The main advantage I see is the ability to only and only math and a little info or physics (or no physical) and no materials related and thus finish (assuming you learn as much without teacher, I believe with good books but it is not the case for everyone) with a higher final level in math. Indeed, as an independent candidate we can do a lot more math. During some days of vacation I happened to do more than 12 hours of maths in the day. Without going at this pace every day, we imagine the level in the long term if someone predisposed to mathematics actually ten hours a day for 2 years - impossible in prep material out with math (mainly physics) too time consuming. However, the higher level he will remain in M1 and M2? Not obvious.
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