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It should be noted that this is a fairly common pattern in graduate mathematics departments at public schools - IMO, it is to give students a chance when given outstanding resources.

I experienced something similar while at UIUC for math, but I passed the comprehensive exams solidly (my first attempt at two of them were thwarted by abnormally difficult exams where almost no one passed).

I ultimately left, but largely due to non-academic reasons combined with the state of Illinois stealing the university's budget allocation. Teaching wasn't too bad, but life in the tech industry sure beats academia.

This sounds like a very strange system to me. Where I graduated (and I believe in most of Europe) the university has to have allocated the full funding for the entire PhD for a student before that student is admitted. So the university cannot afford to run a scheme like you describe, which is good since that sounds to me like a borderline predatory system.

Teaching positions for grad students aren't predatory. They are really a form of financial assistance. In return for teaching 3 hours a week 2 hours sitting in your office with the occasional student visitor (with say 5 hours of prep work that could be done during office hours and 3 12 hour days grading exams). That's 8 hours of work a week which works out to a pretty decent hourly salary.

It's hardly luxury and when the state/university system yanks funding out during your tenure THAT is somewhat predatory but usually most departments find a way to tighten belts and make sure current students have sufficent funding.

I've got six hours of teaching a week plus 2 hours of office hours plus meetings related to teaching plus prep plus grading.

Plus classes, homework, exams, plus research meetings, plus doing research, plus seminars, plus commute.

My university's administration has a rule that our department can't pay us more than a fixed amount, and that amount happens to be lower than the living wage in the city I live in. In other words, by the university's own admission they don't pay us enough to live off of.

For what it's worth, when I was still in college trying to decide between pursuing a math Ph.D. or going into the tech industry as a programmer, I remember being advised to think very hard about Berkeley as a graduate school due to the reasons cited above.

So, while this is just anecdata and I ultimately chose the second option, my experience researching graduate math departments is that Berkeley is specifically known for this practice and very few other departments are.

Hmm, my experience in 2001-2008 wasn't the same. While there were certainly funding issues the department worked pretty hard to try and do what it could to help. Then again technically I was in the logic group so things were a bit different for me but I'm conveying what my math grad officemates and friends experienced (i.e. they said they had pretty much the same situation).

Yes, some people didn't finish but math is hard and while the department is large and can be impersonal there were no barriers and efforts were made to assist the students.

The cheap labor argument doesn't really hold water (at least during my time). More students wanted teaching positions than positions were available.

Glad to hear the situation improved after my time. Even back then, I observed that logic treated its students better than maths did. There was precious little help for us in prelim prep, just a student-run seminar and problem book, while I don't remember logic even having a comparable test, or if they did, it was not designed to filter out over 50% of students as the maths one was.

Don't understand your last paragraph. If demand for jobs exceeds supply from the employer, that suggests there will be downward pressure on wages, i.e. the labour becomes even cheaper. Maybe you're suggesting that the jobs can't be that bad if people want to work at them, but that wasn't what I said. I enjoyed being a TA immensely, and it was a flexible job that fit my studies well so I did it even though I had funding - but that doesn't mean I wasn't still massively cheaper for the university than hiring Dr. Coward, or that there wasn't a cynical strategy of getting us students to teach calculus cheaply and then dumping half of us on the street.

I chose not to be a grad student in Berkeley's math department for exactly this reason. I went to a smaller school that didn't have this sort of weeding out.

(I started my PhD in 2005, and it's possible that this was not the situation at the time and I was acting on outdated information. I don't regret it, though.)

If hard working students fail a test, the failure is on the teacher, not the students.

I highly doubt the majority of students at berkeley would be anything other than hard working.

Unfortunately, hard work is not always effective work. When you embark on a journey of learning, it is your own responsiblity to make sure that you learn effectively. Hard work alone does not justify any merits - you have to make it count.

That is exactly the job of a teacher - to make sure you learn effectively.

How many of your teachers focused on efficient learning ? I can't remember one. Even the handful of teacher that left a deep trace in my memory never mentioned 'learning'. They were just so well aware of their subject, they could be the catalyst to bridge gaps in my view of things, triggering inspiration and desire.

There needs to be a desire in the student to learn, but the teacher must also be able to impart things clearly. Otherwise, why bother having teachers at all? Why not have everyone self-learn? Ironically, that's what I'm actually doing right now, but still it's good to get recorded lectures as this tends to really help fill in blanks.

I'm doing a lot of self studies too, and what I'm missing the most is a little peer pressure to focus and test, especially tests. That's why I personally enjoyed MOOCs since they provide that. My experience is doubly biased, I don't recall any teacher being really helping in learning as I said, but I went to college at a time I couldn't interact with them normally too.

It should also be the responsibility of the teacher, however, to guide you towards effective learning techniques.

Just to get into berkeley you have to be the cream of the crop or the best of the best. These students, in general, work hard and study effectively.

When a test fails a majority of these types of students, you can't blame ineffective learning on students that represent the best of the best.

There is a third option: the test is unfairly structured to reduce the number of people Berkeley can put through its PhD program. If Berkeley knows it cannot teach more than x students, yet it consistently enrols y students, then it could use a test to weed out y-x students (regardless of whether those students are capable of completing a PhD).

> I left the university, and mathematics, and have been much happier as a result

is the second bit true? why lump mathematics with your leaving of the university?

what does it mean to leave mathematics?

i stopped looking at the stars because i left the business that hires engineers to build commercial lenses?

Yes, the second bit is true, for me - I am much happier as a consulting CTO than I ever would have been as a maths professor (abandonment of the latter career is what I meant by "leaving mathematics"). I guess I have to thank Berkeley for helping me to discover this fact relatively quickly.

I did not mean to lump maths and Berkeley together - I happened to leave both at the same time, but that doesn't mean I had to, or indeed that this was necessarily best for me, or would be best for others.

i see now that you meant the career: Mathematics; and i am glad you are happier now

my concern was that if you ever found happiness in research that you dropped that happiness assuming the career and research were the same

what happened to all the open thoughts you developed in your area of interest?

I still pursue them for fun occasionally, and my papers (very minor, and never properly published) are cited or used even more occasionally. That's fine with me, as I've been able to do much more in my new field.

A relief, glad to hear this as well