Quote:

Originally Posted by **DrRocket**

Question: I have been told recently by facultyat two major state universities that average first-year graduate students are no longer capable of handling what I used to think of as the usual rigorous class in measure and integration. This rather surprises me. Is that your experience as well ?

I find it unlikely that graduate students are having particular trouble with the measure theory and integration

*courses*. These courses tend to be structured more or less like advanced undergraduate courses. So since the format of these courses is familiar to 1st yr graduates students, I would expect them to do okay in them.

That said, I've never really been in a position to observe how 1st yr students do in measure theory/integration. I took their equivalent when I was in college, and never really looked back.

My overall sense is that the quality of 1st year grad students varies from year to year. I did get assigned as a teaching assistant for Differentiable Manifolds, which is traditionally more challenging to 1st yr grad students than measure theory. And I thought my students performed pretty well. In every new batch there are always going to be a few people who don't belong of course.

I think mathematics faculty can sometimes be over-dramatic when they express disappointment in their students. It's easy for a professor to conflate his idea of how he performed in a course with his idea of how the average student performs. Think back to your time in grad school. Who do you remember the most?--the students who did well, and stayed for 4 or 5 years, or the students who dropped out after the 1st year?

As I see it, the real crisis in graduate math education is that the faculty do very little to prepare their students for careers outside of academia. I think a lot of mediocre graduate students entertain the notion that they will follow in the footsteps of their advisers, without realizing, and without being told that there are simply not enough tenure track positions out there to accommodate everyone. If these students are really so sub-par, why isn't anyone taking the time to pull them aside and provide a realistic assessment of their career options? Instead of grumbling, faculty members would do their students a greater favor by taking an active interest in their future.