For grad school this completely depends upon the department and the specialization. Go to any department website and you can find the requirements. Where I was there were no course requirements of any kind for PhD. It was completely at the discretion of the advisor and committee of each student. We did have to have a minor outside of EE, though, and those that chose math were required to take a bunch of theoretical math. I know many EEs that never learned PDEs because it is seldom necessary for those that specialize in the "applied math" portions of EE (comms, signal processing); those in the "applied physics" specialties (electromagnetics, solid state, quantum electronics, plasma physics) typically do need PDEs, of course.
For BS EE you can again look at web sites, but I have never run across a BS EE that did not have to take probability, and the vast majority are required to take linear algebra. In my opinion, any EE program that does not require intro linear algebra is failing their students, and students in those programs should take it as an elective.
jason