Part I -- General

> Why not quit my job and go back to
school? Well, that’s not really for me.
Reading books at my own pace lets me try a
subject out without fully committing to it
and making it a necessity that I find work
based off of it.

I respond here in three parts, the first
general, the second more specific and
about linear algebra, and the third about
statistics.

Really, in school, you still have to learn
the stuff. And, there a class might help
but won't be enough; so, right, again,
during the course and in the hours not in
the class, you still have to study and
learn the stuff. Or for the class,
"mathematics is not a spectator sport".
That means you still have to study the
stuff, get it between your ears,
understand it.

Eventually you can conclude that mostly
college and its courses are more for
certification than education. For the
education, that's heavily up to you.

But there are some dangers in self
learning: Not all the ideas and learning
materials are good; the really good ones
are only a small fraction of all the ones
you will likely encounter.

So, in praise of college and profs, they
can (1) get you on a good track with good
ideas and learning materials and (2) get
you unstuck and keep you on track. In
such study, it's possible to do too much
or too little -- from some experts you can
see about what is the right amount to do.

I said "college"; revise that to read "one
of the world's best research
universities", say, in the US, 1-2 dozen.
The ideas and materials you will see in
such a university really do stand to be
better than nearly all you will encounter
otherwise. Such learning is where there's
not much substitute for quality. But,
still, just to learn the material, you
don't really have to enroll in such a
university and, instead, just borrow from
their course descriptions and materials.
Indeed, some of the best such universities
are working hard to make their learning
materials available to all for free over
the Internet. Why? Because those
universities want to concentrate on
pushing forward with research.

Here's a way: Show up at such a
university and appropriate department, in
your case, applied math, mathematical
sciences, operations research, statistics,
whatever. Maybe show up at some public
department seminars. Talk with some of
the students. Say you have a career
going, for your career are interested in
what the department is doing, and want to
learn more about the program and the
mathematical content. So, get some of the
students to talk and explain.

Then for some of the courses you are
interested in, see who the profs are and
look at the course materials, say, texts,
handouts, on-line files, etc.

Then after looking at the materials and,
say, have made some progress with them,
try to get 15 minutes to chat with a prof.

Then take what you just got from that
department for free -- broad directions,
what they regard as more/less important,
texts, course materials, etc. -- and go
off and study on your own. When you think
that maybe you have some course studied
well, try to get a copy of the course
final exam or Ph.D. qualifying exam, work
through it, and, if it appears you did
well, ask a prof to check your solution to
a few of the most difficult questions. If
your solutions look good, then you will
start to look good and may get asked if
you would like to apply as a student in
the department. So, here you and the prof
and department are interviewing each
other.

Such things worked for me: (A) In my
career I kept running into the work of
John Tukey at Princeton and Bell Labs.
So, it was stepwise regression,
exploratory data analysis, power spectral
estimation, convergence and uniformity in
topology, his statement equivalent to the
axiom of choice, etc. So, I wrote him at
Princeton asking about graduate study,
mentioned those topics, and got back a
nice letter from the department Chair
basically inviting me to apply.

(B) I applied to Cornell and got rejected.
But largely independently I visited a prof
there to discuss optimization, asked about
being a grad student, and soon got another
letter accepting me to grad study.

(C) At least at one time, the Web site of
the Princeton math department said,
"Graduate courses are introductions to
research by experts in their fields. No
courses are given for preparation for the
qualifying exams. Students are expected
to prepare for the qualifying exams on
their own." or some such.

Lesson: In grad school at Princeton, are
still expected to learn the qualifying
exam materials on your own. Well, to do
that, don't have to be in the high rent
area around Princeton, NJ.

When I did go to grad school and got my
Ph.D., what really saved my tail feathers
was what I had done and did on my own as
independent study. Some of the courses
helped in providing high quality
directions and materials, but the real
work was nearly all independent.

And, one of the crucial inflection
points was when I took a problem in a
course but not solved in the course, did
some research, and found a solution.
The solution was novel, and word spread
around the department quickly. My halo
got a high polish, and that greatly eased
my path through my Ph.D. That is, I had
proven results on the most important
research academic and Ph.D. bottom line
-- I'd done good, novel, "new, correct,
significant" research. Then my hair cut
or lack there of, sloppy hand writing,
occasional upchuck at some bad course
material, etc. no longer mattered.

My research looked publishable, and it was
-- I did publish it later, in one of the
best journals, easily, no revisions. So,
lesson: That inflection point was from
independent work.

So, don't feel that your independent work
is inferior to enrolling as a student.
Instead, in the best universities, as a
student, nearly all the work is for you to
do independently anyway.

Still, I'd repeat -- try to pick the
brains, for free, without hurting your
present career, of the courses, profs, and
materials at a world class department in a
world class research university.

Why a research university? World class
research is a very high bar and some of
the best evidence of good expertise,
insight, and judgment in the field -- and
you don't want the opposites.