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I am a pure mathematics undergraduate at an American school interested in pursuing internships in quantitative finance. The past few summers I have worked at various universities doing NSF-sponsored Research Experience for Undergraduates (REU) programs, where I worked on pure mathematics research problems. I am struggling to explain what I did in these programs on my resume. Almost all of the work was theoretical (i.e. pen and paper) and highly technical.

Should I phrase my experience and responsibilities in layman's terms so that HR can process my resume efficiently? Or should I state exactly what I proved?

Even if I were told to phrase it in every-day language, I would struggle. The most recent project, for example, was on a regularity problem. How do I phrase my theoretical results without making my resume inaccessible?

  • Did any papers result from your work? – Patricia Shanahan Jul 19 '16 at 14:21
  • Who are you writing your resume for? Is it people familiar with mathematics research or people unfamiliar with it? – enderland Jul 19 '16 at 14:32
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    A resume should give a overview, not a technical specification on what you did. If your name is Einstein, you would say, "I helped proved my Theory of Relativity by demonstrating high level abstract thinking. Recently Stephan Hawking found blackholes that proved parts of my theory." – Dan Jul 19 '16 at 18:52
  • @PatriciaShanahan yes, I have bullet points for those – user305815 Jul 19 '16 at 22:13
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    The folks who might hire a mathematician will not have HR discarding resumes that refer to math they aren't familiar with. – keshlam Jul 21 '16 at 4:12
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Frame the research experience around what employers like to hear as well as any accomplishments that you may have. If you worked in a team, frame it as "Worked in a team of X students on a novel mathematics research paper", "Presented Mathematics research to audience of X faculty members", "Published mathematics research in industry journal" or similar. Unless what you proved is specific to the job (i.e. a large advancement on the Netflix problem, and you want to work for Netflix in the department that develops the algorithms for showing suggested movies), the hiring managers and HR will care more about the thought process and how you went about solving and presenting your solution to the problem than about what the solution or even problem itself was. They'll also want to see that you were successful and have the commensurate experiences to prove it.

Chances are the interviewer will ask you to describe your project. When that happens, focus more on the implications of the solution and general methods you used to figure out that solution rather than getting into the weeds.

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    The exception to not getting into the weeds is if you are being interviewed by a mathematician who asks questions specifically about your research. – Patricia Shanahan Jul 19 '16 at 23:53
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    But that's in the interview, not in the resume. – keshlam Jul 23 '16 at 14:47
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The first rule to a CV is:

The aim of your CV is to represent your experience and education in light of the job you want to have.

And that really depends on the audience you want to reach. People who would be familiar with the kind of work you've done would expect to see a certain amount of details. For those who aren't (HR?) would not appreciate, might misunderstand, and would essentially frown on that amount of information.

So you should keep the name of the places, dates, research centres, etc. But try to see how that experience is relevant to finance. Why does that experience make you desirable in finance, compared to someone who did not have that experience?

And, the best would be to get to layman's language... but financial language would be very good as well. It shows you are already projecting yourself on the job.

Avoid:

Project to solve the Bob McDuck matrix inversion in the case suggested by Tim Smith with the parameters belonging the Group of Jon J. Fitz.

Prefer:

Algebraic analysis of complex matrices, allowing for prediction of evolution of a multi-dimensional model.

You get the idea.

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+150

The core of your question relates to, "how important is it that my resume be understandable by someone who is completely unfamiliar with the subject?"

A hypothetical situation would be to imagine the two examples below are bullet points on your resume. Part of it is written in slkjf, a specific language I just invented which is used in mathematics research.

Case study - a tale of two resume bullet points

Example 1 - no care for the layman

  • REU - skoj jjk kjlw ff oklj
    • Worked on kljf jj lslk jskljb lslkj
    • Proved sjklj jfjkl lkw wjkljkls
    • Assisted Dr. John with asjkljl wlkjf lkjlkjw

Example 2 - taking care for the layman

  • REU - Pure Mathematics Research
    • Worked on kljf jj lslk jskljb lslkj
    • Proved sjklj jfjkl lkw wjkljkls
    • Assisted Dr. John with asjkljl wlkjf lkjlkjw

Analysis

Notice how there are two subtle differences. First, the position is bolded in one - this draws attention to the "HR understandable" part. You want HR to know you did research but the specifics of the content are likely not as important at that level.

Most HR systems have criteria like, "X years experience with Y" or for people doing internships, "work experience" or "number of relevant internships" or otherwise generic requirements. You can find these just by looking at job applications.

So your goal isn't to convey to HR the content of what you have done but allow them to check the boxes they are looking for. Notice that your job title is clear now too. It is important to ensure that your job title is understandable and meaningful to HR. You can do this by writing it like that, or even such as:

  • REU - Pure Mathematics Research (skoj jjk kjlw ff oklj)

I have in some cases clarified my job title when it was different from my "HR" title in order to help with this. It is particularly important the further your actual job responsibilities are from your official HR position/title.

With all this in mind:

Should I phrase my experience and responsibilities in layman's terms so that HR can process my resume efficiently?

Sort of. Make sure that HR can get the necessary information that they need. As discussed above, the exact details of your work are generally not as important as the ability to identify the bigger position responsibilities.

Or should I state exactly what I proved?

Follow normal resume guidelines for this. Specifics of what you did are good, but don't write a book. There are many other questions that can address how to do this a bit more comprehensively but in general specifics are helpful, so don't be afraid of them.

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+250

There aren't easy answers here. You need to decide what level of acuity you can sacrifice for making your research understandable.

So for instance if you know your hiring manager will be the head of research at a company, you can afford to go into more (otherwise prohibitively detailed) explainations as to what it was.

In essence, you have to tailor your resume based on who will be reading it.

In general, you can do some things to make it more readable for non-tech people though:

  • Avoid using slang or deeply technical language (whereever possible)
  • Move away from trying to sound intelligent and instead have your primary ideal be to convey the information. If you're good at this, you'll end up sounding intelligent without also dispensing a "better-then-thou" attitude
  • Focus on the real world implications of your research - make analogies that help laypersons to understand why and what it is you've been doing
  • Highlight the skills you developed doing the research. Its often beneficial to make it easy for HR people to extract some positive qualities from your research. The actual acuity of your research experience will probably be evaluated by a technical person anyways.
  • Keep it short, broad and interesting for your resume. Good interviewers will ask follow up questions and give you time to explain further. Your goal isn't to convey the subject of your research in all its brevity, its to pique interest and set up a opportunity for you
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Technical people always struggles with that, I really know how it is like.

If you want to work with finance, you'll have to explain your research in a way three kinds of people understand. The main: finance professionals. Yet HR and management people must understand it either, if you're applying for finance industry companies, HR and management will probably have a reasonable finances knowledge to understand you. So, in that case, you can strongly frame it in finance language.

You should focus on what your research might contribute with finances, or, at least, what skills you've developed doing that. Skills directly related to the positions you're looking for. Some examples:

  • My research developed a X model which can be used for cash flow optimization in linear models.
  • I've developed a Y kind of research, which developed my statistical skills, what improved my ability to purpose stock models.

But if you're not applying for a finance industry company, but for a finance position in another industry, the picture changes. You'll have to frame it simpler, as the HR will probably not be used to financial vocabulary, and your probable boss might understand nothing about finance. In that case, you'll have to expose the same things, but in a way everyone with high school understands. Some examples:

  • My research developed a model for cash flow that ensures your company will keep enough money available yet optimizes investment and return.
  • I've developed a research which developed my statistical skills to develop a model that picks the best stocks.

And please note, my examples are a way to illustrate what I've meant, only. They're not exactly properly ways to express it when actually applying.

You'll also have to be careful to the difference between writing this, in an application form or resume (like question asked), and, in the future, how to explain it verbally, to a person, in an interview. The approach is the same, but the way to frame is different.

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