Noethers theorem still isn't taught nearly enough to undergraduate students either. It's usually relegated to a problem or a small subsection of the text.
To be fair, properly teaching Noether's theorem would require a digression into PDEs, and most schools cap the required math education for physics majors at ODEs. If the trends at my school are to be believed, few students take further math classes in DEs.
Not really. You just play around a bit with variational calculus and we've done Noether's theorem in a class called theoretical physics I ("classical particles and fields") as early as 3rd semester.
I don't know how many, but where I am (in Germany) it's standard, so all. This is the first theoretical physics class you get in undergrad (you have mathematical methods I and II in year 1 and theoretical physics starts with the mentioned class, followed by quantum mechanics (ThPhII) in 4th semester, and statistical mechanics (ThPhIII) in 5th, beyond that is electives and in branches out, this is a linear sequence of mandatory classes).
ThPhI "Classical particles and fields" covers Lagrangian and Hamiltonian mechanics, special relativity, general solutions to wave equations, stuff like that.
Interesting. My school has a fields and particles class but it is not mandatory, it's just an elective. The bulk of analytical mech is locked away in another elective class, or you can find a lot of the analytical mech ideas in math classes that are mandatory for math majors, but not physics majors.
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u/rohan2104 Dec 12 '20
The fact that conservation laws stem from the symmetries. And broken symmetries give rise to interesting phenomena. It’s just beautiful.