> I've already done a pure math
(+business) undergrad from a mid-tier
university and have been working as a
product manager at a financial services
company for 3yrs post undergrad. I've
been thinking of getting a PhD in an
engineering sub-discipline, but not sure
how to go about doing it especially since
I have no research experience.

It would appear that you might pursue
something in "financial engineering".

Since you are in the financial industry,
you might ask around and grow a network:
E.g., ask person A; maybe can get them to
suggest person B; tell person B that
person A recommended them and ask person
B; etc. I.e., apply social networking
techniques. E.g., try to get to some
people who can outline some of what James
Simons did. If you can, talk to Simons.
Similarly for various quants and people
who create algorithms and code for
automatic trading. Look into the
programs in financial engineering at
Princeton (E. Cinlar), NYU (M.
Avellaneda), Columbia (I. Karatzas), and
CMU (S. Shreve).

If you want to get into some other field
of engineering, then gather some
information, meet some people and get some
input, and start to pick some fields or
one field.

> (i) spend 1 year doing research with a
professor nearby then apply (I live close
to a major research university)

Maybe. If you can find a good situation
and like it, maybe, sure.

I have been suggesting that you start with
your own problem and make some progress on
it, maybe with a little advice (once I got
just three words), and maybe then consider
a professor as a official or unofficial
mentor or dissertation adviser.

> (ii) apply now and hopefully my work
experience can cover for research
experience

For a graduate program, in most fields,
you are not expected to have experience in
research. So don't have to "cover for
research experience".

> (iii) Rethink the whole PhD thing and
get a professional degree like an MBA (did
well on GMAT)

And, with that MBA, what will you do with
it? Consulting? Try to work your way up
as a C-level guy? Try to do portfolio
management or be a venture capitalist?

I'm a former MBA prof -- typically an MBA
is not very technical, but, now,
especially with some much in computing,
being technical can be seen as an
advantage. Or, maybe the flip side is,
soon all the work that the techies can do
will be done and what will be left is the
non-technical work. Your guess.

As far as I can see, still need to hustle
and/or be lucky to have a good career.

Also, an MBA is expensive while a Ph.D.
often costs $0.00 for tuition and might
provide a stipend.

> (iv) Just continue to learn on the side
and try to use my skills for opportunities

That can be a short-term approach that can
lead to a degree later.

If you sense that your background is not
good enough to go for a degree, then,
sure.

A major cause of my success in grad school
is the math I studied independently
between my Bachelor's and my Ph.D.
program.

In particular, for a Ph.D., will likely
have to pass qualifying exams, and you
will want to have enough preparation for a
path to do that.

> How did you narrow your interests before
applying for a PhD?

I attacked some practical problems with
applied math and computing. I did this,
first, in work in US national security
around DC.

> Is it possible to get a masters level
pure math education through self study?
I've taken until PhD level measure theory.

IIRC at one time the Web site of the math
department at Princeton said that the
graduate courses were introductions to
research by experts in their fields, that
no courses were offered for preparation
for the qualifying exams, and that
students were expected to prepare via
independent study. For this, you will
need a good undergraduate background.

There is some question how much a student
or anyone should attempt via independent
study. As a researcher, a lot of
independent study is usually just part of
the work, but there are seminars, etc.
that can help.

Mostly I did well with independent study,
but once in statistics I picked a poor
book and wasted some time. And, for some
subjects, I did get and really needed the
good, mature overview of a good course --
else there are too many places along the
way where can waste time, get stuck, or go
off on a tangent. Also it can be good to
be around good researchers and learn their
attitudes and approaches: E.g., often
researchers go through new material
surprisingly quickly and, really, without
the thorough mastery often implied as
important or even essential in high school
and undergraduate school. E.g., in
research, for some new material are trying
to make use of it, not get a high score on
some GRE exams.