The math required for Relativity and QM ?

[Skynt]

I'm sure this has been posted before, but I did a quick search and couldn't spot anything.
I was wondering what textbooks I might be able to self-study in order to get up to speed in mathematics and physics so that I might be able to understand GR, SR, and QM.
Currently I'm up to speed on basic Calculus and a semester of physics but I want to study on ahead. I suppose the textbooks for introduction into GR, SR, and QM would not be necessary since it would take me a while to work up to them.

Can anyone recommend some good books that would cover the necessary material for a solid understanding? Thank you!

 

[Pinu7]

Approximately in this order-

Linear Algebra- Hoffman/Kunze
Advanced Calculus of Several Variables-Edwards
Introductory Real Analysis-Kolmogorov(my favorite)
Complex Analysis-Lang
Analysis on Manifolds-Munkres
Topology-Munkres
Introduction to Topological Manifolds-Lee
Measure Theory-Halmos
Functional Analysis-Yosida

 

[Skynt]

Thank you very much! I appreciate it.

 

[martin_blckrs]

Approximately in this order-

Linear Algebra- Hoffman/Kunze
Advanced Calculus of Several Variables-Edwards
Introductory Real Analysis-Kolmogorov(my favorite)
Complex Analysis-Lang
Analysis on Manifolds-Munkres
Topology-Munkres
Introduction to Topological Manifolds-Lee
Measure Theory-Halmos
Functional Analysis-Yosida

I don't understand why everyone has the urge to list Measure Theory and Functional Analysis as a prerequisite to QM. Unless you're doing some hardcore mathematical quantum mechanics course, which I would estimate 99% of QM students/practitioners haven't taken, the only thing you'll need and use is some basic Hilbert space theory. You don't need to take Differential Geometry to be able to integrate in polar coordinates.

 

[planethunter]

you need to study tensor calculus and and ODE/PDE. These are the more applied courses you can study.

Functional analysis would be nice to study as well

 

[Feldoh]

An introductory QM class would require just Calc I-III and differential equations.

The probability, linear algebra, PDE (mostly seperable), Fourier theory can be picked up. If you use Griffiths book for QM he goes over the mathematics well enough to understand the concepts.

 

[Heresy]

If you have some good linear algebra and multivariable calculus you can probably tackle Schutz's A First Course in General Relativity

 

[ahmadmz]

Approximately in this order-

Linear Algebra- Hoffman/Kunze
Advanced Calculus of Several Variables-Edwards
Introductory Real Analysis-Kolmogorov(my favorite)
Complex Analysis-Lang
Analysis on Manifolds-Munkres
Topology-Munkres
Introduction to Topological Manifolds-Lee
Measure Theory-Halmos
Functional Analysis-Yosida

Your 15 and have gone through these !?

I am in the same level as the OP. I am starting with linear algebra.

 

[Daverz]

I don't understand why everyone has the urge to list Measure Theory and Functional Analysis as a prerequisite to QM. Unless you're doing some hardcore mathematical quantum mechanics course, which I would estimate 99% of QM students/practitioners haven't taken, the only thing you'll need and use is some basic Hilbert space theory. You don't need to take Differential Geometry to be able to integrate in polar coordinates.

I think Pinu7 was "taking the piss" as the Brits say.

Trig is enough for basic SR.

For QM, I suggest taking a look through Shankar to get an idea of the math involved. It helps to be strong in matrix algebra and Fourier analysis. Exposure to Hamiltonian mechanics is also helpful.

Most GR books develop the needed math. It helps to be strong in multi-variate calculus.

Physics background: The Feynman Lectures, Volumes 1 & 2.

I would start with some books that emphasize physics over math:

Taylor & Wheeler: Spacetime Physics and Exploring Black Holes
Eisberg & Resnick: Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles