The best curriculum for every goal

post by Randomized, Controlled (BossSleepy) · 2022-01-08T18:47:31.006Z · LW · GW · 1 comment

This is a question post.

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In the fine tradition of Best Textbook [LW · GW], Best Software [LW · GW] and Best Visualization [LW · GW]:

For our purposes a curriculum is one or more discrete resources (website, book, article, tutorial, whatevs) plus one or more goal-states, such as acquiring or practicing a new skill, learning about a subject, or similar. Type signature is:

curriculum is (List<resource>, List<goal-state>)

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(NB: "comparing to other curricula" could be comparison of resources OR goal-states OR both; I think a certain amount of comparison between goal-states could be really interesting, but my hope is that this thread has significant attention devoted to discussing resources.)

This was motivated by looking at one of Gwern's self-experimentation posts and realizing that I wanted to be able to do that kind of [self-]experimental design + data analysis + visualization. This is my attempt to manifest that curriculum [plus many others] into being.

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answer by Algon · 2022-01-09T12:20:32.717Z · LW(p) · GW(p)

The curriculum is https://www.goodtheorist.science/ for the goal of becoming a theoretical physicist. Of course, you can forget about supersymmetry and super string theory. 

Though if you want the classical stuff in one text(Classical Mech, Stat Mech/Thermo, SR, Optics, EM) try "Modern Classical Physics". 

Also, try "New Foundations for Classical Mechanics" if you want to get comfortable with geometric algebras (an intuitive subalgebra of the tensor algebra which is enough for near any physicist). This pairs well with either of the above. 

And remember the three book rule! 

↑ comment by Edward Pascal (edward-pascal) · 2022-01-09T17:36:43.241Z · LW(p) · GW(p)

Are there great physics books that use a Programmed Learning approach? I have a couple of math books like that, and it's a very nice way to learn.

Replies from: Algon
↑ comment by Algon · 2022-01-10T01:19:00.863Z · LW(p) · GW(p)

I've never heard of Programmed Learning before, but I don't think it is too different from going through a text and doing the exercises right away? Maybe following these procedures will give you the experience you want:

  1. Try to prove every statement yourself, physically or mathematically.
  2. When you prove something, rederive all its pre-requisites. If there are a great deal, then just sketch out the pre-requisites in your head or use some sort of heuristic proof.
  3. Summarise parts of the book, including proofs, models etc. so it is easier to rederive stuff and link it to things (see 8).
  4. For bonus points, try proving some stuff in a different way.
  5. Try to anticipate what should be coming next on a page by page to section by section to chapter by chapter level
  6. Try to predict what problems they'll ask you in the exercises. If you can't predict the first question, try predicting the next (again ties into 3).
  7. Generate interesting questions if you think there aren't enough.
  8. Constantly link the ideas in the text to other bits of knowledge you have (this ties into the prior point), especially the earlier parts of the book. Note that this is a good way to prove old things in a novel manner. A way to reduce the complexity of this is to have a few scenarios you apply new ideas to. IIRC that's what Atiyah did.
  9. For definitions, think of some concrete models to fit the formalism into your native ontology. Then you can leverage your intuitions to figure out what the right sorts of questions to ask are and how to answer them.

In some sense, this is how you should be reading a maths/physics book.

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comment by philip_b (crabman) · 2022-01-09T12:47:52.062Z · LW(p) · GW(p)

A better type signature would be (List<resource>, List<goal-state>, List<prerequisites>). An even better type signature would be a directed acyclic graph where nodes are skills or knowledge areas, edges are dependencies, parentless nodes are prerequisites, childless nodes are end goals, and each non-prerequisite node has a list of resources associated with it.