Abstract Algebra

Very. Luckily it's considerably easier to learn than the other types of mathematics that are important to physicists.

>>7963299

What area? I've heard it's most used in theoretical physics, but I'm still not sure if it's worth learning it.

>>7963306
I don't understand. The very worst case scenario is that you learn something interesting that you don't have an immediate use for. What do you mean "if it's worth learning?"

>>7963320

I'm interested in the topic, but it seems like a very broad area and I'm afraid I'll dig too much of it for nothing.

>>7963324
>I'm afraid I'll dig too much of it for nothing.
By reading an intro textbook? I really am not sure what you're afraid is going to happen if you read an algebra book. If you're interested, check it out and see if you like it. Once you understand it, maybe you'll find something new to do with it.

>>7963335

I'm just trying to figure out it's use in physics. Like I said, is it restricted to the theoretical domain? Like in what? I simply cannot see an area where abstract algebra comes together with physics.

>>7963351
I think Group Theroy and Representation theory are important while studying continuous symmetries and Lie Algebras.

>>7963296

Can't do anything in string theory without tensors, I'd say its bretty important if you want a grant and to work in a field that isnt basically composed of just you, your professor, that 40 y o grad student that smells like onions, your professor's sworn enemy from the netherlands, and his female asian grad student.

>>7963438

I can see the importance of tensors and all of which is comprised in linear algebra, but I can't really see any area which would make use of galois theory or cohomology for instance. It's those more abstract parts in which I need more examples.

>>7963464
>I can see the importance of tensors and all of which is comprised in linear algebra,
No it isn't.

>>7963464
>but I can't really see any area which would make use of galois theory or cohomology for instance
You won't learn cohomology in an abstract algebra course. Galois theory is used in describing solutions to polynomials, so you probably won't ever use it. Groups are what are important, because physicists care a great deal about symmetries.

>>7963468

Ok, so it's mainly theoretical. I would be glad to hear a few more examples though. When you mentioned symmetries, what exactly are you referring to?

>>7963502
>Ok, so it's mainly theoretical.
You said that 3 times in the thread, I don't get it. Of course, experimentalists hardly know what a Banach space is.

I'd argue any math you learn helps you understand math and theoretical physics better, even if it's number theory. Especially if you go on and do your own new (theoretical) physics. The ones who know lots of math can have and translate their ideas.

>>7963296

Mathematicians refuse to explain it in a way that can be understood by engineers (that is through life like examples and solvable problems), so we need physicists to learn it and teach its possible applications to engineers.

>>7963502
I am a grad student in representation theory and only had a physics course on quantum mechanics and met a few things I knew already.

Lie-Algebras given by spin/angular momentum operators. Especially U(2), O(3). Math can classify these things.

The pauli principle is mathematically simply just the invariants of the symmetric group S_n acting on the n-fold tensor product. Again group/representation theory has this mostly worked out completely.

Multiple particles without interaction in a common system is given by the tensor product and thus closely related to the tensor functor.

Linear algebra stuff often pops up, e.g. clebsch gordan coefficients.

>>7963640

That's exactly what I was looking for, thanks a lot!

>>7963428
I really need to start learning lie algebras, keep seeing it reading about subjects but not got to anything yet that has needed it. Imagine I will soon as I start to do more advanced quantum mechanics.

>>7963882
Do you know Banach spaces and how its used in quantum?

>>7963438
And only one of you

>>7963438
Why are the dickhead profs always from the Netherlands?