How much linear algebra and calculus do I need to learn for game development, and which specific concepts should I focus on to effectively apply them in 3D games and physics-based mechanics?
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Hi.
You can start developing games with basic pre-algebra knowledge.
As for which concepts to focus on that depends on what you are trying to create, for physics based games learn physics, for commonly used concepts focus on vector calculus, for a well rounded programmer I suggest learning as much as you can about trigonometry.
If you are looking to fully understand complex things like quaternions then you are in for a ride, because it deals into imaginary concepts, here’s the formula: i² = j² = k² = ijk = -1
That sort of thing is taught in masters level degrees, but you can also read it as a matrix, which is a lot simpler and how Unity uses it, also focus on matrices, they are a huge part of game development if you want to create really fancy stuff.
Edit:
Almost forgot, try also learning about computer engineering (which is math), learning how things work in background is really useful because it opens up a lot of possibilities, like saving 32 bools in a single int using bit masks. Here’s an example of that: Rogue Tank | Holistic 3D - Math Course by Yee, it is a game that saves 64 board tiles status into a single long variable, you can see how useful it can be having that sort of knowledge. There’s a link to the code at the bottom of that page, it has an MIT license, feel free to download it and do whatever you want with it.
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