What class is general relativity taught in?

[HeLiXe]

I'm in the United States, taking undergraduate courses, and I believe I had what was an introduction to special relativity in Modern Physics class (Lorenz transformations, time dilation, the relativistic doppler effect, time dilation, length contraction, etc.). I just wonder what class general relativity is taught in.

 

[demonelite123]

I'm in the United States, taking undergraduate courses, and I believe I had what was an introduction to special relativity in Modern Physics class (Lorenz transformations, time dilation, the relativistic doppler effect, time dilation, length contraction, etc.). I just wonder what class general relativity is taught in.

depending on the schools, you may find an introduction to general relativity covered in an undergraduate differential geometry class from the math department. you can also check to see if your school offers a graduate general relativity course.

 

[ModusPwnd]

For the most part, its not taught. Most people even with PhDs in physics have never taken a course in general relativity or differential geometry. Its not relevant to most research out there so its usually only taken up by the small class of physicists whos research does use it.

 

[HeLiXe]

Thanks so much demonelite123 and ModusPwnd :) Checking the math dept. now to see if there is a differential geometry class.

Modus...what research is it relevant to? You can give me a broad answer and I will look into it.

 

[dextercioby]

He definitely doesn't mean the scientific reasearch done by mathematical/theoretical physicists in the areas of (quantum) gravity and string theory.

Still for a graduate of physics, a course on and let's say decent knowledge of GR is a must, even if working at CERN attempting to find traces of SUSY.

 

[ZombieFeynman]

For me, GR falls into the category of: "Things I more than likely won't need directly for research but was glad I learned about when I could"!

It's the study of a full fundamental force of nature, gravity! I think a PhD Physicist should be embarrassed if (s)he could not explain it lucidly to an undergraduate!

 

[WannabeNewton]

I'm not sure what ModusPwnd means. I have many friends doing physics at various institutions in the states and they all say their course catalogs list an undergraduate GR class, my uni included. I don't think it is all that uncommon anymore.

 

[bcrowell]

I think the textbook by Hartle was influential in bringing GR into the undegraduate curriculum.

 

[WannabeNewton]

I think the textbook by Hartle was influential in bringing GR into the undegraduate curriculum.

Yeah it would seem so because most of the textbook listings for said undergraduate GR classes seem to be either Schutz or Hartle.

 

[Jorriss]

I'm not sure what ModusPwnd means. I have many friends doing physics at various institutions in the states and they all say their course catalogs list an undergraduate GR class, my uni included. I don't think it is all that uncommon anymore.

It's not that uncommon, but it's still an elective at all institutions I've seen and many people get a PhD without ever seeing GR.

 

[I like Serena]

I'm in the United States, taking undergraduate courses, and I believe I had what was an introduction to special relativity in Modern Physics class (Lorenz transformations, time dilation, the relativistic doppler effect, time dilation, length contraction, etc.). I just wonder what class general relativity is taught in.

When I was studying physics, GR was only an upper level physics course that was optional.
It wasn't part of any real program.
I guess that was because it has a very limited application in real life.
I followed it myself because I was very much interested in it.
Differential geometry was an optional upper level math course.
I did not see any physicists there and it was only a handful of people attending the classes.

 

[Astronuc]

I'm in the United States, taking undergraduate courses, and I believe I had what was an introduction to special relativity in Modern Physics class (Lorenz transformations, time dilation, the relativistic doppler effect, time dilation, length contraction, etc.). I just wonder what class general relativity is taught in.

When I first attended university, GR was either upper level (4th year) or a graduate level course, and it was an elective. These days it seems to be a graduate level course because of the prerequisites.

Here is one example:

Rice University, PHYS 561 General Relativity

Prerequisites: Special Relativity, Classical Mechanics, Classical Electrodynamics, Tensor Calculus
or instructor consent
Text: Hans Stephani: Relativity: An Introduction to Special and General Relativity
(Cambridge Paperback, 2004)

Other Useful References:
Stephani (S): General Relativity (Cambridge 1990)
Lightman, Press, Price & Teukolsky (LPPT): Problem Book in Relativity &
Gravitation (Princeton 1975)
Hartle (H): Gravity (Addison-Wesley 2003)
Hobson, Efstathiou and Lasenby (HEL): General Relativity (Cambridge 2006)
Landau & Lifgarbagez (LL): Classical Theory of Fields (Pergamon 1989)
Weinberg (W): Gravitation & Cosmology (Wiley 1972)
Schutz (Sh): First Course in General Relativity (Cambridge 1985)
Misner, Thorne & Wheeler (MTW): Gravitation (Freeman 1973)
Rindler (R): Essential Relativity (Springer 1969)
Adler, Bazin & Schiffer (ABS): General Relativity (McGraw Hill 1965)

Course outline - http://physics.rice.edu/Content.aspx?id=170

An introductory to GR course may be taught in undergraduate programs at some universities.

 

[bcrowell]

I guess that was because it has a very limited application in real life.

Except for every time you use a GPS.

 

[WannabeNewton]

It's not that uncommon, but it's still an elective at all institutions I've seen and many people get a PhD without ever seeing GR.

Yes, quite unfortunately this is true.

 

[Catria]

My school teaches it at the undergraduate level but it's an upper-division class.

 

[Lavabug]

GR is a mandatory 4th year course at my university (not in the US).

 

[VantagePoint72]

While this debate about the merits of teaching GR to undergraduates is interesting, I don't think it's especially on point for the OP's question.

HeLiXe: as GR is a very involved subject, it is unlikely to be taught within another course—with the possible exception of a very extensive differential geometry class, as someone else mentioned. Unless you are mathematician, attempting such a rigorous course as your first look at GR is probably too ambitious. If your university offers it to undergraduates, it will likely be an upper level class (possibly cross listed from the list of first year graduate courses) simply called "General Relativity" (or some variant). Such undergraduate courses are usually pretty self-contained mathematically, and so the instructor would spend roughly the first half of the course developing the necessary differential geometry before introducing the physics.

 

[tahayassen]

None of these courses have general relativity or special relativity, right? That's a shame. :( I'll be forever stuck in classical physics and I won't ever touch quantum physics. =\

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[HeLiXe]

None of these courses have general relativity or special relativity, right? That's a shame. :( I'll be forever stuck in classical phyiscs and I won't ever touch quantum physics. =\

not from the looks of it >_>
usually after physics with calculus I and II you can take Modern Physics or some other variant which is an upper level course...usually 3000 level. An introduction to special relativity and quantum physics is there...specifically quantum mechanics. Modern physics is usually a prequisite for Quantum Mechanics, so if you have some free electives and really want to learn quantum mechanics, you can take modern physics and then quantum mechanics.

Thanks for your replies everyone. I am reading through them now.

 

[HeLiXe]

I think the textbook by Hartle was influential in bringing GR into the undegraduate curriculum.

This book?
Gravity: An Introduction to Einstein's General Relativity...ISBN 978-0805386622

 

[HeLiXe]

He definitely doesn't mean the scientific reasearch done by mathematical/theoretical physicists in the areas of (quantum) gravity and string theory.

Still for a graduate of physics, a course on and let's say decent knowledge of GR is a must, even if working at CERN attempting to find traces of SUSY.

I thought that research was not yet accepted by mainstream. Thanks for the info. I plan to go for my graduates in physics once I finish undergrad.

I'm not sure what ModusPwnd means. I have many friends doing physics at various institutions in the states and they all say their course catalogs list an undergraduate GR class, my uni included. I don't think it is all that uncommon anymore.

Thanks WannabeNewton. I do not see any such class at my university which is why I asked. I am majoring in physics.

For me, GR falls into the category of: "Things I more than likely won't need directly for research but was glad I learned about when I could"!

It's the study of a full fundamental force of nature, gravity! I think a PhD Physicist should be embarrassed if (s)he could not explain it lucidly to an undergraduate!

Thanks Zombie Feynman

When I was studying physics, GR was only an upper level physics course that was optional.
It wasn't part of any real program.
I guess that was because it has a very limited application in real life.
I followed it myself because I was very much interested in it.
Differential geometry was an optional upper level math course.
I did not see any physicists there and it was only a handful of people attending the classes.

Thanks ILS. My school does not seem to offer differential geometry either. I also checked the courses listed for math and statistics majors and found a course called advanced geometry

When I first attended university, GR was either upper level (4th year) or a graduate level course, and it was an elective. These days it seems to be a graduate level course because of the prerequisites.

Here is one example:

Rice University, PHYS 561 General Relativity

Prerequisites: Special Relativity, Classical Mechanics, Classical Electrodynamics, Tensor Calculus
or instructor consent
Text: Hans Stephani: Relativity: An Introduction to Special and General Relativity
(Cambridge Paperback, 2004)

Thanks so much for this Astronuc. Great info. The physics department chair at my university told me we do not have tensor calculus and it is usually a graduate course...maybe this is why I do not see any general relativity classes for undergrad...and my school does not offer grad degrees in physics. I wonder now what math is required for tensor analysis

My school teaches it at the undergraduate level but it's an upper-division class.

Thanks Catria

GR is a mandatory 4th year course at my university (not in the US).

Thanks lavabug.

While this debate about the merits of teaching GR to undergraduates is interesting, I don't think it's especially on point for the OP's question.

HeLiXe: as GR is a very involved subject, it is unlikely to be taught within another course—with the possible exception of a very extensive differential geometry class, as someone else mentioned. Unless you are mathematician, attempting such a rigorous course as your first look at GR is probably too ambitious. If your university offers it to undergraduates, it will likely be an upper level class (possibly cross listed from the list of first year graduate courses) simply called "General Relativity" (or some variant). Such undergraduate courses are usually pretty self-contained mathematically, and so the instructor would spend roughly the first half of the course developing the necessary differential geometry before introducing the physics.

Thanks so much last one standing. I have taken calc I through III and differential equations so far. I plan to take pde, number theory, statistics and probability, and numerical analysis...still undecided on vector analysis. However because I am a double major with physics and a non-math subject, a few of those courses will be taken after I graduate. I am hoping to do research in nuclear astrophysics and thought that general relativity would be of particular importance in this area.

 

[tahayassen]

not from the looks of it >_>
usually after physics with calculus I and II you can take Modern Physics or some other variant which is an upper level course...usually 3000 level. An introduction to special relativity and quantum physics is there...specifically quantum mechanics. Modern physics is usually a prequisite for Quantum Mechanics, so if you have some free electives and really want to learn quantum mechanics, you can take modern physics and then quantum mechanics.

Thanks for your replies everyone. I am reading through them now.

I attend Ryerson University and I have 3 types of courses I can choose from:

1) Mandatory courses (I need these or else I won't graduate)
2) Professional courses (I need these skills to actually work in my career)
3) Liberal studies (history, geography, psychology, etc)

I've listed my mandatory courses and professional courses already. Since general/special relativity and quantum physics aren't in the list, that pretty much means I'm boned. Is this normal for a computer engineering degree? I'm starting to regret going to Ryerson University.

 

[dipole]

If you want to learn about GR, take a course which specifically focuses on it. It'll be a waste of your time otherwise, there's just too much there to cover in less than a full semester, and even a full semester is barely scraping the surface. I know some top-schools offer a three-course sequence in GR at the graduate level.

GR it's self isn't useful for much to most people, but the skills you learn are. Understanding how to build up a relativistic field theory, getting comfortable with tensor calculus, and learning to apply a theory to physical situations which you can't humanly visualize or understand and still get the right answer are all invaluable to someone who wants to go into theoretical physics.

I plan on doing computational condensed matter physics, I'll never use GR for the rest of my life most likely, but I'm still really glad I took it (and I'd have taken a second course if I had had the chance!).

 

[George Jones]

Most people even with PhDs in physics have never taken a course in general relativity

many people get a PhD without ever seeing GR.

Including me.

I think a PhD Physicist should be embarrassed if (s)he could not explain it lucidly to an undergraduate!

The above notwithstanding, I think I could have a go at this. I once taught a course (to students with a wide variety of backgrounds) that used Exploring Black Holes by Taylor and Wheeler as a text.

 

[jtbell]

that pretty much means I'm boned

Don't you have any room in your schedule for elective courses?

 

[WannabeNewton]

Hi HeLiXE! Even if your school doesn't offer an undergraduate course on the subject, you could always self study it if you really want to learn it. There are a ton of books you could use and they are usually broken down into different classes based on their pedagogy and difficulty. I haven't actually taken a course in GR yet as I have a good number of courses to still take pertaining directly to my undergraduate career but self - studying has been going fine for me especially with the availability of this exceptional forum to seek help on problem sets / queries. If you really want to learn the subject then go for it! This should help you out: http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html. Best of luck!

 

[HeLiXe]

If you want to learn about GR, take a course which specifically focuses on it. It'll be a waste of your time otherwise, there's just too much there to cover in less than a full semester, and even a full semester is barely scraping the surface. I know some top-schools offer a three-course sequence in GR at the graduate level.

GR it's self isn't useful for much to most people, but the skills you learn are. Understanding how to build up a relativistic field theory, getting comfortable with tensor calculus, and learning to apply a theory to physical situations which you can't humanly visualize or understand and still get the right answer are all invaluable to someone who wants to go into theoretical physics.

I plan on doing computational condensed matter physics, I'll never use GR for the rest of my life most likely, but I'm still really glad I took it (and I'd have taken a second course if I had had the chance!).

Thanks so much for this valuable info dipole :)

Hi HeLiXE! Even if your school doesn't offer an undergraduate course on the subject, you could always self study it if you really want to learn it. There are a ton of books you could use and they are usually broken down into different classes based on their pedagogy and difficulty. I haven't actually taken a course in GR yet as I have a good number of courses to still take pertaining directly to my undergraduate career but self - studying has been going fine for me especially with the availability of this exceptional forum to seek help on problem sets / queries. If you really want to learn the subject then go for it! This should help you out: http://math.ucr.edu/home/baez/physics/Administrivia/rel_booklist.html. Best of luck!

Thanks WannabeNewton and thanks for the link, I'll check it out :)

 

[ahsanxr]

If your school doesn't offer a specialized GR class, another option might be an independent study. If your school does offer the option of doing an independent study with a professor, contact one and tell him/her that you'd like to learn GR. Most likely, you will find someone who would be happy to do so if this sort of thing is done commonly at your school.

 

[HeLiXe]

This is really great advice ahsanxr :) One really good professor comes to mind. I'll ask him if he can guide me through my self study if needed and I can help him grade papers or something. I'm looking for the math prereqs for tensor analysis and I think I'll tackle those first.

 

[HeLiXe]

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!

 

[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!