the latter phenomenon occurs at least three or four times over in good (rigorous, proof-based) math classes.
I've had this happen for
- everything from linear algebra (at least 20 things)
- all kinds of stuff from mathematical optimization
- inequalities, which are really difficult until something "clicks" and then when to apply them becomes obvious, cauchy-schwartz and jensen's in particular
- induction (this was a long time ago / early in my math career)
- diagram chases
- the entire typeclass stack from FP (functor applicative monad, then all the monad interfaces)
- huge chunks of axiomatic probability and measure theory (what do sigma algebras really mean, what is a good definition for integration, what is continuity of measure, dinkin's pi-lambda theorem)
- and so it goes on
I am still waiting on some of the following things to click so that I may abuse them productively as well:
- LLL
- yaos min-max theorem
- lots of results from logic
I surmise this happens for monads and freaks developers out because it's one of the few pieces of serious math (i.e. no handwaving, given as a rigorous construction, etc) most people come across, so the phenomenon catches people off-guard.
I do like this thing! I love math. I tutor young people in math at a local school. I've applied to an undergrad math program at Toronto and Waterloo as well. Hopefully I can get in...
I've had this happen for
- everything from linear algebra (at least 20 things) - all kinds of stuff from mathematical optimization - inequalities, which are really difficult until something "clicks" and then when to apply them becomes obvious, cauchy-schwartz and jensen's in particular - induction (this was a long time ago / early in my math career) - diagram chases - the entire typeclass stack from FP (functor applicative monad, then all the monad interfaces) - huge chunks of axiomatic probability and measure theory (what do sigma algebras really mean, what is a good definition for integration, what is continuity of measure, dinkin's pi-lambda theorem) - and so it goes on
I am still waiting on some of the following things to click so that I may abuse them productively as well:
- LLL - yaos min-max theorem - lots of results from logic
I surmise this happens for monads and freaks developers out because it's one of the few pieces of serious math (i.e. no handwaving, given as a rigorous construction, etc) most people come across, so the phenomenon catches people off-guard.
If you like this thing, do more math!