Lets say you want to study General relativity in grad school

In summary, the conversation discusses the requirements for studying general relativity in graduate school and whether a degree in both pure math and physics is necessary. The options of majoring in physics and minoring in math or using online resources to teach oneself math are considered. The conversation also touches on the importance of different mathematical topics in general relativity and its relevance in current research. It is noted that general relativity is not as difficult as often thought and that many undergraduates are unsure of their specific interests when applying to graduate school.
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Putting all essentials aside, is a degree in both pure math and physics required? I am thinking of reducing the number of majors I have to just a minor in math and a BS in physics. Mainly because I had to retake some math classes and I do not think I will finish my degree in math at the same time I would finish my degree in physics.

Is it just okay to major in physics and minor in pure math in I want to study topics in General relativity in grad school? Or should I continue with my degree in both Pure math and physics.

I have consider the option of using MIT courseware site to teach myself pure math if I decided not to get a full degree in pure math. Would that be a good alternative to choosing to a degree in pure math.
 
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  • #2
I would say go into Mathematics over Physics. I don't know too much about it, but it seems to make sense to learn more about the tools available for theoritical physics than to learn the tools being used and none of the others which might be applicable in the future.
 
  • #3
JasonRox said:
I would say go into Mathematics over Physics. I don't know too much about it, but it seems to make sense to learn more about the tools available for theoritical physics than to learn the tools being used and none of the others which might be applicable in the future.

well how many graduates who were only physics majors went to grad school to study general relativity?

I don't mind doing a dual degree in math and physics, but personal financial reasons will not allow my to double major.
 
  • #4
couldn't your minor in math just focus on courses in mathematical topics related to General relativity like Differential geometry?

what math courses would an undergrad need to know in order to become a potential grad applicant for grad school in general relativity ?

Do you use real analysis in General Relativity ?
 
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  • #5
Is general relativity still an active area of research? Note that quantum theories of gravity, e.g. loop quantum gravity, string theory, etc., are not the same as general relativity, even though they attempt to reconcile the discrepancies between general relativity and quantum theory.
 
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  • #6
las3rjock said:
Is general relativity still an active area of research? Note that quantum theorees of gravity, e.g. loop quantum gravity, string theory, etc., are not the same as general relativity, even though they attempt to reconcile the discrepancies between general relativity and quantum theory.

It has to be. Otherwise , wouldn't it just be another undergrad course like quantum mechanics?
 
  • #7
...it was for me. I took it last year.
 
  • #8
"Classical" General Relativity is mostly studied now via numerical simulations and astronomy, although there's other things like Gravity Probe B going on.

What I don't understand is why the OP has (apparently) decided on an extremely narrow specific course in graduate training, while apparently only partway through the undergraduate curriculum.
 
  • #9
Andy Resnick said:
"Classical" General Relativity is mostly studied now via numerical simulations and astronomy, although there's other things like Gravity Probe B going on.

What I don't understand is why the OP has (apparently) decided on an extremely narrow specific course in graduate training, while apparently only partway through the undergraduate curriculum.

I don't understand what you mean. I have no clue what math courses I should during undergrad that would prepare me for undergraduate training in general relativity. In response to what the early posters said, I don't want to major in just Mathematics because I am only considering general relativity as an option as a topic I want to study for graduate school. I am not eliminating all my other topic of interests in physics.
 
  • #10
I'm pretty sure nearly everyone will take a course in general relativity as part of the standard grad school curriculum. It's not an active area of research. And really, the math is not all that difficult, once you get a handle on basic tensor calculus.

For your area of study, you might want to consider something more like cosmology or astronomy; these will make extensive use of general relativity. Other fields like particle physics will also make use of tensor calculus and group theory.

GR is not anywhere near the esoteric thing it is often thought to be among undergrads. It doesn't take an Einstein to understand it; it's something all physicists have some experience with.
 
  • #11
Ben Niehoff said:
I'm pretty sure nearly everyone will take a course in general relativity as part of the standard grad school curriculum. It's not an active area of research. And really, the math is not all that difficult, once you get a handle on basic tensor calculus.

For your area of study, you might want to consider something more like cosmology or astronomy; these will make extensive use of general relativity. Other fields like particle physics will also make use of tensor calculus and group theory.

GR is not anywhere near the esoteric thing it is often thought to be among undergrads. It doesn't take an Einstein to understand it; it's something all physicists have some experience with.

Is it normal for most undergrads to not have a complete idea of what they want to study as they are applying to grad school? I am bouncing around maybe studying topics in cosmology or topics in atomic physics, preferably quantum computers.
 
  • #12
Sure. I am applying next year, and I'm in the same boat as you: some ideas, but nothing specific. The grad students I've talked to say pretty much the same thing.
 
  • #13
Hell, I'm not even sure whether I want to do graduate study in a physics department or some tangential field. :/
 
  • #14
General relativity is still an active (though small) area of research. It doesn't require that much math. Doing GR properly does require a different kind of geometry than most other parts of physics, but you pick it up as you go along. Even that isn't really required if you just want to understand simple things like cosmology or light bending problems.

There are mathematicians working on problems related to GR, but that's true of almost all fields of physics with well-defined theories. Hardly anyone pays attention to these people, to be honest. Physicists rarely care about esoteric existence theorems and such.
 
  • #15
No way you can learn enough maths for GR during undergrad... haha... I think you should just do both. Hardly any maths major get to tensor calculus and differential geometry during undergrad year.
 
  • #16
leon1127 said:
No way you can learn enough maths for GR during undergrad... haha... I think you should just do both. Hardly any maths major get to tensor calculus and differential geometry during undergrad year.

Every GR class I've ever seen spends a considerable portion of its time teaching you the relevant math. By design, the prerequisites are just standard bits of math known by most grad students in physics. The classes that math majors take have almost no direct application to GR or any other part of physics. Even courses in differential geometry would be unlikely to help very much. Mathematicians emphasize completely different points.
 
  • #17
What sort of research is currently being done with GR?
 
  • #18
Pick up an intro GR book. They don't assume that you've had real analysis, or differential geometry, or anything beyond Calc 3 and Linear Algebra.

To answer another question, trying to learn pure math from MIT's open courseware is the same thing as not learning pure math. You'll never be able to do it.
 
  • #19
zhentil said:
To answer another question, trying to learn pure math from MIT's open courseware is the same thing as not learning pure math. You'll never be able to do it.

why not? I taught myself calculus and geometry on my own while in high school. why do you think I'm unable to teach myself differential geometry?
 
  • #20
Helical said:
What sort of research is currently being done with GR?

The most popular problems are related to the behavior of binary black hole or neutron star systems. Their orbits decay and the two objects eventually collide. These systems are expected to be observed by gravitational wave detectors in the near future. There is a large amount of analytical work related to systems like these in different regimes. Numerical simulations have also started to be useful in the past few years. There's now starting to be some interplay between these methods. They add a lot to each other.

Somewhat more generally, there is work on the underlying structure of mechanics in general relativity. This comes in several different forms.

People also work on the structure of neutron stars. What materials are they made of and what kind of phases are they in? Are there interesting internal dynamics? Does a star naturally lose a large amount of spin due to instabilities leading to large gravitational wave emissions?

There's also the formal theory of dynamical black holes. This has been greatly improved in the last ten years, and is even to the point where some of its results are routinely used in numerical work.

These are the main areas of what I'd call GR research, although there is much more than this scattered around. There are also other fields like quantum gravity and cosmology which sometimes use significant amounts of GR.
 
  • #21
Benzoate said:
I don't understand what you mean. I have no clue what math courses I should during undergrad that would prepare me for undergraduate training in general relativity. In response to what the early posters said, I don't want to major in just Mathematics because I am only considering general relativity as an option as a topic I want to study for graduate school. I am not eliminating all my other topic of interests in physics.

My mistake, then- from the title of this thread it appeared that you wanted to focus on a particular area of research.
 

1. What is General Relativity?

General Relativity is a theory of gravity that was developed by Albert Einstein in the early 20th century. It describes how massive objects interact with each other and how the curvature of space and time is affected by these interactions.

2. Why is it important to study General Relativity?

General Relativity is an essential theory in modern physics that has been successfully tested and verified through numerous experiments and observations. It has a wide range of applications, including understanding the motion of planets, stars, and galaxies, as well as the structure of the universe.

3. What are some key concepts in General Relativity?

Some key concepts in General Relativity include the equivalence principle, which states that the effects of gravity are indistinguishable from acceleration, and the concept of spacetime curvature, which describes how gravity affects the shape of the universe.

4. How is General Relativity studied in grad school?

In grad school, General Relativity is typically studied through advanced courses in theoretical physics and through research projects. Students may also attend seminars and conferences to learn about the latest developments in the field and collaborate with other researchers.

5. What career opportunities are available for those who study General Relativity in grad school?

Graduates with a background in General Relativity can pursue careers in academia, research institutions, and government agencies. They may also find opportunities in industries that involve advanced technologies, such as aerospace and defense.

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