What class is general relativity taught in?

[WannabeNewton]

You forgot me in one day :[

 

[Astronuc]

Okay so I cannot remember who told me this...I think it was in chat yesterday...but someone told me general relativity is sometimes called gravitation theory. The school I want to go to for my graduate studies offers a class called "gravitational theory" subtitled theory of general relativity. It is a 5000 level class and is required for my major. Still looking for tensor analysis there so I can check out the prereqs. Thanks so much everyone!

I think one should have a background in vector calculus and linear algebra/analysis as prerequisites to tensor calculus.

This book seems interesting - Introduction to Tensor Calculus, Relativity and Cosmology (Dover Books on Physics) [Paperback]
D. F. Lawden (Author), https://www.amazon.com/dp/0486425401/?tag=pfamazon01-20

and it's inexpensive. I can't vouch for the quality.

 

[VantagePoint72]

For self-study, A First Course in General Relativity by Schutz is a nice book that does exactly what it says on the label. Familiarity with linear algebra and vector calculus is assumed, but the rest of the mathematics is developed in a self-contained manner. One issue with the text is that in some places it is too informal and—for me, at least—can leave the reader unconvinced by some of the mathematical statements. If you find this is the case, I'd suggest just taking it at face-value and plowing on so that you get a reasonably comprehensive overview; then grab a more rigorous book. I find that having an informal introduction to something makes later formal study much easier to swallow. I'd suggest that a good sequence would to read Schutz' book, then "Spacetime and Geometry" by Sean Carroll (my favourite GR text—covers essentially the same ground as Schutz but more formally), and then "General Relativity" by Robert Wald. By the end of Wald, you could expect to have a very comprehensive and rigorous understanding of GR.

Some will swear by the book by Misner, Thorne, and Wheeler, but personally I think MTW are best for people who already have a solid grounding in GR, not those just starting out. You might prefer to use their book in place of Wald's after reading the introductory texts.

 

[HeLiXe]

You forgot me in one day :[

Who are you again? Just kidding! Thanks so much WannabeNewton :) I could not remember if it was you or PhysKid

I think one should have a background in vector calculus and linear algebra/analysis as prerequisites to tensor calculus.

This book seems interesting - Introduction to Tensor Calculus, Relativity and Cosmology (Dover Books on Physics) [Paperback]
D. F. Lawden (Author), https://www.amazon.com/dp/0486425401/?tag=pfamazon01-20

and it's inexpensive. I can't vouch for the quality.

Thank you so much once again Astronuc! I checked out these classes and their prereqs at my school. I will also have a look at this book.

For self-study, A First Course in General Relativity by Schutz is a nice book that does exactly what it says on the label. Familiarity with linear algebra and vector calculus is assumed, but the rest of the mathematics is developed in a self-contained manner. One issue with the text is that in some places it is too informal and—for me, at least—can leave the reader unconvinced by some of the mathematical statements. If you find this is the case, I'd suggest just taking it at face-value and plowing on so that you get a reasonably comprehensive overview; then grab a more rigorous book. I find that having an informal introduction to something makes later formal study much easier to swallow. I'd suggest that a good sequence would to read Schutz' book, then "Spacetime and Geometry" by Sean Carroll (my favourite GR text—covers essentially the same ground as Schutz but more formally), and then "General Relativity" by Robert Wald. By the end of Wald, you could expect to have a very comprehensive and rigorous understanding of GR.

Some will swear by the book by Misner, Thorne, and Wheeler, but personally I think MTW are best for people who already have a solid grounding in GR, not those just starting out. You might prefer to use their book in place of Wald's after reading the introductory texts.

LastOneStanding I cannot thank you enough for all of this valuable information. Thank you for taking the time to answer me in regards to this.

I would like to thank everyone who replied because you have all given me so much perspective. I now have a few questions in regards to my math sequence, but I think I will start a new thread for that as it is a little off of this topic.

 

[ahsanxr]

I'm going to be taking a GR class next semester which will be following Schutz. I plan on supplementing it with a more rigorous book such as Wald though. I think it's possible to tackle a rigorous GR book from the get-go depending on your math background. If you've already seen some rigorous math such as in a rigorous linear algebra class and basic topology, then you can read Schutz "Geometrical Methods of Mathematical Physics" (although he does already cover the basics in the first chapter). It introduces "tensor analysis" and several other topics that would be needed for GR and several other physics fields. Once you've worked through that book, I think you could probably go straight to Wald's book. Note that I haven't tried this myself but I've heard of other people who had a strong math background and were able to go straight to Wald's book.

 

[HeLiXe]

Thanks for your response ahsanxr :) At the present moment my math background is moderately weak...I have only taken calc I-III and ordinary differential equations. I intend to take linear algebra, advanced algebra, vector analysis, numerical analysis and number theory. I also want to take probability and statistics but am undecided about it in light of the information I gathered from this thread.

It is so exciting that you are going to be taking a GR class next semester! All the best to you!