How to/Can you get a PhD position when you need more experience first? My friend loves mathematics and wants to continue research as a
mathematics PhD student, but this doesn't seem possible!
She did a prestigious but inadequate bachelors program (almost no math) and
because of this she is having a very hard time getting good grades for her master courses.
Thus she feels she has inadequate knowledge for a PhD position; which is probably right.
Her thesis adviser told her that she cannot continue a career in
research mathematics: no university would consider her given the situation now nor if she took an extra year or two to study more.


*

*Question: Is this true? Does it really stop here?

*I'm interested in similar experiences, opinions and suggestions (from
experienced professionals).

*I'm particularly not looking for a rosy picture!


In my opinion she is very talented, motivated, original and quick! She
would flourish given more time to take specific foundational bachelor
and deepening masters courses. Until now she performed extremely well
(near perfect score) and this is confirmed by for example two scholarships she
won (BA and MA).
PS. I tried to keep it terse but please ask for further details if needed.
Thanks a lot!

Update: Thank you all very much for the responses and useful comments.
It turns out that there is much more "staff rotation" in applied PhD programs and
  it seems plausible that she can find a nice position there; from which to continue
  her studies.
Thanks again.

 A: I'm not sure if we do it anymore, but Berkeley has (used to have?) a "pre-PhD" program. See page 25 of this. Probably some other schools have similar programs as well.
A: Her thesis advisor's opinion of her chances may weigh heavily in any PhD application packets, since the advisor would normally be expected to write a recommendation letter.  Usually, if you are advising a very strong Master's candidate, you would not be dismissive of her chances, especially if she has offered to study for an extra two years to make up any gaps in her knowledge.  I'm sorry that this isn't rosier.
But perhaps there is more to understand...  There seems to be a contradiction in your question when you say she is having trouble getting good grades, but has at the same time won two scholarships and has near perfect scores.
A: I don't know whether this is true today, but 30 years ago I had the impression that there were Math Ph. D. programs in the United States that would accept anybody with a pulse, just so they would have warm bodies to put in front of their Calculus classes. Naturally, we're not talking about Princeton here, but there were (and are) a lot of Ph. D. programs in the US, and they couldn't all be real choozy. Where there's a will, there's a way. 
A: To supplement Kevin Lin's point about the Berkeley pre-PhD program, Smith College (in the U.S.) runs an analogous post-baccalaureate program that has been successful in placing students in various graduate programs. It seems a good fit for the situation and aspirations of the person described:

"This program is open to all women with a serious interest in pursuing a higher degree in the mathematical sciences."

A: Here is a wild and crazy idea: answers to similar MathOverflow questions suggested going for a Master's degree en route to a Ph.D.  Perhaps she (after finishing her current Masters) can enter another Master's program at the university in which she wants to do Ph.D. research.  She can at least ask at that university what her chances are for trying such.  (It may be possible to do cross discipline; for example a Masters in statistics or computer science might be acceptable before trying for a Ph.D. in mathematics.)
Gerhard "Thinking Outside The Normal Framework" Paseman, 2011.02.23
A: Does she really need to become PhD Student in Mathematics? Why doesn't she try with something different?
I mean, a mathematician is, in my experience, not just a person who studies abstract mathematics. There are plenty of other occupations that involve the same skills and duties as pure mathematics. There is a lot of mathematics needed into other similar subjects, like computer science. Moreover, the interdisciplinarity of computer science should help her in getting such a position. Finally, original thinking and ability to formalize and being a hardworker are skills really needed and rewarded in this field!
To say my experience, I graduated in Mathematics (in the field of arithmetic geometry) but now I'm a PhD Student in computer science... and despite my lack of knowledge in specific topics, like programming, I feel I'm really helpful here!
Moreover, in some areas of Mathematics the research borders are quite far, so starting "late" could imply facing with difficulties in the future... or at least, I feel that this is what the most mathematicians think about this, and probably is the reason why she's having hard times in finding a PhD position in Maths...
A: Getting top grades in GRE will probably help her a long way to get into a PhD program. Trying past and practice GRE exams will probably give her a good idea whether she is ready to face a graduate program in mathematics.
