Contrary to popular opinion, z/OS is not the only operating system on the mainframe. You also have z/VM and (gasp!) z/VSE! z/Linux was already mentioned multiple times, so no need to repeat. :)
I learned to read dumps back in College by reading dumps. It was much easier to debug COBOL and Fortran programs by looking at the LISTX than to actually check the logic of those 3 GLs... ;) Took a class given by GOAL about VSE control blocks and other such stuff, and then built on that without a mentor per se. Ken snip..
