Career advice - Getting a Math PhD admit in a good program with computer engineering background
A concern (raised by your background) that occurs to me is that do you really have a clear idea what graduate programs in math are all about? I don't think that any reputable grad school would allow you to study numerical analysis alone ... [Edit taking note of Willie's remark] within a graduate program in pure math - the scene is markedly different if you are applying into a program in applied and/or computational math. I apologize for not knowing that such possibilities exist. My smalltown background left me with the false impression that math and applied math always come together. Such programs may be better suited for you![/Edit] (continued rant) ... For the simple reason that doing research in math requires familiarity with a variety of tools and theories from adjacent, nearby and occasionally relatively remote areas of mathematics.

Is entering a computer science/computer engineering graduate program not an option? Probably you can specialize in scientific computing/numerical analysis in such a program. It may actually be easier to find an advisor in such a topic at a CS department? I don't know for sure, but it sounds like such a plan would entail less risk.

Our resident experts on numerical analysis/scientific computing can give you more useful advice. Below I will say my bit.



Before you burn your boats I would recommend, as an extra-curricular activity, that you take a look at what the obligatory 1st year courses of math programs have in store for you.
The core math at a typical US grad school (for 1st year grad students) contains at lest topology, abstract algebra, real analysis (sorry the link is only to measure theory, couldn't find a more fitting Wikipedia article at this time) and complex analysis. Some places would offer/recommend/require also mathematical logic. After the first year, you are expected to display a working understanding of the theories and results that those articles link to, and be able to reproduce their proofs on demand (ok, the committees will likely give you some slack on the more esoteric proofs, but don't count on it). The depth of those course probably depends on how much ivy the school has. I cannot give details on that for the simple reason that my experience is from a reputable but not top notch grad school, and I have only heard rumors about the others :-).

Only after having covered those basics can you start specializing on a topic that interests you the most.

I don't want to dampen your enthusiasm. I just had a few fellow grad students who were surprised by the graduate curriculum, and either dropped out or had a hard time making through the 1st year. My concern is that you may not fully appreciate how limited your exposure to math actually is (given your background). GRE is a joke, but it does test that you can speedily pick the correct calculus concept/theorem off the shelf in your brains and apply it.

So if going through those links just makes you hungry to learn more, then 'full steam ahead!', but otherwise you may want to reconsider.