Admitted into M.S. in mathematics! Need some help from students in the math department.

I would caution you on taking 500, 525, and 540 all at once on your first semester. Those three courses are "comp courses" used to fulfill PhD comprehensive exam/requirements and are generally more time-intensive than non-comp courses.

A lot of graduate students started off with 2 comp courses in their first semester, there were definitely a few who did at least 3 comp courses in one semester and did well.

Secondly, how large a chance is it to be hired as a teaching assistant? What would be the salary?

It's been a few years since I graduated: If you were in the Teaching Mathematics concentration, you would get Teaching Assistantships (TA) to support and complement the concentration.

For other concentrations, you could be on a department waitlist/stand-by list but it's extremely unlikely you'll be hired as one and you should never assume you'll get one.

Instead of TA, some M.S. students took on research assistantships (RA), but there was no formal process for it: you had to network, cold-call/e-mail, and just search around on your own initiative. The department will occasionally e-mail RA opportunities, but those were rarely and highly competitive.

Finally, from the coursework, it looks like you're ultimately looking into PhD in Math. If so, there's a process for M.S. students to request to be converted to PhD after their first semester or two depending how well they do in those comp courses. Those comp courses you take as a M.S. student carries on to fulfill requirements as a PhD student so you don't need to start over like you would if you went to get PhD outside of UIUC.

/r/UIUC Thread