It is commonly claimed that if you make it to ‘level N’ in your mathematics education you will only remember level n − 1 or level n-2 longterm. Obviously there is no canonical way to split knowlege into levels. But one could imagine a chain like:
1) Algebra
2) Calculus (think AP calc in the USA)
3) Linear Algebra and Multi-variable Calculus
4) Basic ‘Analysis’ (roughly proofs of things in Calculus)
5) Measure Theory
6) Advanced Analysis topic X (ex Evan’s Partial Differential Equations)
It is commonly claimed that if you make it to ‘level N’ in your mathematics education you will only remember level n − 1 or level n-2 longterm. Obviously there is no canonical way to split knowlege into levels. But one could imagine a chain like:
1) Algebra
2) Calculus (think AP calc in the USA)
3) Linear Algebra and Multi-variable Calculus
4) Basic ‘Analysis’ (roughly proofs of things in Calculus)
5) Measure Theory
6) Advanced Analysis topic X (ex Evan’s Partial Differential Equations)
This theory roughly fits my experience.