The Japanese learned early on that practice is at the heart of expertise. What you cannot do reliably, you do not understand.
Western culture has almost completely forgotten about practice, unless you're a musician.
Western culture has almost completely forgotten about practice, unless you're a musician.
This is what I use The Art of Computer Programming books for. I'll watch a lecture in basic computer science I'd forgotten long ago to get the intuition being explained of concepts like generating functions, then look up the subject in TAOCP series to read Knuth's explanation, and do all the exercises possible. Most universities I've found with open calendars or lectures have been locking down their assignments to prevent students from cheating and looking up answers like 15-251 at CMU. They have public lectures but no tests or exercises available so TAOCP complements these lectures for anybody self-learning by giving you hard problems to reason about so you remember the material. https://scs.hosted.panopto.com/Panopto/Pages/Sessions/List.a...
We don't do this for math as standard because most parents don't value math as much as reading. We know it works, we just don't care enough as a population.