Your starting curriculum will typically include two semesters of introductory chemistry along with one semester each of Newtonian modern physics. You'll typically have a couple of semesters of English, History, and Liberal studies (just for torture). Then, all the math up to and including diff eq, linear systems, and calc III. You'll likely get a smattering of the other schools of study such as a semester each of static structures, dynamic structures, and thermodynamics.
Then, you're ready to dig into electronics :)
Basics include circuit theory, linear systems (good for understanding control and communications systems), motors / generators, numerical methods (using computers with math to solve problems).
A little higher is electromagnetic fields and waves (a fairly tough course - lots of math), control systems, semiconductor circuits, digital design
Finally, you get to choose what you want to concentrate on for your career: communications, signal processing, programming, advanced control systems, logic design (a very profitable one these days), power electronics (my original direction), bio-med.
A heads up is in order. It's hard for a newbee to break into a good job without a Masters. Generally, a BSEE has to settle for a rotten job, put in a few years, and develop his talent. I've seen guys go home at night and teach themselves the specialty that helps them break into a good paying job, but that takes talent.
A Masters degree is a different story altogether. Get a Masters in a desirable field and you don't have to compete nearly as much.
I wish you well,
Mike