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I am looking for both a course hierarchy of mathematics education (for example, Galois theory is part of abstract algebra) and a representation of all competences involved in learning mathematics (possibly with prerequisites links, for example a student needs to know what is a limit in order to understand derivation).

The only ontology I found for the latter is there. And I think a good start to build a course hierarchy would be to use this tag graph of Mathematics Stack Exchange. Can you provide any other valuable resources?

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    $\begingroup$ You should check math.niu.edu/~rusin/known-math, even if the classification is not a real tree. $\endgroup$ – cynddl Mar 17 '14 at 3:30
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    $\begingroup$ Similar to the tag graph of MathSE, there is the Mathematics Subject Classification of Math Reviews and Zentralblatt. Since this is not entirely what you are looking for (just a subject classification, not a competency tree), this is only a comment. $\endgroup$ – Roland Mar 17 '14 at 9:33
  • $\begingroup$ Thanks a lot! zbMATH seems to be an easier way to browse the database. If I don't get any reply, I will ask you to transform your comment into an answer :) $\endgroup$ – Jill-Jênn Vie Mar 17 '14 at 9:49
  • $\begingroup$ I'm not quite sure what you're looking for. Math classes and their prerequisites? Check college catalogs (or the tag graph linked). More generally, one often uses Bloom's Taxonomy (BT) in order to present a hierarchy on cognitive tasks (e.g. nrich.maths.org/5826). BT was revised in 2001 (citation: Anderson, L. W., Krathwohl, D. R., & Bloom, B. S. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's taxonomy of educational objectives. Allyn & Bacon.); you can find a summary of the revision at unco.edu/cetl/sir/stating_outcome/documents/Krathwohl.pdf. $\endgroup$ – Benjamin Dickman Mar 26 '14 at 0:21
  • $\begingroup$ You might want to consider looking at how Khan Academy classifies/codifies proficiency. It's not necessarily going to be extensively based on research literature and hierarchied and stuff like that, but there is a real life feedback loop there between him and his users that has probably grown somewhat organically. $\endgroup$ – msouth Mar 26 '14 at 22:08
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Since this question is still in the unanswered category, I'll repost my comment as an answer:

Similar to the tag graph of MathSE, there is the Mathematics Subject Classification of Math Reviews and Zentralblatt. The search/browse mask of the Zentralblatt looks nicer than the one of Math Reviews.

Unfortunatly, this is just a classification tree by topic, and not a competency tree.

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