This is an interesting approach, but I am wondering if reversing the process wouldn’t be more helpful. The problem is that you can’t just jump from propositional logic to chaos theory, since you must first learn algebra, calculus, and linear algebra. So an unordered list of mathematical subjects has some pitfalls.
If there existed some graph of dependencies in mathematical knowledge (basically a Diablo skill tree, or Khan Academy with lower resultion), we could note on each node any applications like quantum theory, music theory, and so on. This would help Capla go about their studies in a more systematic way, and also help show the rather elegant, unified structure underlying many fields of scientific inquiry.
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.
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.
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.
This is an interesting approach, but I am wondering if reversing the process wouldn’t be more helpful. The problem is that you can’t just jump from propositional logic to chaos theory, since you must first learn algebra, calculus, and linear algebra. So an unordered list of mathematical subjects has some pitfalls.
If there existed some graph of dependencies in mathematical knowledge (basically a Diablo skill tree, or Khan Academy with lower resultion), we could note on each node any applications like quantum theory, music theory, and so on. This would help Capla go about their studies in a more systematic way, and also help show the rather elegant, unified structure underlying many fields of scientific inquiry.
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.