>>11471213X students are engineers in name only. They are taught extremely advanced physics and maths just for the sake of it. Some of them even do QFT just because they can and because they could be tempted to do research after their 4 years of military service.
(most X students don't actually serve in the Army, they get "head-hunted" and the company which hires them pays back the costs of "deserting".)
>>11471497>>11471520Maybe it was true 20 years or so ago. Prépa's programme has been slightly watered down and most of the "encyclopedism" the prépa were known for happens at the Graduate level if they are accepted in ENS, X, or other high-level grandes écoles.
Prépas nowadays mostly give you a very solid and very throughout mathematics and physics background corresponding to a good undergrad's knowledge. Emphasis is put on developing techniques to quickly read and adapt to different problems, context, and notions, even ones you couldn't study in prépa for the lack of time. You don't need to digest an incredibly abstract and huge amount of material to do that.
One of the most egregious examples of that was a prépa analysis textbook which developed extremely powerful and intricate properties of integrals and estimates without once using Lebesgue theory or calculus of residues.
To give names, the biggest "named theorems" you will see in a prépa are on the level of Cayley-Hamilton, Cauchy's integral theorem, D'Alembert-Gauss (fundamental theorem of Algebra), you may also venture into group actions and shit like that.
This is even more impressive in physics. The curriculum is more or less designed to squeeze the most of Newton's formalism without ever mentioning, Lagrangians, Hamilltonians, or the general theorem of ODE which helps to put these things into context.
"normal" engineering schools will use this material as a basis. X and ENS will however give you things you never learnt before in the intro and ask questions about it to test your adaptability.
