Reddit reviews Applications of Lie Groups to Differential Equations (Graduate Texts in Mathematics)

There's a notion of "generalized symmetry" that gives you a bijective correspondence between generalized symmetries of the Lagrangian and conservation laws. Probably a better candidate than the "usual" version of Noether's theorem which gives a conservation law for each symmetry.

See here: https://www.math.uwaterloo.ca/~karigian/papers/noether.pdf (also covered in Olver's book)

I'm doing a reading course with a professor this fall. It is on Lie group applications in differential equations using Applications of Lie Groups to Differential Equations by Peter J. Olver.

The structure is that I will prepare a set of notes for each class and essentially lecture to the prof. Then I will also do some basic questions at the end of each chapter on the board, mostly by myself, but him jumping in whenever I need help. Can't promise pictures of that, but I can upload my own notes each week for who ever wants to follow along and we can even work on questions together. We plan on doing the first four chapters. Hell, I could definitely use some company.

You mean Applications of Lie Groups to Differential Equations by Peter Olver? That looks like an awesome book -- it's been on my list of things to read for a while -- but perhaps a bit advanced for the OP. Or were you thinking of another book?

You could try https://www.amazon.com/Applications-Differential-Equations-Graduate-Mathematics/dp/0387950001 for a "mathy" approach.

But if you're just trying to learn how to look at the things, read Arnold and don't worry if it builds intuition.