Mathematics most used in GR and QM

[cmcraes]

Hi all! Been a while since I was on PF and I greatly regret it. Forgot how great the community was. Anyways on to my point.

I'm going into my second ywar of post secondary and planning to major in physics, and have the eventual goal of understanding both General relativity, and Quantum mechanics extremely thoroughly. Although I'm told I'll be given the formula's and some math I'll need IN THE COURSE, I wish to learn the math required seperately, so to best master the physics and understand where the math comes from etc.

So my question is; can anyone tell me what branches of mathematics are most useful for General relativity, and/or which ones are best for Quantum mechanics?

*I have already taken Calculus 1 & 2, linear algebra, and Statistics (all first year courses) so please be more specific than this! Thanks!

 

[Geofleur]

For general relativity, you'll want to learn some tensor calculus for sure. For quantum mechanics, partial differential equations, complex analysis, Fourier analysis, and Hilbert spaces are all important. Also, make sure your linear algebra is good and solid, for either quantum or GR.

For a first course in quantum, if you know what separation of variables is and understand the Fourier series and Fourier transform, that should help a lot.

 

[Cruz Martinez]

For GR you will need smooth and pseudo-riemannian manifolds. How rigorous a knowledge of them you will need depends a lot on the book from which you choose to learn GR.

 

[micromass]

For GR you will need smooth and pseudo-riemannian manifolds. How rigorous a knowledge of them you will need depends a lot on the book from which you choose to learn GR.

Right. The OP needs to specify how rigorous he wants things to be. For example, you could learn the math necessary to just understand the equations and to apply it. Then a mathematical methods book will be ideal. Or you can learn the math so you can really understand the very foundations of a subject. Then you will have to study quite some heavy math. What you want to have is possibly somewhere in between this. So you'll need to specify this.

For examples, do you want to learn math proofs?

 

[cmcraes]

Hi all! Sorry I didn't specify the degree of rigor of which I wish to understand the math required for the physics.

My goal is to understand these principles and domains of math for GR & QM analogous to how much I understand the relationship between Calculus and kinematics, or Linear algebra and Dynamics. That being that I understand the fundamental theorems of calculus and where they come from, and how we use calculus to derive kinematic formula's for constant v or constant a, etc. I apologize if this is not specific enough I hope this can provide some insight into the degree of which I wish to understand.

EDIT: I do as well find it incredibly revealing when I understand a proof of a mathematical concept.