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Vaniver comments on Beyond Statistics 101 - Less Wrong
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Not familiar with Noether's theorem. Seems useful for constructing models, and perhaps determining if something else beyond mass, momentum, and energy is conserved. Is the converse true as well, i.e., does conservation imply that symmetries exist?
I'm also afraid I know nearly nothing about non-linear stability, so I'm not sure what you're referring to, but it sounds interesting. I'll have to read the Wikipedia page. I'd be interested if you know any other good resources for learning this.
I think this is what Lie groups are all about, but that's a bit deeper in group theory than I'm comfortable speaking on.
I learned it the long way by taking classes, and don't recall being particularly impressed by any textbooks. (I can lend you the ones I used.) I remember thinking that reading through Akella's lecture notes was about as good as taking the course, and so if you have the time to devote to it you might be able to get those from him by asking nicely.