How to present participation in undergraduate research experience programs on CV when applying for jobs in industry? 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?
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?