hence, I suspect it would be very possible to go through a PhD in PDE theory and not learn more about numerical methods for solving PDEs than your average math/physics PhD student.

 

[Arsenic&Lace]

Correct me if I'm mistaken, but in order to effectively work on numerical methods for PDEs, wouldn't Hercuflea or others in his/her position (Hercuflea, I believe you are male, but correct me if I'm mistaken) need to have an advanced understanding of PDE theory, such as analytic techniques? So it's not as if in pursuing PDE theoretical research that numerical methods will somehow be neglected. And besides, so long as a solid understanding of PDEs are developed which can then be translated into actionable use for industry, I'm certain that Hercuflea can be very marketable.

Unfortunately I'm not enough of an expert to really say for sure. However applied math departments, which I considered applying to, actually had flexibility about pure math requirements. My undergraduate institution requires everybody to take theory courses. Numerous institutions had no such requirement. The fact that it is optional is a warning to me that it may be a waste of time. Of course there are details I don't know; maybe if you're in an applied math department and you work on numerical methods in PDE's, your mentor will require you to take functional analysis and PDE theory so it really isn't optional.