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I am completing a computer science-related graduate application for a highly competitive school in the US that has an optional section for a "skills statement." In paraphased form, here it is:

The degree requires that you enter with knowledge of fundamental concepts including: (concept A), (concept B), (concept C), and (concept D). If you do not have prior coursework in these areas, please describe your relevant work experience or self-study in these concepts. Please describe how you acquired the knowledge and your level of proficiency.

I have a short, 1-page long statement summarizing how I acquired the knowledge through previous my academic coursework and my professional work experience with each concept.

My question is: How should I describe my level of proficiency? What would an admissions officer look for here? Would it be beneficial to pose this question directly to the school?

I have provided some quantitative data such as number of relevant undergrad and grad courses taken and years of relevant work experience, with brief summaries of each.

Should I try to rate myself on some arbitrary scale of 1-10? That seems rather pointless and subjective.

Should I try to give myself some kind of qualitative label such as "novice", "expert", etc.?

Any advice would be appreciated.

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This sounds to me like a good place to follow the dictum of "show, don't tell." Giving a numerical or qualitative judgement will be useless, because they can't tell how your rating scale relates to their own. What you can do meaningfully, however, is talk about what you have actually done which demonstrates facility with the concepts by putting them to use in classes, projects, or real work.

For example, if one of the concepts was "algorithms," then you might talk about a piece of software that you wrote that required understanding and applying complicated algorithms, or an undergraduate research project in which you created and analyzed an algorithm, or something of the like. This will then give the evidence that the reader needs to assess you accurately, however they calibrate their scale.

If you don't have strong examples like that, then just say whatever the truth is about what you've done with the concept, e.g., "I got an A in my algorithms class." It's not very satisfying, but in a case like that you really don't have much facility with the concept (peopler generally understand a concept much more deeply once they have applied it outside of the classroom). Better a less than satisfactory truth than trying to guess what somebody who you've never met would think differentiates "pretty good" from "expert."

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