I am currently two years into a math PhD program at a mid-tier state school. I read a lot of advice about getting a STEM PhD on the Internet, but a lot of it seems very inapplicable to mathematics. I don't have a lab or a PI, I don't need data, and my assistantship consists solely of teaching. None of the advice I read sounds anything like the experience I'm having here.
Compared to other STEM fields,
How common is it for math students to be supported by external funding (e.g. NSF GRFP) rather than a TAship? How common is it for math students to do internships in industry to gain practical experience? How common is it for math students to do outreach or volunteer work during graduate school?
Does a math department generally provide support and guidance to students when it comes to finding and applying for fellowships and internships? Is it a common attitude that it is the student's responsibility, if he wants those things, to undertake all steps of this process by himself?
Is it normal for math departments to disregard students' research interests in favor of mandatory coursework? For example, because all of my time is tied up in the 1st/2nd year courses and exams, I have been unable to do any research for the last two years, despite being very prepared and capable on my first day. (I published during undergrad and was chasing several promising ideas when I arrived.) When I asked to be allowed time to do research instead of taking classes, I was rudely shut down.
How often do mathematics departments get together in social or community events, such as departmental happy hours?
How is networking different in mathematics? Do professors generally have connections in industry or prominent members of their field, or is that a rare thing?
(Note. I'm sure it is evident from some of the above questions that I am feeling a little put off by my department. The point of this question is not to seek out sympathy or validation. The department just seems stubbornly uncooperative, and completely uninvested in my future, which is not what I was expecting. I want to know how common this is- whether it is unique to my department, or the nature of the discipline. But this is a peripheral point, the question I'm asking is about how these factors work in general, not just with me.)