> At a point in history when self tutoring often provides more than the average Graduate course, it blows my mind how difficult it can be to get into a Masters program.

Things to consider:

(1) Take the GRE tests for both aptitude and your
speciality. Really good scores will be tough to
ignore. And if your speciality is in a STEM field,
then you get to f'get about all the English literature,
history, etc. and your grades in those nonsense subjects.

(2) Emphasize points of success in your career. Why?
Because you will look like you are taking your career
seriously and might later in your career be able to
make significant financial contributions to the university.
Yes, Virginia, universities like rich students!

(3) As in the quote, do some independent study. Then
in your application, describe the significant books
and journal papers you have studied. You may be doing
enough independent study now just for your career.

(4) Get the description of the Ph.D. qualifying
exams. Mostly the coursework for a Master's and
for preparation for the exams are similar. So,
just study the darned material on your own, apply
to the Ph.D. program, and offer to sit for the
qualifying exams before being admitted. Offer tough
to turn down.

Note, at one time the Web site of the Princeton
math department just flatly stated that the graduate
courses were introductions to research by experts,
no courses were given for preparation for the qualifying
exams, and students were expected to prepare for these
exams on their own. So, do it, on your own, without
going to campus.

That you successfully prepared for the qualifying exams
on your own is big time impressive and a big point
for any graduate program because one of the basic
necessary conditions for success in a Ph.D. program
is good ability at independent study. So, showing
such ability can make a graduate department really
happy, i.e., no longer afraid they will have to
write your dissertation for you.

(5) Find a problem, maybe at work, that needs
solving and get a good solution, both in theory
and in practice. Write a paper and submit it
for publication in a peer-reviewed journal or
a conference.

If are unsure on just how to do
this, then find a friendly Ph.D., researcher,
professor to give you the 101 Big Secrets
They Never Taught You in College on
How Get a Paper Published or some such.

Pretend to look for a recommendation of a
suitable journal and write to a suitable
professor in the program you want to enter
and send a copy of your paper. So,
prime the pump via a backdoor. If he
likes your paper, then it can be that all
the rest goes quickly. E.g., once I applied
to a graduate program at Cornell and got
turned down. It happened that there was a prof there
I wanted to talk to about a problem I had
at work and flew up. We took a campus tour,
and back at his office I showed him my problem
and my progress on it. Suddenly I got another
letter from the department admissions saying
I was in. I didn't go. Via such things I
also got into Brown, Princeton, and Hopkins.
I went to Hopkins.

(6) Typically a STEM department has a
seminar series. These can be painful as
a toothache because you may be listening
to stuff you don't have the prerequisites
to understand. But they can also be good
because they can, on a good day, give you
some great help in picking a research problem.

Well, typically such seminars are open to the
public, and maybe also the department tea
before the seminar. So, crash the party
and meet some of the profs and/or graduate
students. From the students, get some of the
'low down' -- they can be quite helpful to
a fellow suffering human.

You need to know that graduate school, really,
is not much about learning. Instead, the three
most important aspects are research, research,
and research, as in "new, correct, and significant"
and/or "worthy of publication". For a prof,
what's important is research good enough to
get a good grant, e.g., from the NSF. E.g.,
that Princeton Web site didn't even want to
teach basic material and only wanted students
to get involved in research; the assumption is
that hard part was doing the research, not
finding, reading, and understanding it in the
library.

As a graduate student, do
some work that is nice and clearly publishable,
especially if you publish it,
and can suddenly find that
life in the department gets much nicer.

Finally, my Secret Guide to Research Success in
STEM Fields is, "be wise, mathematize". Basically
get an ugrad math major with emphasis on topics
that can be important in the other STEM fields
and then make the research basically
some new theorems and proofs. It's worked for
me.

For the admissions office, try to f'get about
them! They just can't be the brightest bulbs
on the tree.