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Capla comments on The "best" mathematically-informed topics? - Less Wrong Discussion
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Comments (113)
Where did you get the Khan Academy image? Could I see the full version?
A dependencies graph would be of great philosophical and practical interest.
After compiling a list of topics, the next step is to figure our what math underpins each one, and order them according to increasing assumed mathematical knowledge.
Sadly, you can no longer see the full version on Khan Academy.
https://khanacademy.zendesk.com/hc/en-us/articles/203353750-Where-is-the-Knowledge-Map-Star-Map-math-overview-
The Exercise Dashboard is not as helpful for highlighting dependencies: https://www.khanacademy.org/exercisedashboard
You may be able to find other knowledge maps; Khan wasn't the first to have the idea. I like Kaj's idea as well. I compared the curricula of several majors at MIT to come up with a core curriculum, useful across engineering, computer science, and biology.
You could assemble a partial dependency graph by looking at the course pages of different math departments and noting which courses are listed as prerequisites for more advanced courses.
Yes, although that wouldn't include the applied math that I'm looking for.
The main problem with the Khan version is that it got huge; they were subdividing things down to about the level of an individual half-hour lesson. For someone interested in wider strategic planning, something like this would be a bit more reasonable, as long as you added in the annotations. This book is also reviewed as a good way to conceptualize the macrostructure of mathematical reasoning, although I can't vouch for it personally.