Math Courses to Understand General Relativity (by Sean Carroll)

[AhmedHesham]

Hi.
What are the math courses should I take in order to understand the mathematics involved in a book such as Sean Carroll in general relativity.
Thanks

 

[haushofer]

Differential geometry (and topology). See e.g. Nakahara's textbook.

 

[Orodruin]

The typical GR textbook (including Carroll) will go through the basics of differential geometry. In order to understand this you will need a good understanding of linear algebra and multivariable calculus.

 

[AhmedHesham]

Thanks for replying

 

[mpresic3]

No prerequisites. If you believe the preface of the book. Carroll writes in the preface, exposure to Lagrangian Mechanics and electromagnetism and linear algebra would be helpful but this is developed as we go along.

I am currently reading the book too, and I have quite strong background, clearly above the stated prerequisites and I find it tough sledding.

If I were to suggest math prerequisites, I would state them as strong familiarity with tensors. Exposure to manifolds, charts, atlases would be useful. When I state "strong familiarity", I mean, that a formal differential geometry course, or topology course from a math department, might be overkill. In addition, math departments emphasize theory in such a way it takes away from the physics (in my experience). You probably do not need that. A good course in mathematical physics at the graduate level is probably necessary though.

I have seen Hartle's book on general relativity highly recommended. I think his approach is more workmanlike and less theoretical, and with less mathematics prerequisites.

 

[AhmedHesham]

No prerequisites. If you believe the preface of the book. Carroll writes in the preface, exposure to Lagrangian Mechanics and electromagnetism and linear algebra would be helpful but this is developed as we go along.

I am currently reading the book too, and I have quite strong background, clearly above the stated prerequisites and I find it tough sledding.

If I were to suggest math prerequisites, I would state them as strong familiarity with tensors. Exposure to manifolds, charts, atlases would be useful. When I state "strong familiarity", I mean, that a formal differential geometry course, or topology course from a math department, might be overkill. In addition, math departments emphasize theory in such a way it takes away from the physics (in my experience). You probably do not need that. A good course in mathematical physics at the graduate level is probably necessary though.

I have seen Hartle's book on general relativity highly recommended. I think his approach is more workmanlike and less theoretical, and with less mathematics prerequisites.

OK. Thanks.