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    You can of course, but what qualifies you better than all of the other applicants? Why would a department choose you given that most of the other applicants will already have an education in these fields? Commented Jun 10 at 17:53
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    Plenty of heavy duty math problems in engineering PhDs to be done (perhaps mostly in simulation). Same holds for other technical fields. One question would be how much basic undergraduate course work in the other fields you have done.
    – Jon Custer
    Commented Jun 10 at 17:58
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    An earlier comment of mine: The "roommate of mine" of mine who I mentioned here got an undergraduate degree in math, skipped a year from school (worked as an assistant car mechanic), then took some undergraduate engineering courses at another university part-time, then applied to and got accepted to MIT's graduate mechanical engineering program, where he got his Ph.D. in mechanical engineering a few years later. So yes, it is possible. Commented Jun 10 at 18:36
  • A question that would only be asked by a math major ... Commented Jun 10 at 20:25