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by Smaug123 2204 days ago
Nielsen has http://cognitivemedium.com/srs-mathematics, for example.

I would strongly recommend not having entire problems as a single card; it's absolutely crucial that answering any particular card is a single mental motion. (You can get by with a very small workload if your cards are more complex than that, but it doesn't scale even in the medium term.) I wouldn't go any more complex than "what is 75 * 43".

As an example, the definition of a red-black tree for me is six cards:

* What, imprecisely, are the colouring rules on a red-black tree? ["global; local; base-case"]

* What are the leaves of a red-black tree? ["null"]

* What is the base-case colouring rule of a red-black tree? ["leaves are black"]

* What is the local colouring rule of a red-black tree? ["red node => black children"]

* What is the global colouring rule of a red-black tree? ["black depth is well defined"]

* What is the black depth of a node in a red-black tree? ["the number of black nodes encountered on a path from that node down to a leaf"]

One might naively have created a single card that is "what is a red-black tree?", but in my experience such a card is too big. The difficulty of learning a card grows at least quadratically with the number of mental motions it takes to answer that card, and small/simple/easily-learned cards are incredibly cheap in that Anki very quickly learns not to show them to you if they're genuinely easy.

Maths-wise, my cards usually look like:

* "Does path-connectedness imply connectedness?" [yes]

* "Does connectedness imply path-connectedness?" [no]

* "Counterexample to connectedness-implies-path-connectedness" [topologist's sine curve]

* "Definition of the topologist's sine curve" [union of the y-axis and a squashed sine]

* "Definition of the squashing of the sine component of the topologist's sine curve" [whatever]

* "Main idea of the proof that path-connectedness implies connectedness" [use "all locally constant functions into [0, 1] are constant"]