On: We ran the numbers, and there really is a pipeline...

[hkmurakami]

There's the "math majors' math track" and the non math majors' math track at most institutions. Even within the majors track, there's separation between experience levels and intended tracks within the discipline. Ex:

MAT215-217: Recommended for math majors, some prior experience in constructing formal proofs is useful but not required.

MAT216-218: Accelerated math major sequence, for students with substantial background in university-level proof-based analysis courses.

MAT214-204-203: Alternative path to majoring in math, with a more algebraic introduction to proofs

MAT203-204-215: Alternative path to majoring in math; good path for the applied math certificate.

https://www.math.princeton.edu/undergraduate/placement/seque...

Lumping all these students into one general course would be a disservice to everyone, like you say, and should be spilt up.

[Mirioron → hkmurakami]

But the difference in your case is that we don't expect, nor care, whether math majors and non-math majors end up at the same destination. It's okay and expected that math majors will end up learning more and becoming better at math. But when we're talking about people studying the same major, then this is not okay. You will either end up slowing down the fast track students or you will give them an advantage over those that weren't on the fast track.

[hkmurakami → Mirioron]

I disagree with your premise, since our current situation is that different students in the same major _already_ end up in different levels of aptitude by the end of their studies. Some far exceed that of the typical student.

Preserve the ability for those with this level of prior experience or aptitude to thrive, while providing support for those who do not have this head start but could either (a) Catch up, given the right initial environment and ramp up, or (b) never catch up to the most well equipped students, but will still be proper graduates of the program.