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I am mathematics undergraduate student interested in joining the workforce out of undergraduate (quant finance and data analysis). The past few summers I have been participating in pure math research programs (REUs), and I am struggling to write a résumé section for the REUs.

If any mathematicians are reading this, my most recent REU problem is PDE regularity. I'm at a loss for words on how to explain that to a layperson without making it sound useless.

How do I effectively talk about my work/results in the context of a resume read by applicant tracking systems and human resources?

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    This sounds like a question for industry people (i.e. The Workplace). I'm not sure a bunch of academics are the most qualified people to answer this... (Don't cross-post, though) – ff524 Jul 7 '16 at 6:49
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    Where did you do REU? Academic institutes or industry companies? Lp regularity and blow-up of solutions to pdes from fluid dynamics are not too far away from industry if you apply for jobs in large aerospace companies. – scaaahu Jul 7 '16 at 6:54
  • I don't think people consider going from undergrad to a job "transitioning from academia to industry". Without demeaning it, it's probably the most normal thing to do after undergrad. You also won't have the same issues as people transitioning from academia. For example, people won't expect you to have experience coming out of undergrad, while after a Ph.D you need to sell your time in academia as a reasonable alternative to industry experience. – Chris Rackauckas Jul 19 '16 at 22:52
  • Buddy its a transition from a resume focused on academia to a resume focused on getting jobs in industry – user305815 Jul 20 '16 at 0:43
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As a general note, do not use so many contractions and abbreviations. Writing terms out in full, at least the first time you use them, will never be wrong and may save a reader some time and effort.

You need to think of your resume in terms of what it tells the expected reader about your suitability for the job you are seeking.

Don't try to explain the subject matter of your research project "to a layperson". If the project does relate to a potential job, the hiring manager will either be a mathematician who understands the area, or will have mathematicians who understand the area on their technical staff, or at least will have arranged to consult a suitable mathematician on the hiring decision. If it does not relate, the reader of the resume probably does not care what the project was actually about.

A research project may tell a potential employer other things about you. Can you work independently on a specified problem? Can you write a coherent, readable report? Is your work good enough to lead to being accepted for a research project at a high prestige institution?

  • Also, this has been asked quite a few other times. Look at the "related" questions as they may be helpful. – Dave Kanter Jul 7 '16 at 15:57
  • @DaveKaye none of the related ones seem actually related. Can you post the ones you find relevant? Thanks! – user305815 Jul 19 '16 at 1:47
  • @small.pde Hmmm....they seemed more related when I first looked. So just to give general advice (from someone who made the transition from industry to academia and back) you have to turn your academic work into more of what industry pros will be looking for. That's going to be things like discrete, accomplished tasks. Did your research unravel some result that had been previously unattainable? Did you give presentations on that work? Did you teach to students and have meaningful outcomes from that? It's gonna be along those lines that you'll have to convert your resume. Good luck! – Dave Kanter Jul 19 '16 at 17:51
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Without demeaning your accomplishments, undergraduate mathematics tends to mean you're barely getting into academia and mathematical research. In fact, I am in the middle of my PhD with some published papers and that's still the case. Because of this, what you're learning/researching in undergrad is not as esoteric as it may seem. The topics at REUs are usually chosen because they are easily approachable by undergraduates and widely applicable.

Let's take Lp-regularity. Sure, you can dig deep into pure-math, looking into Lp-regularity of PDEs on manifolds etc., but this is actually a very relevant topic.

You say you're interested in quantitative finance? One of the biggest areas of research and application in quantitative finance is stochastic (partial) differential equations (SPDEs). Many models in the field (including the Black-Scholes model) use different forms of stochastic differential equations. Understanding the regularity results of these equations is crucial to understanding the error estimates for the numerical methods which are used to solve these models. One of the biggest recent results in the field (which resulted in a Fields Medal in 2014) is Holder-regularity of some solutions to SPDEs (and using a Holder-regularity approach, "Regularity Structures", to famously solve the KPZ equation), and people have already shown how this framework can be used to make numerical methods for previously-intractable SPDEs. In fact, in many cases one can only understand "the solution to SPDEs" via Sobolev spaces and Lp-regularity, making it essential to understand the numerical methods and simulation. So simulating financial models with low error requires the mathematics you learned.

But many PDEs require understanding Lp-regularity since many PDEs require talking about Sobolev spaces. In fact, one of the main uses of modern mathematics in industry is Finite Element Methods (FEM, or Finite Element Analysis, FEA). All of these numerical methods are derived for solutions in Sobolev spaces, this is not a fringe topic: this is central to the simulations used in the areospace industry, the petroleum industry, NASA, etc.

Also, some of the main methods in Data Analysis (especially in manifold learning) these days are closely related to optimization on PDEs, usually proving convergence in some weak norm and using facts about the eigenvalues of LaPlacians that you'd be familiar with.

All of this said, I think the best thing to do would be to scramble through Wikipedia and find out how what you learned is related to all of these different fields. Or pick up the Princeton Companion to Applied Mathematics and see how the study of PDEs is showing up in systems biology, genomics, medicine, finance, computer science, etc. You don't need to know all of it, but a good understanding of where you currently stand would give you a good perspective on how you're useful. I am not an industry person so I can't recommend on how exactly to put this in your resume, but with this understood you should be able to cater resumes to the jobs you're applying for.

Even if you don't end up doing something directly related to PDEs, I think most people would like that you have some understanding all the new stuff that's going on. At the very least, you will seem "experienced with math and number stuff".

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    I feel that this doesn't answer my question. My question is how to put my work on a resume so that it gets past the human resources desk and into a trader's hands – user305815 Jul 20 '16 at 0:39
  • Understand how what you've done is useful for the fields you're applying to. I told you where to look in quantitative finance. You're one step away from having a theoretical background in the PDEs for Black Scholes under certain conditions etc., and understanding what "the Greeks" really mean. Having that on a resume can be key for some quant positions. If you truly look at how these parts of PDEs are related to the jobs you're applying for, your resume will write itself. As I said, this type of research is not esoteric at all, and it's highly applicable. – Chris Rackauckas Jul 20 '16 at 0:43

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