<p>You mentioned that you are majoring in computer engineering and that your university gives you zero choice about the classes you are taking. I assume that means that you are not taking any rigorous math classes either? </p>
<p>If that’s the case, your odds of getting into a legitimate PhD program in pure math are vanishingly small. If you are serious about math, your best bet might be to apply to Master’s programs at mid-ranked universities first. However, Master’s programs in math are not usually funded. (Also note that the top programs don’t offer stand-alone Master’s degrees.) </p>
<p>Applied math programs are more open to applicants from non-math backgrounds, but a lack of advanced math will put you at a disadvantage here as well, especially for the top programs.</p>