The math required for Relativity and QM ?

In summary, the individual is seeking recommendations for textbooks to self-study mathematics and physics in order to understand General Relativity, Special Relativity, and Quantum Mechanics. The suggested textbooks include Linear Algebra by Hoffman/Kunze, Advanced Calculus of Several Variables by Edwards, Introductory Real Analysis by Kolmogorov, Complex Analysis by Lang, Analysis on Manifolds by Munkres, Topology by Munkres, Introduction to Topological Manifolds by Lee, Measure Theory by Halmos, and Functional Analysis by Yosida. It is noted that some suggest Measure Theory and Functional Analysis as prerequisites for QM, but it is argued that a strong understanding of Hilbert space theory and basic math concepts is sufficient.
  • #1
Skynt
39
1
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!
 
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  • #2
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
 
  • #3
Thank you very much! I appreciate it.
 
  • #4
Pinu7 said:
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.
 
  • #5
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
 
  • #6
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.
 
  • #7
If you have some good linear algebra and multivariable calculus you can probably tackle Schutz's A First Course in General Relativity
 
  • #8
Pinu7 said:
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.
 
  • #9
martin_blckrs said:
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
 
Last edited:

1. What level of math is required to understand Relativity and Quantum Mechanics?

The math required for Relativity and Quantum Mechanics is typically at the advanced undergraduate or graduate level. This includes knowledge of calculus, linear algebra, and differential equations.

2. Is it necessary to have a strong background in math to understand these theories?

While a strong background in math can certainly be helpful, it is not necessarily a requirement. It is possible to gain a basic understanding of Relativity and Quantum Mechanics without an extensive math background, although a basic understanding of calculus is still recommended.

3. What specific mathematical concepts are important for understanding these theories?

Some of the key mathematical concepts used in Relativity and Quantum Mechanics include tensors, complex numbers, and probability theory. Knowledge of vector calculus and differential geometry is also helpful in understanding these theories.

4. Can you provide an example of how math is used in Relativity and Quantum Mechanics?

In Relativity, math is used to describe the curvature of spacetime and the effects of gravity. In Quantum Mechanics, math is used to describe the behavior and interactions of subatomic particles, as well as the probabilistic nature of quantum systems.

5. How can I improve my understanding of the math involved in Relativity and Quantum Mechanics?

One way to improve your understanding of the math involved in these theories is to practice solving problems and working through equations. It can also be helpful to seek out additional resources, such as textbooks or online tutorials, to supplement your learning.

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