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## Main Question or Discussion Point

Hello friends.

I was thinking that if you study physics, you learn first the basic math to understand it, but you don't go beyond, or deeper, you just learn the minimum math necessary to understand what you are going to see in your physics leassons.

For example, if you are going to learn quantum mechanics, you first learn about linear algebra, Hilbert Spaces... but you don't learn beyond that, in this particular example I would like you to tell me that I could learn about Banach Spaces, Functional Analysis etc.

I was wondering if you can recommend me books, or tell me about the discipline inside mathematics that is more advanced than the used in physics.

There are several formulations of quantum mechanics, you have differential equations, matrices, you have path integral, gauge theory, abelian gauge theory,

In other words, I would like to learn math a lot more advanced than the used in physics, Is there any book, blog post or thread talking about it?

I was thinking that if you study physics, you learn first the basic math to understand it, but you don't go beyond, or deeper, you just learn the minimum math necessary to understand what you are going to see in your physics leassons.

For example, if you are going to learn quantum mechanics, you first learn about linear algebra, Hilbert Spaces... but you don't learn beyond that, in this particular example I would like you to tell me that I could learn about Banach Spaces, Functional Analysis etc.

I was wondering if you can recommend me books, or tell me about the discipline inside mathematics that is more advanced than the used in physics.

There are several formulations of quantum mechanics, you have differential equations, matrices, you have path integral, gauge theory, abelian gauge theory,

In other words, I would like to learn math a lot more advanced than the used in physics, Is there any book, blog post or thread talking about it?