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Someone could absolutely do both things at the same time. The categories at the US Department of Labor, or the exact wording of the job title on the plaque on your desk, have very little to do with your actual life as an engineer.</p>
<p>As another example, there is a major at MIT called “Math and Computer Science” (18C). There is no job title at the US Department of Labor called “mathematician and computer scientist”, and no job position at any company in the US with that name. But surely you can see the utility of studying both math and computer science at the undergraduate level for someone who wants to do one or the other.</p>