Advanced Math for Graduate Theoretical Physics: What to Take?

[Lateralus17]

Which "advanced" math courses are needed to prepare for graduate theoretical physics?

I am a first year physics student preparing my schedule for next year. I would greatly appreciate advice on what kind of math will help me prepare for graduate studies in theoretical physics. Here is a list of courses I am unsure will help me in the future :

Discrete Structures
Real Analysis
Set Theory and Mathematical Logic
Modern Algebra
Advanced Linear Algebra
Number Theory
Combinatorics and Graph Theory
Game Theory
Cryptography
Topology

Thanks.

 

[Rob001]

Id be interested in knowing the answer to this as well.

 

[eri]

The only one of those I can see coming in useful for a physicist is topology, which you'd need for math-intensive study of general relativity. Most physics students won't study it, even at the PhD level. If you want to, a course in differential geometry would be good too.

 

[Lateralus17]

The only one of those I can see coming in useful for a physicist is topology, which you'd need for math-intensive study of general relativity. Most physics students won't study it, even at the PhD level. If you want to, a course in differential geometry would be good too.

At my university, discrete and real analysis are prerequisites for topology, so I will probably take those. As for differential geometry, I can't seem to find any courses listed with anything relevant to it. Is it possible that it's seen in other physics or math courses?

 

[Msh1]

discrete math, logic, combinatorics, number theory and graph theory have absolutely no use physics. In your list advanced linear algebra, is the most important one you should take as it is used everywhere in quantum and classical mechanics. After linear algebra I would say take real analysis, modern algebra and topology. Although I think a course in partial differential equations and complex analysis would be more useful. Differential geometry is heavily used in general relativity but it will probably be taught in a general relativity course. I was told a theoretical physicist should have taken the following courses so take as many of them as you can,

Calculus I, II, Multi variable Calculus
Ordinary differential equations, linear algebra I, II
Partial differential equations, Differential geometry
Complex analysis, real analysis, modern algebra I, II
General topology

 

[Vanadium 50]

You don't need topology for differential geometry.

 

[JaWiB]

discrete math, logic, combinatorics, number theory and graph theory have absolutely no use physics.

That's an awfully strong statement. I would think combinatorics at least would be useful for statistical mechanics (though I've never taken a course in any of these)

 

[Vanadium 50]

I've studied both, and no, not really.

 

[Coto]

discrete math, logic, combinatorics, number theory and graph theory have absolutely no use physics.

That's an awfully strong statement.

I agree with JaWiB... this isn't just strong--it's false. A much more appropriate statement is that initially other areas of mathematics would complement your route better than these ones.

 

[twofish-quant]

I am a first year physics student preparing my schedule for next year. I would greatly appreciate advice on what kind of math will help me prepare for graduate studies in theoretical physics

First of all, more math is better. Even if some class doesn't have any obvious connection to physics, doing math just builds up your skills.

Now as far as what is absolutely essential...

* multivariable calculus/differential equations
* linear algebra

Now what is very useful but not included in the standard physics curriculum

* some exposure to numerical analysis
* some exposure to statistics

Everything else, more is better...

 

[Ashuron]

well..twofish-quant..

I am assuming a numerical method for PDE will be worth taking?

 

[twofish-quant]

well..twofish-quant..

I am assuming a numerical method for PDE will be worth taking?

It's going to be very, very useful.

Also, one reason that it's useful to take a wide variety of math classes is that you are going to end up doing a lot of self-study in math. If you don't take a class on numerical analysis, there is a very good chance that you will end up having to teach it to yourself.