Electrical Engineering is a very broad subject that includes everything from small digital circuits in a cellular telephone all the way up to systems that operate at several thousand volts to power millions of customers. The field of electrical engineering is responsible for putting electrical signals to practical use.

 

When I got my electrical engineering degree back in 1975 there was no discrete electronics eng'g degree. Nor was there a computer engineering, although the 'classical' EE was a precursor for these fields as well. So, as you might expect, these curricula grew out of the increased specialization of our age.

As you cite, electrical eng'g is still a much broader curriculum and better if you don't really know what may interest you. But don't get too concerned as the degree just gets you in the door and the discipline you enter will more specifically develop your skills. I actually started my first job, in micro-computer control systems, with a guy that was a math major and he did fine. As we say, it takes a couple years for a recent grad to really be productive in the corporate sphere.

I've actually spent most of my career in radio frequency and telecommunications engineering (but have power/signal wired a number of homes, as well as other diversions). Of course for quite a number of years now I've directed an engineering group and so have gotten away from day-to-day design, but I still try to keep my hand in.

Feel free to pm me, but you'll probably be better served by insight from a much more recent graduate.

All the best with your decision and future. The ol' EE has served me very well.