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I'm a third-year undergraduate student, preparing to apply for Ph.D. programs in physics (and aiming to do research in theoretical physics). I'm planning to graduate with a double major in mathematics and physics, and I have significant research experience in experimental high-energy physics (both as a research assistant for the past 3 academic years, and through several related REU programs). While I have not published anything, I have presented my work at symposia, and have contributed substantially to various software projects, data analysis efforts, and more.

Last summer, I completed IBM's "Machine Learning Professional Certificate" and "Full-Stack Software Developer Professional Certificate" programs on Coursera. I'm considering listing these on my CV (and perhaps in my application), however I'm not sure on what side of the line between resume filler and something more meaningful and substantial these lie.

Should I mention these and, if so, to what extent?

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This is useful information and should be included in your CV. Research in quantitative disciplines may involve data analysis and statistical programming work (and in rare cases maybe even larger data engineering pipelines) depending on the research topic. For various types of jobs and research positions it is useful to know whether the candidate has previous experience, knowledge, accreditation, etc., in data engineering and data science work. It can also be useful to know what particular tools/languages you know and what level of skill you have in each.

I recommend you add a short section to your CV for Data Science/Programming Skills and Accreditation and give a short summary of your skills and accreditation in that area. This could include some simple dot points of particular tools/languages you are familiar with and your level of skill in them (e.g., basic, intermediate, advanced, expert). You should also include any relevant accreditations you have for any particular tools/languages or for general processes. I have a short section in my own CV setting out this information; it doesn't take up much room and it is not the highlight, but it tells people what tools/languages I already know well and what skills I have.

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