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Re:How to choose a textbook that is pedagogically optimal fo... by CamelCaseName on Saturday July 20, 2024 @01:38PM (#41018166)
Is there a map of this? Would love to see which topics branch of each other and which start from scratch
Re:How to choose a textbook that is pedagogically optimal fo... by plonk on Saturday July 20, 2024 @01:55PM (#41018294)
Big schools' curricula? Look at some top school's math undergrad courses and graph them
Re:How to choose a textbook that is pedagogically optimal fo... by 4ad on Saturday July 20, 2024 @02:02PM (#41018345)
I am not aware of any good one, but I realized you could probably mechanically extract such a map from Lean's mathlib[0][1].

Since Lean builds everything from scratch, this should be doable, albeit Lean builds everything on top of type theory which is not the only choice possible. Different foundations will result in a different graph.

Also the best way to learn math is probably not by following this sort of graph, it would be far too abstract and disconnected from both the real world and usual practical applications.

[0] https://leanprover-community.github.io/mathlib4_docs/

[1] https://github.com/leanprover-community/mathlib4

Re:How to choose a textbook that is pedagogically optimal fo... by nextos on Sunday July 21, 2024 @12:34AM (#41022393)
Garrity's All the Math You Missed book, mentioned elsewhere in the comments, draws a nice map of subjects, along with little introductions and book recommendations. The map is good for continuous mathematics, but IMHO fails to consider logic and type theory, which is a bit odd given the separate chapter for category theory. It also does not do proper justice to computation and clumps everything together under the label "algorithms".

Good alternatives are The Princeton Companion to Mathematics by Gowers and Mathematics: Its content, Methods and Meaning by Alekxandrov, Kolmogorov, et al. Those present much more detailed maps so YMMV.