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really nice what you got going here. I am a math, physics and computer science teacher in early retirement and was thinking about starting something similar and stumbled on your repo.
Your structure is pretty interesting and I like that you just got going without working yourself up in a billion details for chapter 1 :-) Of course you could add to each chapter a thousand more pages, but it is a good start and point of entry.
What I had in mind when i brainstormed an "online math compendium" for students was more math-focused, you are more into the coding angle which is fine. Some ideas I had you might want to consider:
use interactive geogebra applets for functions with parameters or to visualize the effect a change of a variable has (for example to make the derivative / tangent interactive or to demonstrate how the Riemann sum converges against the integral). There are a ton of examples for these applets online and they might be easy to implement
give references to further reading material, books and online resources
An open problem I was thinking about is the dynamic generation of practice and test material, ideally self-correcting or maybe with an AI assisted mode (in my experience most "school level" math problems can be very reliably solved and verified by a capable AI, i had good experiences with the Gemini models while my results with local models was rather not so great sadly... so there is the API cost sadly). For some subjects like solving quadratic equations or simplifying algebraic expressions or even basic stuff like calculations with fractions it is pretty doable to have some "templates" for questions that can be dynamically varied (either hardcoded or with AI) and then checked for correctness. Others are a bit more tricky (for example finding derivatives can get ugly if you do not pre-verify the solutions somehow and judge the difficulty... integral functions are even worse, a minor change can make the task very hard or even impossible). I stumbled on this really great German site that calculates integral functions and can even give you very detailed step by step solutions: www.integralrechner.de. Sadly there is no API and it isn't opensource, though he describes his approach in detail and I might try replicate it.
To sum this up without losing myself in details: If your goal is to give a summary or overview for students, it is a good start. If your goal is to enable students to actually DO these things, they need more examples and practice material. If your goal is to be a point of entry for further learning, more resources and learning material should be linked.
If you like to discuss or go into more detail on anything, feel free to contact me.
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Hey Henry,
really nice what you got going here. I am a math, physics and computer science teacher in early retirement and was thinking about starting something similar and stumbled on your repo.
Your structure is pretty interesting and I like that you just got going without working yourself up in a billion details for chapter 1 :-) Of course you could add to each chapter a thousand more pages, but it is a good start and point of entry.
What I had in mind when i brainstormed an "online math compendium" for students was more math-focused, you are more into the coding angle which is fine. Some ideas I had you might want to consider:
An open problem I was thinking about is the dynamic generation of practice and test material, ideally self-correcting or maybe with an AI assisted mode (in my experience most "school level" math problems can be very reliably solved and verified by a capable AI, i had good experiences with the Gemini models while my results with local models was rather not so great sadly... so there is the API cost sadly). For some subjects like solving quadratic equations or simplifying algebraic expressions or even basic stuff like calculations with fractions it is pretty doable to have some "templates" for questions that can be dynamically varied (either hardcoded or with AI) and then checked for correctness. Others are a bit more tricky (for example finding derivatives can get ugly if you do not pre-verify the solutions somehow and judge the difficulty... integral functions are even worse, a minor change can make the task very hard or even impossible). I stumbled on this really great German site that calculates integral functions and can even give you very detailed step by step solutions: www.integralrechner.de. Sadly there is no API and it isn't opensource, though he describes his approach in detail and I might try replicate it.
To sum this up without losing myself in details: If your goal is to give a summary or overview for students, it is a good start. If your goal is to enable students to actually DO these things, they need more examples and practice material. If your goal is to be a point of entry for further learning, more resources and learning material should be linked.
If you like to discuss or go into more detail on anything, feel free to contact me.
Cheers,
ilkerol
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