The answers above are quite comprehensive - I'd just like to add a little more about aerospace engineering. Each university's aerospace program will have minor differences, which you can learn about by reviewing the program syllabus/outline, but for the most part aerospace programs will have classes covering the following disciplines: aerodynamics, thermodynamics, propulsion, vehicle performance, structures, control systems, and aircraft/spacecraft design.
Each program may have minor variations in terms of what the classes are called, how they're structured, how much detail they go into, and so on. But in general, those are the kinds of subjects you can expect to study. The design class(es), which are usually taught towards the end of the program, will combine the knowledge learned in other classes and will likely have you design some type of aircraft.
Last updated Nov 30 '17 at 12:17